General Analytics: Cal Insurance

knitr::opts_chunk$set(echo = TRUE)

library(tweedie)
library(cplm)
library(statmod)

library(rstan)
library(actuar)
library(fishMod)

library(ggplot2)
library(tidyr)
library(dplyr)
library(tibble)
# library(rbokeh)

library(openxlsx)
library(readr)
library(readxl)

library(knitr)
library(kableExtra)
# library(formattable)
library(RColorBrewer) # display.brewer.all()
# library(plotly)
# library(gapminder)

Disclaimer: This document is written by a Cal Insurance intern and is intended for the other members of the intern team as audience. We include detailed documentation and code in hopes of helping the intern better familiarize with working in R as well as open room for improvement moving forward. The analyses contained herein are for internal use within Cal Insurance only.

Completing the Data (Calculating Charged Premiums)

At the start of the project, we are given data from various tables. Consolidating these together into one table involves some simple index(...match(...)...) lines in Excel. This gives us a complete data table claims_history.csv, and all that remains is to calculate the filed premiums for each policyholder over each year from 2013 through 2018.

This can be automated in R in a real workplace setting if multiple .xlsx files are given with a common structure.

# # import base .csv
tbl <- as_tibble(read_csv("/Users/dsury/Dropbox/Actuary/proj/case-comp/GA/ga-csv/claims_history.csv")) # "https://files.dsury.com/claims_history.csv"

# quick kable for this document
qkable <- function(x, height="360px") {
  x %>% kable(format = "html") %>% kable_styling(bootstrap_options = c("condensed", "responsive", "striped", "hover", "bordered"), font_size = 11, position = "center") %>% scroll_box(width="100%", height= height, fixed_thead =  list(enabled = TRUE, background = "lightgrey") ) 
}

tbl[1:20,] %>% qkable()

Vehicle Number	Policy Year	Policy Number	Marital Status	Driver Age	Driver Age Band	Annual Mileage	Territory	Credit Score	Car Value	Car Value Band	Liability Limit	Physical Damage Deductible	Conviction Points	Base Pure Premium	Marital Status Relativity	Driver Age Relativity	Annual Mileage Relativity	Territory Relativity	Car Value Relativity	Liability Limit Relativity	Physical Damage Deductible Relativity	Multi-Car	Multi-Car Relativity	Accident Points (AP) last 3 years	AP Relativity	Conviction Points (CP) last 3 years	CP Relativity
6125	2010	1	Single	18	16-19	0-7500	4	High	3220	0-10000	5e+04	100	1	1500	1.2	3.0	0.7	0.8	0.720	0.60	1.080	2	0.9	-1	-1	-1	-1
10332	2010	1	Married	45	40-49	7500-10000	3	High	20090	20000-30000	5e+05	250	0	1500	0.8	0.9	0.9	0.9	1.000	1.12	1.045	1	1.0	-1	-1	-1	-1
1965	2010	2	Married	54	50-59	15000+	1	Medium	13810	10000-20000	1e+05	500	0	1500	0.8	0.8	1.2	1.2	0.880	0.88	1.000	2	0.9	-1	-1	-1	-1
14130	2010	2	Married	49	40-49	10000-15000	1	High	37060	30000-40000	1e+05	100	1	1500	0.8	0.9	1.0	1.2	1.045	0.88	1.080	1	1.0	-1	-1	-1	-1
2976	2010	3	Single	31	30-39	7500-10000	4	High	20860	20000-30000	5e+04	250	0	1500	1.2	1.0	0.9	0.8	1.000	0.60	1.045	1	1.0	-1	-1	-1	-1
76	2010	4	Married	53	50-59	15000+	2	High	80850	40000+	5e+04	100	0	1500	0.8	0.8	1.2	1.1	1.080	0.60	1.080	1	1.0	-1	-1	-1	-1
8571	2010	5	Single	21	20-24	0-7500	3	Low	5610	0-10000	1e+05	500	0	1500	1.2	2.0	0.7	0.9	0.720	0.88	1.000	1	1.0	-1	-1	-1	-1
8530	2010	6	Single	28	25-29	7500-10000	2	High	20000	20000-30000	5e+04	250	0	1500	1.2	1.5	0.9	1.1	1.000	0.60	1.045	1	1.0	-1	-1	-1	-1
6104	2010	7	Single	33	30-39	0-7500	1	High	13020	10000-20000	5e+04	500	0	1500	1.2	1.0	0.7	1.2	0.880	0.60	1.000	2	0.9	-1	-1	-1	-1
12468	2010	7	Single	27	25-29	0-7500	2	High	26350	20000-30000	1e+05	250	0	1500	1.2	1.5	0.7	1.1	1.000	0.88	1.045	1	1.0	-1	-1	-1	-1
1547	2010	8	Married	52	50-59	0-7500	4	Low	39180	30000-40000	5e+05	1000	0	1500	0.8	0.8	0.7	0.8	1.045	1.12	0.935	1	1.0	-1	-1	-1	-1
736	2010	9	Married	49	40-49	10000-15000	4	Medium	30150	30000-40000	1e+05	500	0	1500	0.8	0.9	1.0	0.8	1.045	0.88	1.000	3	0.8	-1	-1	-1	-1
12236	2010	9	Single	50	50-59	0-7500	4	Medium	22600	20000-30000	5e+04	100	0	1500	1.2	0.8	0.7	0.8	1.000	0.60	1.080	2	0.9	-1	-1	-1	-1
14398	2010	9	Single	47	40-49	0-7500	3	Medium	28950	20000-30000	5e+04	1000	0	1500	1.2	0.9	0.7	0.9	1.000	0.60	0.935	1	1.0	-1	-1	-1	-1
6386	2010	10	Single	16	16-19	7500-10000	2	Low	1020	0-10000	5e+04	100	0	1500	1.2	3.0	0.9	1.1	0.720	0.60	1.080	1	1.0	-1	-1	-1	-1
5284	2010	11	Married	27	25-29	7500-10000	3	High	1270	0-10000	1e+05	250	0	1500	0.8	1.5	0.9	0.9	0.720	0.88	1.045	1	1.0	-1	-1	-1	-1
999	2010	12	Married	65	60-69	10000-15000	3	Medium	62030	40000+	1e+05	500	0	1500	0.8	0.8	1.0	0.9	1.080	0.88	1.000	1	1.0	-1	-1	-1	-1
1553	2010	13	Single	37	30-39	15000+	2	High	39430	30000-40000	3e+05	500	0	1500	1.2	1.0	1.2	1.1	1.045	1.00	1.000	1	1.0	-1	-1	-1	-1
8480	2010	14	Single	20	20-24	7500-10000	3	High	23570	20000-30000	5e+04	100	0	1500	1.2	2.0	0.9	0.9	1.000	0.60	1.080	2	0.9	-1	-1	-1	-1
10430	2010	14	Single	51	50-59	10000-15000	2	High	11020	10000-20000	1e+05	250	0	1500	1.2	0.8	1.0	1.1	0.880	0.88	1.045	1	1.0	-1	-1	-1	-1

Setting (Ordered) Factor Levels

Before going further into exploratory data analysis, we must treat our categorical variables (bands and groups) as factors in R. For our ggplots and GLM to function as desired, we assign orders to the variables.

# set factor levels and order

tbl$`Marital Status` <- factor(
  tbl$`Marital Status`, levels= sort(unique(tbl$`Marital Status`), decreasing = TRUE), ordered = TRUE # 1 : single, 2 : married
)

tbl <- tbl %>% mutate(`Driver Experience` = `Driver Age` - 15) # gives ceiling of driver experience years, includes instructional period prior to license

tbl <- tbl %>% mutate(`Driver Experience Band` = `Driver Age Band` )

tbl$`Driver Experience Band` <- recode(tbl$`Driver Experience Band`, 
       `16-19` = "0-3",
       `20-24` = "4-8",
       `25-29` = "9-13",
       `30-39` = "14-23",
       `40-49` = "24-33",
       `50-59` = "34-43",
       `60-69` = "44-53",
       `70-79` = "54-63",
       `80-89` = "64-73",
         `90+` = "74+"
       )

tbl$`Driver Experience Band` <- factor(
  tbl$`Driver Experience Band`, levels = c("0-3", "4-8", "9-13", "14-23", "24-33", "34-43", "44-53", "54-63", "64-73", "74+"), ordered = TRUE
)

tbl$`Annual Mileage` <- factor(
  tbl$`Annual Mileage`, levels = c("0-7500", "7500-10000", "10000-15000", "15000+"), ordered = TRUE
)

tbl$`Credit Score` <- factor(
  tbl$`Credit Score`, levels = c("Low", "Medium", "High"), ordered = TRUE
)

tbl$`Car Value Band` <- factor(
  tbl$`Car Value Band`, levels = c("0-10000", "10000-20000", "20000-30000", "30000-40000", "40000+"), ordered = TRUE
)


tbl$`Policy Year` <- factor(
  tbl$`Policy Year`, levels = as.character(2010:2020), ordered = TRUE
) # maximum is 2018, but we'll go to 2020 here


tbl$`Conviction Points (CP) last 3 years` <- factor(
  tbl$`Conviction Points (CP) last 3 years`, levels = 0:3, ordered = TRUE
)

tbl$`Accident Points (AP) last 3 years` <- factor(
  tbl$`Accident Points (AP) last 3 years`, levels = 0:3, ordered = TRUE
)

tbl$Territory <- factor(
  tbl$Territory, levels = 1:4, ordered = FALSE # make un-ordered to allow permutation in GLM
)

Assuming we are in California (Cal Insurance), for regulatory compliance, we know that the filed premiums use certain relativities and exclude certain information. Particularly, California’s Proposition 103 requires that we calculate rates via sequential analysis using a primary set of three factors:

Primary Auto Rating Factors

Driver Safety Record
Annual Mileage
Years Licensed (Driving Experience)

These above 3 factors must be used before considering other variables from the following prescribed list of “optional factors”:

Optional Factors

Type of vehicle
Vehicle performance capabilities
Type of use of vehicle (pleasure only, commute, business, farm, etc)
Percentage use of the vehicle by the rated driver
Multi-vehicle households
Academic standing
Completion of driver training or defensive driver courses
Vehicle characteristics (engine size, safety devices, theft deterrent devices, etc)
Marital status
Persistency
Non-smoker
Secondary Driver Characteristics (combination of: Safety Record, Years Licensed, Marital Status, Driver Training, and Academic Status)
Multi-policies with the same or affiliated company
Relative claims frequency (maximum of 20 categories/bands)
Relative claims severity (maximum of 20 categories/bands)

Notice that gender, Credit Score, and driver’s age are not on this prescribed list and hence cannot be used as rating factors. However, with Driver Age, we can transform this easily into Driving Experience with the simplifying assumption that all registered policyholders begin driving at age 16. We exercise actuarial judgment here that although this is a biased transformation, it is the simplest and most transparent.

Because our later analyses are not applied to any immediate compliance filings, we use Driver Age and Driver Experience interchangeably as they are equivalent (simply offset by -16) and this variable does not involve the above assumption.

Technically, there is a mandatory “Good Driver Discount” (GDD) of at least $20\%$ compared to “the lowest rate available to a comparable driver who is not a good driver.” Moreover, the calculation of factor weights is also regulated. Lacking information on these specifications, we choose not to make assumptions and modifications here.

As given by insurance.ca.gov, for Sequential Analysis via the Prior Relativities Method under the Multiplicative Algorithm, we have:

\[ \text{Premium} = \text{(Base Pure Premium)} \times F_1 \times F_2 \times F_3 \times GDD \times F_4 \times \cdots \times F_k\] where $F_1, F_2, F_3$ are the relativites for the first, second and third factors in sequential analysis, respectively, all the way until the $k$th.

Ratemaking is prospective, meaning that we are estimating future claims and not recouping for past losses. Because we are only interested in the historical losses versus charged premiums, for our purposes we need not reinvent the Sequential Analysis technique used to arrive at the given values of relativities.

Recall the balancing fundamental insurance equation:

\[ \text{Premium} = \text{Loss} + \text{LAE} + \text{UW Expenses} + \text{UW Profit}. \]

In Excel, to get the Premium per policy, we first calculate the premium per vehicle for each year via:

\[ \begin{align*} \text{Premium} &= \text{(Base Pure Premium)} \times \text{[(3 yr Accident Points)} \times \text{(3 yr Conviction Points)]} \\ & \qquad \times \text{(Annual Mileage)} \times \text{(Driving Experience)} \times \text{(Physical Damage Deductible)} \\ & \qquad \times \text{(Liability Limit)} \times \text{(Car Value)} \times \text{(Multi-Car)} \times \text{(Marital Status)} \times \text{(Territory)} \end{align*} \]

where each factor multiplied to Base Pure Premium is the relativity of that factor.

Here’s an exhibit of the filed prices, loaded in from doing inputting the above formula into Excel. Notice these are adjustments to the Base Premium.

prems <- as_tibble(read_csv("Dropbox/Actuary/proj/case-comp/GA/ga-csv/filed_premiums.csv")) # "https://files.dsury.com/filed_premiums.csv"

prems[1:20,] %>% qkable()

Policy Number	Vehicle Number	Premium	Policy Year	Marital Status	Driver Age	Driver Age Band	Annual Mileage	Territory	Credit Score	Car Value	Car Value Band	Liability Limit	Physical Damage Deductible	Reported Losses	Late Fees	Conviction Points	Base Pure Premium	Marital Status Relativity	Driver Age Relativity	Annual Mileage Relativity	Territory Relativity	Car Value Relativity	Liability Limit Relativity	Physical Damage Deductible Relativity	Multi-Car	Multi-Car Relativity	Accident Points (AP) last 3 years	AP Relativity	Conviction Points (CP) last 3 years	CP Relativity	Driver Experience	Driver Experience Band
1	6125	1218.9981	2013	Single	21	20-24	0-7500	4	High	3220	0-10000	5e+04	100	200.0692	0	0	1500	1.2	2.0	0.7	0.8	0.720	0.60	1.080	2	0.9	1	1.2	1	1.2	6	4-8
1	10332	1023.8659	2013	Married	48	40-49	7500-10000	3	High	20090	20000-30000	5e+05	250	0.0000	0	0	1500	0.8	0.9	0.9	0.9	1.000	1.12	1.045	1	1.0	0	1.0	0	1.0	33	24-33
2	1965	963.4775	2013	Married	57	50-59	15000+	1	Medium	13810	10000-20000	1e+05	500	0.0000	0	0	1500	0.8	0.8	1.2	1.2	0.880	0.88	1.000	2	0.9	0	1.0	0	1.0	42	34-43
2	14130	1144.1295	2013	Married	52	50-59	10000-15000	1	High	37060	30000-40000	1e+05	100	0.0000	0	0	1500	0.8	0.8	1.0	1.2	1.045	0.88	1.080	1	1.0	0	1.0	0	1.0	37	34-43
3	2976	812.5920	2013	Single	34	30-39	7500-10000	4	High	20860	20000-30000	5e+04	250	0.0000	0	0	1500	1.2	1.0	0.9	0.8	1.000	0.60	1.045	1	1.0	0	1.0	0	1.0	19	14-23
4	76	886.8372	2013	Married	56	50-59	15000+	2	High	80850	40000+	5e+04	100	0.0000	0	0	1500	0.8	0.8	1.2	1.1	1.080	0.60	1.080	1	1.0	0	1.0	0	1.0	41	34-43
5	8571	2069.2869	2013	Single	24	20-24	0-7500	3	Low	5610	0-10000	1e+05	500	10121.7588	0	1	1500	1.2	2.0	0.7	0.9	0.720	0.88	1.000	1	1.0	1	1.2	1	1.2	9	4-8
6	8530	1608.9322	2013	Single	31	30-39	7500-10000	2	High	20000	20000-30000	5e+04	250	28602.5937	1	1	1500	1.2	1.0	0.9	1.1	1.000	0.60	1.045	1	1.0	1	1.2	1	1.2	16	14-23
7	6104	718.5024	2013	Single	36	30-39	0-7500	1	High	13020	10000-20000	5e+04	500	0.0000	0	0	1500	1.2	1.0	0.7	1.2	0.880	0.60	1.000	2	0.9	0	1.0	0	1.0	21	14-23
7	12468	1784.3918	2013	Single	30	30-39	0-7500	2	High	26350	20000-30000	1e+05	250	0.0000	0	1	1500	1.2	1.0	0.7	1.1	1.000	0.88	1.045	1	1.0	0	1.0	2	1.4	15	14-23
8	1547	588.3086	2013	Married	55	50-59	0-7500	4	Low	39180	30000-40000	5e+05	1000	0.0000	0	0	1500	0.8	0.8	0.7	0.8	1.045	1.12	0.935	1	1.0	0	1.0	0	1.0	40	34-43
9	736	565.0022	2013	Married	52	50-59	10000-15000	4	Medium	30150	30000-40000	1e+05	500	0.0000	0	0	1500	0.8	0.8	1.0	0.8	1.045	0.88	1.000	3	0.8	0	1.0	0	1.0	37	34-43
9	12236	470.2925	2013	Single	53	50-59	0-7500	4	Medium	22600	20000-30000	5e+04	100	0.0000	0	0	1500	1.2	0.8	0.7	0.8	1.000	0.60	1.080	2	0.9	0	1.0	0	1.0	38	34-43
9	14398	508.9392	2013	Single	50	50-59	0-7500	3	Medium	28950	20000-30000	5e+04	1000	0.0000	0	0	1500	1.2	0.8	0.7	0.9	1.000	0.60	0.935	1	1.0	0	1.0	0	1.0	35	34-43
10	6386	3990.7676	2013	Single	19	16-19	7500-10000	2	Low	1020	0-10000	5e+04	100	6483.2473	0	0	1500	1.2	3.0	0.9	1.1	0.720	0.60	1.080	1	1.0	3	1.6	0	1.0	4	0-3
11	5284	772.2874	2013	Married	30	30-39	7500-10000	3	High	1270	0-10000	1e+05	250	0.0000	0	0	1500	0.8	1.0	0.9	0.9	0.720	0.88	1.045	1	1.0	0	1.0	1	1.2	15	14-23
12	999	821.1456	2013	Married	68	60-69	10000-15000	3	Medium	62030	40000+	1e+05	500	0.0000	0	0	1500	0.8	0.8	1.0	0.9	1.080	0.88	1.000	1	1.0	0	1.0	0	1.0	53	44-53
13	1553	2234.6280	2013	Single	40	40-49	15000+	2	High	39430	30000-40000	3e+05	500	0.0000	0	0	1500	1.2	0.9	1.2	1.1	1.045	1.00	1.000	1	1.0	0	1.0	0	1.0	25	24-33
14	8480	1700.6112	2013	Single	23	20-24	7500-10000	3	High	23570	20000-30000	5e+04	100	0.0000	0	0	1500	1.2	2.0	0.9	0.9	1.000	0.60	1.080	2	0.9	0	1.0	0	1.0	8	4-8
14	10430	1538.2186	2013	Single	54	50-59	10000-15000	2	High	11020	10000-20000	1e+05	250	0.0000	0	0	1500	1.2	0.8	1.0	1.1	0.880	0.88	1.045	1	1.0	0	1.0	1	1.2	39	34-43

Before we look into the premium structure, we’ll take a quick detour to understand more about the data and the factors.

1. Data Cleaning: Validation and Investigation

Here we’ll perform a pivot on our data. Our given data is very ‘tall’, with repeated entries. We notice that the Vehicle Number entries are periodic, where we have \[135,000 \text{ total rows of data} = 15,000 \text{ rows} \times 9 \text{ years}.\] Because we’ve sorted by Policy Year (PY) and Policy Number, each ‘block’ of 15000 rows corresponds to a year (we confirm this in data validation, but this will be evident in a moment). We’ll break these apart with pivot_wider().

# just run once

# rearrange to compare years
# select(tbl, `Vehicle Number`, `Policy Year`, `Marital Status` )
if  (names(tbl)[2] != "Policy Year") { print("Error: Make sure tbl has Policy Year as second column!") }

# tblnames <- c()

# generate tibbles
for (i in names(tbl)[- c(1,2) ]) {
  assign( paste0("tbl.",i), 
          select(tbl, `Vehicle Number`, `Policy Year`, i) %>%
            pivot_wider(names_from = "Policy Year", 
                        values_from = i,
                        names_prefix = paste0(i, " PY"))
          )
  # tblnames <- c(tblnames, paste0("tbl.",i))
  print(i) # debugging
}

This gives us a number of tables, one for each original column. A couple of examples is shown below. Notice that each row no longer has the Policy Year column, and now each row contains data for each year (as opposed to multiple rows before corresponding to the same Vehicle Number).

Now we’ll stitch these together back into a consolidated database. We’ll generally keep the same order as given in the original .xlsx file.

for (k in tblcols) {
  tbl.wider <- tbl.wider %>% left_join( k )
}

tbl.wider[1:20,] %>% qkable()

Vehicle Number	Policy Number PY2010	Policy Number PY2011	Policy Number PY2012	Policy Number PY2013	Policy Number PY2014	Policy Number PY2015	Policy Number PY2016	Policy Number PY2017	Policy Number PY2018	Marital Status PY2010	Marital Status PY2011	Marital Status PY2012	Marital Status PY2013	Marital Status PY2014	Marital Status PY2015	Marital Status PY2016	Marital Status PY2017	Marital Status PY2018	Driver Age PY2010	Driver Age PY2011	Driver Age PY2012	Driver Age PY2013	Driver Age PY2014	Driver Age PY2015	Driver Age PY2016	Driver Age PY2017	Driver Age PY2018	Driver Age Band PY2010	Driver Age Band PY2011	Driver Age Band PY2012	Driver Age Band PY2013	Driver Age Band PY2014	Driver Age Band PY2015	Driver Age Band PY2016	Driver Age Band PY2017	Driver Age Band PY2018	Annual Mileage PY2010	Annual Mileage PY2011	Annual Mileage PY2012	Annual Mileage PY2013	Annual Mileage PY2014	Annual Mileage PY2015	Annual Mileage PY2016	Annual Mileage PY2017	Annual Mileage PY2018	Territory PY2010	Territory PY2011	Territory PY2012	Territory PY2013	Territory PY2014	Territory PY2015	Territory PY2016	Territory PY2017	Territory PY2018	Credit Score PY2010	Credit Score PY2011	Credit Score PY2012	Credit Score PY2013	Credit Score PY2014	Credit Score PY2015	Credit Score PY2016	Credit Score PY2017	Credit Score PY2018	Car Value PY2010	Car Value PY2011	Car Value PY2012	Car Value PY2013	Car Value PY2014	Car Value PY2015	Car Value PY2016	Car Value PY2017	Car Value PY2018	Car Value Band PY2010	Car Value Band PY2011	Car Value Band PY2012	Car Value Band PY2013	Car Value Band PY2014	Car Value Band PY2015	Car Value Band PY2016	Car Value Band PY2017	Car Value Band PY2018	Liability Limit PY2010	Liability Limit PY2011	Liability Limit PY2012	Liability Limit PY2013	Liability Limit PY2014	Liability Limit PY2015	Liability Limit PY2016	Liability Limit PY2017	Liability Limit PY2018	Physical Damage Deductible PY2010	Physical Damage Deductible PY2011	Physical Damage Deductible PY2012	Physical Damage Deductible PY2013	Physical Damage Deductible PY2014	Physical Damage Deductible PY2015	Physical Damage Deductible PY2016	Physical Damage Deductible PY2017	Physical Damage Deductible PY2018	Reported Losses PY2011	Reported Losses PY2012	Reported Losses PY2013	Reported Losses PY2014	Reported Losses PY2015	Reported Losses PY2016	Reported Losses PY2017	Reported Losses PY2018	Late Fees PY2011	Late Fees PY2012	Late Fees PY2013	Conviction Points PY2010	Conviction Points PY2011	Conviction Points PY2012	Conviction Points PY2013	Conviction Points PY2014	Conviction Points PY2015	Base Pure Premium PY2010	Base Pure Premium PY2011	Base Pure Premium PY2012	Base Pure Premium PY2013	Base Pure Premium PY2014	Base Pure Premium PY2015	Base Pure Premium PY2016	Base Pure Premium PY2017	Base Pure Premium PY2018	Marital Status Relativity PY2010	Marital Status Relativity PY2011	Marital Status Relativity PY2012	Marital Status Relativity PY2013	Marital Status Relativity PY2014	Marital Status Relativity PY2015	Marital Status Relativity PY2016	Marital Status Relativity PY2017	Marital Status Relativity PY2018	Driver Age Relativity PY2010	Driver Age Relativity PY2011	Driver Age Relativity PY2012	Driver Age Relativity PY2013	Driver Age Relativity PY2014	Driver Age Relativity PY2015	Driver Age Relativity PY2016	Driver Age Relativity PY2017	Driver Age Relativity PY2018	Annual Mileage Relativity PY2010	Annual Mileage Relativity PY2011	Annual Mileage Relativity PY2012	Annual Mileage Relativity PY2013	Annual Mileage Relativity PY2014	Annual Mileage Relativity PY2015	Annual Mileage Relativity PY2016	Annual Mileage Relativity PY2017	Annual Mileage Relativity PY2018	Car Value Relativity PY2010	Car Value Relativity PY2011	Car Value Relativity PY2012	Car Value Relativity PY2013	Car Value Relativity PY2014	Car Value Relativity PY2015	Car Value Relativity PY2016	Car Value Relativity PY2017	Car Value Relativity PY2018	Liability Limit Relativity PY2010	Liability Limit Relativity PY2011	Liability Limit Relativity PY2012	Liability Limit Relativity PY2013	Liability Limit Relativity PY2014	Liability Limit Relativity PY2015	Liability Limit Relativity PY2016	Liability Limit Relativity PY2017	Liability Limit Relativity PY2018	Physical Damage Deductible Relativity PY2010	Physical Damage Deductible Relativity PY2011	Physical Damage Deductible Relativity PY2012	Physical Damage Deductible Relativity PY2013	Physical Damage Deductible Relativity PY2014	Physical Damage Deductible Relativity PY2015	Physical Damage Deductible Relativity PY2016	Physical Damage Deductible Relativity PY2017	Physical Damage Deductible Relativity PY2018	Multi-Car PY2010	Multi-Car PY2011	Multi-Car PY2012	Multi-Car PY2013	Multi-Car PY2014	Multi-Car PY2015	Multi-Car PY2016	Multi-Car PY2017	Multi-Car PY2018	Multi-Car Relativity PY2010	Multi-Car Relativity PY2011	Multi-Car Relativity PY2012	Multi-Car Relativity PY2013	Multi-Car Relativity PY2014	Multi-Car Relativity PY2015	Multi-Car Relativity PY2016	Multi-Car Relativity PY2017	Multi-Car Relativity PY2018	Accident Points (AP) last 3 years PY2010	Accident Points (AP) last 3 years PY2011	Accident Points (AP) last 3 years PY2012	Accident Points (AP) last 3 years PY2013	Accident Points (AP) last 3 years PY2014	Accident Points (AP) last 3 years PY2015	Accident Points (AP) last 3 years PY2016	Accident Points (AP) last 3 years PY2017	Accident Points (AP) last 3 years PY2018	AP Relativity PY2010	AP Relativity PY2011	AP Relativity PY2012	AP Relativity PY2013	AP Relativity PY2014	AP Relativity PY2015	AP Relativity PY2016	AP Relativity PY2017	AP Relativity PY2018	Conviction Points (CP) last 3 years PY2010	Conviction Points (CP) last 3 years PY2011	Conviction Points (CP) last 3 years PY2012	Conviction Points (CP) last 3 years PY2013	Conviction Points (CP) last 3 years PY2014	Conviction Points (CP) last 3 years PY2015	Conviction Points (CP) last 3 years PY2016	Conviction Points (CP) last 3 years PY2017	CP Relativity PY2010	CP Relativity PY2011	CP Relativity PY2012	CP Relativity PY2013	CP Relativity PY2014	CP Relativity PY2015	CP Relativity PY2016	CP Relativity PY2017	CP Relativity PY2018	Driver Experience PY2010	Driver Experience PY2011	Driver Experience PY2012	Driver Experience PY2013	Driver Experience PY2014	Driver Experience PY2015	Driver Experience PY2016	Driver Experience PY2017	Driver Experience PY2018	Driver Experience Band PY2010	Driver Experience Band PY2011	Driver Experience Band PY2012	Driver Experience Band PY2013	Driver Experience Band PY2014	Driver Experience Band PY2015	Driver Experience Band PY2016	Driver Experience Band PY2017	Driver Experience Band PY2018
6125	1	1	1	1	1	1	1	1	1	Single	Single	Single	Single	Single	Single	Single	Single	Single	18	19	20	21	22	23	24	25	26	16-19	16-19	20-24	20-24	20-24	20-24	20-24	25-29	25-29	0-7500	0-7500	0-7500	0-7500	0-7500	0-7500	0-7500	0-7500	0-7500	4	4	4	4	4	4	4	4	4	High	High	High	High	High	High	High	High	High	3220	3220	3220	3220	3220	3220	3220	3220	3220	0-10000	0-10000	0-10000	0-10000	0-10000	0-10000	0-10000	0-10000	0-10000	5e+04	5e+04	5e+04	5e+04	5e+04	5e+04	5e+04	5e+04	5e+04	100	100	100	100	100	100	100	100	100	0.000	0.0000	200.0692	0.0000	0.0000	12602.418	0.000	0.000	0	0	0	1	1	0	0	0	0	1500	1500	1500	1500	1500	1500	1500	1500	1500	1.2	1.2	1.2	1.2	1.2	1.2	1.2	1.2	1.2	3.0	3.0	2.0	2.0	2.0	2.0	2.0	1.5	1.5	0.7	0.7	0.7	0.7	0.7	0.7	0.7	0.7	0.7	0.720	0.720	0.720	0.720	0.720	0.720	0.720	0.720	0.720	0.60	0.60	0.60	0.60	0.60	0.60	0.60	0.60	0.60	1.080	1.080	1.080	1.080	1.080	1.080	1.080	1.080	1.080	2	2	2	2	2	2	2	2	2	0.9	0.9	0.9	0.9	0.9	0.9	0.9	0.9	0.9	-1	-1	0	1	1	1	1	1	1	-1	-1	1.0	1.2	1.2	1.2	1.2	1.2	1.2	-1	-1	2	1	0	0	0	0	-1	-1	1.4	1.2	1.0	1.0	1.0	1.0	1	3	4	5	6	7	8	9	10	11	0-3	0-3	4-8	4-8	4-8	4-8	4-8	9-13	9-13
10332	1	1	1	1	1	1	1	1	1	Married	Married	Married	Married	Married	Married	Married	Married	Married	45	46	47	48	49	50	51	52	53	40-49	40-49	40-49	40-49	40-49	50-59	50-59	50-59	50-59	7500-10000	7500-10000	7500-10000	7500-10000	7500-10000	7500-10000	7500-10000	7500-10000	7500-10000	3	3	3	3	3	3	3	3	3	High	High	High	High	High	High	High	High	High	20090	20090	20090	20090	20090	20090	20090	20090	20090	20000-30000	20000-30000	20000-30000	20000-30000	20000-30000	20000-30000	20000-30000	20000-30000	20000-30000	5e+05	5e+05	5e+05	5e+05	5e+05	5e+05	5e+05	5e+05	5e+05	250	250	250	250	250	250	250	250	250	0.000	0.0000	0.0000	0.0000	0.0000	0.000	0.000	0.000	0	0	0	0	0	0	0	1	0	1500	1500	1500	1500	1500	1500	1500	1500	1500	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.9	0.9	0.9	0.9	0.9	0.8	0.8	0.8	0.8	0.9	0.9	0.9	0.9	0.9	0.9	0.9	0.9	0.9	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.12	1.12	1.12	1.12	1.12	1.12	1.12	1.12	1.12	1.045	1.045	1.045	1.045	1.045	1.045	1.045	1.045	1.045	1	1	1	1	1	1	1	1	1	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	-1	-1	0	0	0	0	0	0	0	-1	-1	1.0	1.0	1.0	1.0	1.0	1.0	1.0	-1	-1	0	0	1	1	1	0	-1	-1	1.0	1.0	1.2	1.2	1.2	1.0	1	30	31	32	33	34	35	36	37	38	24-33	24-33	24-33	24-33	24-33	34-43	34-43	34-43	34-43
1965	2	2	2	2	2	2	2	2	2	Married	Married	Married	Married	Married	Married	Married	Married	Married	54	55	56	57	58	59	60	61	62	50-59	50-59	50-59	50-59	50-59	50-59	60-69	60-69	60-69	15000+	15000+	15000+	15000+	15000+	15000+	15000+	15000+	15000+	1	1	1	1	1	1	1	1	1	Medium	Medium	Medium	Medium	Medium	Medium	Medium	Medium	Medium	13810	13810	13810	13810	13810	13810	13810	13810	13810	10000-20000	10000-20000	10000-20000	10000-20000	10000-20000	10000-20000	10000-20000	10000-20000	10000-20000	1e+05	1e+05	1e+05	1e+05	1e+05	1e+05	1e+05	1e+05	1e+05	500	500	500	500	500	500	500	500	500	0.000	0.0000	0.0000	0.0000	0.0000	0.000	0.000	0.000	0	0	0	0	0	0	0	0	0	1500	1500	1500	1500	1500	1500	1500	1500	1500	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	1.2	1.2	1.2	1.2	1.2	1.2	1.2	1.2	1.2	0.880	0.880	0.880	0.880	0.880	0.880	0.880	0.880	0.880	0.88	0.88	0.88	0.88	0.88	0.88	0.88	0.88	0.88	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	2	2	2	2	2	2	2	2	2	0.9	0.9	0.9	0.9	0.9	0.9	0.9	0.9	0.9	-1	-1	0	0	0	0	0	0	0	-1	-1	1.0	1.0	1.0	1.0	1.0	1.0	1.0	-1	-1	0	0	0	0	0	0	-1	-1	1.0	1.0	1.0	1.0	1.0	1.0	1	39	40	41	42	43	44	45	46	47	34-43	34-43	34-43	34-43	34-43	34-43	44-53	44-53	44-53
14130	2	2	2	2	2	2	2	2	2	Married	Married	Married	Married	Married	Married	Married	Married	Married	49	50	51	52	53	54	55	56	57	40-49	50-59	50-59	50-59	50-59	50-59	50-59	50-59	50-59	10000-15000	10000-15000	10000-15000	10000-15000	10000-15000	10000-15000	10000-15000	10000-15000	10000-15000	1	1	1	1	1	1	1	1	1	High	High	High	High	High	High	High	High	High	37060	37060	37060	37060	37060	37060	37060	37060	37060	30000-40000	30000-40000	30000-40000	30000-40000	30000-40000	30000-40000	30000-40000	30000-40000	30000-40000	1e+05	1e+05	1e+05	1e+05	1e+05	1e+05	1e+05	1e+05	1e+05	100	100	100	100	100	100	100	100	100	0.000	0.0000	0.0000	0.0000	0.0000	0.000	0.000	0.000	0	0	0	1	0	0	0	0	0	1500	1500	1500	1500	1500	1500	1500	1500	1500	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.9	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.045	1.045	1.045	1.045	1.045	1.045	1.045	1.045	1.045	0.88	0.88	0.88	0.88	0.88	0.88	0.88	0.88	0.88	1.080	1.080	1.080	1.080	1.080	1.080	1.080	1.080	1.080	1	1	1	1	1	1	1	1	1	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	-1	-1	0	0	0	0	0	0	0	-1	-1	1.0	1.0	1.0	1.0	1.0	1.0	1.0	-1	-1	1	0	0	0	0	0	-1	-1	1.2	1.0	1.0	1.0	1.0	1.0	1	34	35	36	37	38	39	40	41	42	24-33	34-43	34-43	34-43	34-43	34-43	34-43	34-43	34-43
2976	3	3	3	3	3	3	3	3	3	Single	Single	Single	Single	Single	Single	Single	Single	Single	31	32	33	34	35	36	37	38	39	30-39	30-39	30-39	30-39	30-39	30-39	30-39	30-39	30-39	7500-10000	7500-10000	7500-10000	7500-10000	7500-10000	7500-10000	7500-10000	7500-10000	7500-10000	4	4	4	4	4	4	4	4	4	High	High	High	High	High	High	High	High	High	20860	20860	20860	20860	20860	20860	20860	20860	20860	20000-30000	20000-30000	20000-30000	20000-30000	20000-30000	20000-30000	20000-30000	20000-30000	20000-30000	5e+04	5e+04	5e+04	5e+04	5e+04	5e+04	5e+04	5e+04	5e+04	250	250	250	250	250	250	250	250	250	0.000	0.0000	0.0000	0.0000	0.0000	0.000	0.000	0.000	0	0	0	0	0	0	0	0	0	1500	1500	1500	1500	1500	1500	1500	1500	1500	1.2	1.2	1.2	1.2	1.2	1.2	1.2	1.2	1.2	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	0.9	0.9	0.9	0.9	0.9	0.9	0.9	0.9	0.9	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	0.60	0.60	0.60	0.60	0.60	0.60	0.60	0.60	0.60	1.045	1.045	1.045	1.045	1.045	1.045	1.045	1.045	1.045	1	1	1	1	1	1	1	1	1	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	-1	-1	0	0	0	0	0	0	0	-1	-1	1.0	1.0	1.0	1.0	1.0	1.0	1.0	-1	-1	0	0	0	0	0	0	-1	-1	1.0	1.0	1.0	1.0	1.0	1.0	1	16	17	18	19	20	21	22	23	24	14-23	14-23	14-23	14-23	14-23	14-23	14-23	14-23	14-23
76	4	4	4	4	4	4	4	4	4	Married	Married	Married	Married	Married	Married	Married	Married	Married	53	54	55	56	57	58	59	60	61	50-59	50-59	50-59	50-59	50-59	50-59	50-59	60-69	60-69	15000+	15000+	15000+	15000+	15000+	15000+	15000+	15000+	15000+	2	2	2	2	2	2	2	2	2	High	High	High	High	High	High	High	High	High	80850	80850	80850	80850	80850	80850	80850	80850	80850	40000+	40000+	40000+	40000+	40000+	40000+	40000+	40000+	40000+	5e+04	5e+04	5e+04	5e+04	5e+04	5e+04	5e+04	5e+04	5e+04	100	100	100	100	100	100	100	100	100	0.000	0.0000	0.0000	0.0000	0.0000	0.000	0.000	0.000	0	2	0	0	0	0	0	0	0	1500	1500	1500	1500	1500	1500	1500	1500	1500	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	1.2	1.2	1.2	1.2	1.2	1.2	1.2	1.2	1.2	1.080	1.080	1.080	1.080	1.080	1.080	1.080	1.080	1.080	0.60	0.60	0.60	0.60	0.60	0.60	0.60	0.60	0.60	1.080	1.080	1.080	1.080	1.080	1.080	1.080	1.080	1.080	1	1	1	1	1	1	1	1	1	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	-1	-1	0	0	0	0	0	0	0	-1	-1	1.0	1.0	1.0	1.0	1.0	1.0	1.0	-1	-1	0	0	0	0	0	0	-1	-1	1.0	1.0	1.0	1.0	1.0	1.0	1	38	39	40	41	42	43	44	45	46	34-43	34-43	34-43	34-43	34-43	34-43	34-43	44-53	44-53
8571	5	5	5	5	5	5	5	5	5	Single	Single	Single	Single	Single	Single	Single	Single	Single	21	22	23	24	25	26	27	28	29	20-24	20-24	20-24	20-24	25-29	25-29	25-29	25-29	25-29	0-7500	0-7500	0-7500	0-7500	0-7500	0-7500	0-7500	0-7500	0-7500	3	3	3	3	3	3	3	3	3	Low	Low	Low	Low	Low	Low	Low	Low	Low	5610	5610	5610	5610	5610	5610	5610	5610	5610	0-10000	0-10000	0-10000	0-10000	0-10000	0-10000	0-10000	0-10000	0-10000	1e+05	1e+05	1e+05	1e+05	1e+05	1e+05	1e+05	1e+05	1e+05	500	500	500	500	500	500	500	500	500	0.000	0.0000	10121.7588	0.0000	0.0000	0.000	0.000	0.000	0	0	0	0	0	0	1	0	0	1500	1500	1500	1500	1500	1500	1500	1500	1500	1.2	1.2	1.2	1.2	1.2	1.2	1.2	1.2	1.2	2.0	2.0	2.0	2.0	1.5	1.5	1.5	1.5	1.5	0.7	0.7	0.7	0.7	0.7	0.7	0.7	0.7	0.7	0.720	0.720	0.720	0.720	0.720	0.720	0.720	0.720	0.720	0.88	0.88	0.88	0.88	0.88	0.88	0.88	0.88	0.88	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1	1	1	1	1	1	1	1	1	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	-1	-1	0	1	1	1	0	0	0	-1	-1	1.0	1.2	1.2	1.2	1.0	1.0	1.0	-1	-1	0	1	1	1	0	0	-1	-1	1.0	1.2	1.2	1.2	1.0	1.0	1	6	7	8	9	10	11	12	13	14	4-8	4-8	4-8	4-8	9-13	9-13	9-13	9-13	9-13
8530	6	6	6	6	6	6	6	6	6	Single	Single	Single	Single	Single	Single	Single	Single	Single	28	29	30	31	32	33	34	35	36	25-29	25-29	30-39	30-39	30-39	30-39	30-39	30-39	30-39	7500-10000	7500-10000	7500-10000	7500-10000	7500-10000	7500-10000	7500-10000	7500-10000	7500-10000	2	2	2	2	2	2	2	2	2	High	High	High	High	High	High	High	High	High	20000	20000	20000	20000	20000	20000	20000	20000	20000	20000-30000	20000-30000	20000-30000	20000-30000	20000-30000	20000-30000	20000-30000	20000-30000	20000-30000	5e+04	5e+04	5e+04	5e+04	5e+04	5e+04	5e+04	5e+04	5e+04	250	250	250	250	250	250	250	250	250	0.000	0.0000	28602.5937	0.0000	0.0000	0.000	0.000	70200.000	2	0	1	0	0	0	1	0	1	1500	1500	1500	1500	1500	1500	1500	1500	1500	1.2	1.2	1.2	1.2	1.2	1.2	1.2	1.2	1.2	1.5	1.5	1.0	1.0	1.0	1.0	1.0	1.0	1.0	0.9	0.9	0.9	0.9	0.9	0.9	0.9	0.9	0.9	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	0.60	0.60	0.60	0.60	0.60	0.60	0.60	0.60	0.60	1.045	1.045	1.045	1.045	1.045	1.045	1.045	1.045	1.045	1	1	1	1	1	1	1	1	1	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	-1	-1	0	1	1	1	0	0	1	-1	-1	1.0	1.2	1.2	1.2	1.0	1.0	1.2	-1	-1	0	1	1	2	1	1	-1	-1	1.0	1.2	1.2	1.4	1.2	1.2	1	13	14	15	16	17	18	19	20	21	9-13	9-13	14-23	14-23	14-23	14-23	14-23	14-23	14-23
6104	7	7	7	7	7	7	7	7	7	Single	Single	Single	Single	Single	Single	Single	Single	Single	33	34	35	36	37	38	39	40	41	30-39	30-39	30-39	30-39	30-39	30-39	30-39	40-49	40-49	0-7500	0-7500	0-7500	0-7500	0-7500	0-7500	0-7500	0-7500	0-7500	1	1	1	1	1	1	1	1	1	High	High	High	High	High	High	High	High	High	13020	13020	13020	13020	13020	13020	13020	13020	13020	10000-20000	10000-20000	10000-20000	10000-20000	10000-20000	10000-20000	10000-20000	10000-20000	10000-20000	5e+04	5e+04	5e+04	5e+04	5e+04	5e+04	5e+04	5e+04	5e+04	500	500	500	500	500	500	500	500	500	0.000	0.0000	0.0000	0.0000	0.0000	0.000	0.000	0.000	0	0	0	0	0	0	0	0	0	1500	1500	1500	1500	1500	1500	1500	1500	1500	1.2	1.2	1.2	1.2	1.2	1.2	1.2	1.2	1.2	1.0	1.0	1.0	1.0	1.0	1.0	1.0	0.9	0.9	0.7	0.7	0.7	0.7	0.7	0.7	0.7	0.7	0.7	0.880	0.880	0.880	0.880	0.880	0.880	0.880	0.880	0.880	0.60	0.60	0.60	0.60	0.60	0.60	0.60	0.60	0.60	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	2	2	2	2	2	2	2	2	2	0.9	0.9	0.9	0.9	0.9	0.9	0.9	0.9	0.9	-1	-1	0	0	0	0	0	0	0	-1	-1	1.0	1.0	1.0	1.0	1.0	1.0	1.0	-1	-1	0	0	0	0	0	0	-1	-1	1.0	1.0	1.0	1.0	1.0	1.0	1	18	19	20	21	22	23	24	25	26	14-23	14-23	14-23	14-23	14-23	14-23	14-23	24-33	24-33
12468	7	7	7	7	7	7	7	7	7	Single	Single	Single	Single	Single	Single	Single	Single	Single	27	28	29	30	31	32	33	34	35	25-29	25-29	25-29	30-39	30-39	30-39	30-39	30-39	30-39	0-7500	0-7500	0-7500	0-7500	0-7500	0-7500	0-7500	0-7500	0-7500	2	2	2	2	2	2	2	2	2	High	High	High	High	High	High	High	High	High	26350	26350	26350	26350	26350	26350	26350	26350	26350	20000-30000	20000-30000	20000-30000	20000-30000	20000-30000	20000-30000	20000-30000	20000-30000	20000-30000	1e+05	1e+05	1e+05	1e+05	1e+05	1e+05	1e+05	1e+05	1e+05	250	250	250	250	250	250	250	250	250	0.000	0.0000	0.0000	0.0000	0.0000	0.000	0.000	0.000	0	0	0	0	1	0	1	1	0	1500	1500	1500	1500	1500	1500	1500	1500	1500	1.2	1.2	1.2	1.2	1.2	1.2	1.2	1.2	1.2	1.5	1.5	1.5	1.0	1.0	1.0	1.0	1.0	1.0	0.7	0.7	0.7	0.7	0.7	0.7	0.7	0.7	0.7	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	0.88	0.88	0.88	0.88	0.88	0.88	0.88	0.88	0.88	1.045	1.045	1.045	1.045	1.045	1.045	1.045	1.045	1.045	1	1	1	1	1	1	1	1	1	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	-1	-1	0	0	0	0	0	0	0	-1	-1	1.0	1.0	1.0	1.0	1.0	1.0	1.0	-1	-1	1	2	2	2	1	0	-1	-1	1.2	1.4	1.4	1.4	1.2	1.0	1	12	13	14	15	16	17	18	19	20	9-13	9-13	9-13	14-23	14-23	14-23	14-23	14-23	14-23
1547	8	8	8	8	8	8	8	8	8	Married	Married	Married	Married	Married	Married	Married	Married	Married	52	53	54	55	56	57	58	59	60	50-59	50-59	50-59	50-59	50-59	50-59	50-59	50-59	60-69	0-7500	0-7500	0-7500	0-7500	0-7500	0-7500	0-7500	0-7500	0-7500	4	4	4	4	4	4	4	4	4	Low	Low	Low	Low	Low	Low	Low	Low	Low	39180	39180	39180	39180	39180	39180	39180	39180	39180	30000-40000	30000-40000	30000-40000	30000-40000	30000-40000	30000-40000	30000-40000	30000-40000	30000-40000	5e+05	5e+05	5e+05	5e+05	5e+05	5e+05	5e+05	5e+05	5e+05	1000	1000	1000	1000	1000	1000	1000	1000	1000	0.000	0.0000	0.0000	0.0000	0.0000	0.000	0.000	0.000	2	0	0	0	0	0	0	0	0	1500	1500	1500	1500	1500	1500	1500	1500	1500	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.7	0.7	0.7	0.7	0.7	0.7	0.7	0.7	0.7	1.045	1.045	1.045	1.045	1.045	1.045	1.045	1.045	1.045	1.12	1.12	1.12	1.12	1.12	1.12	1.12	1.12	1.12	0.935	0.935	0.935	0.935	0.935	0.935	0.935	0.935	0.935	1	1	1	1	1	1	1	1	1	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	-1	-1	0	0	0	0	0	0	0	-1	-1	1.0	1.0	1.0	1.0	1.0	1.0	1.0	-1	-1	0	0	0	0	0	0	-1	-1	1.0	1.0	1.0	1.0	1.0	1.0	1	37	38	39	40	41	42	43	44	45	34-43	34-43	34-43	34-43	34-43	34-43	34-43	34-43	44-53
736	9	9	9	9	9	9	9	9	9	Married	Married	Married	Married	Married	Married	Married	Married	Married	49	50	51	52	53	54	55	56	57	40-49	50-59	50-59	50-59	50-59	50-59	50-59	50-59	50-59	10000-15000	10000-15000	10000-15000	10000-15000	10000-15000	10000-15000	10000-15000	10000-15000	10000-15000	4	4	4	4	4	4	4	4	4	Medium	Medium	Medium	Medium	Medium	Medium	Medium	Medium	Medium	30150	30150	30150	30150	30150	30150	30150	30150	30150	30000-40000	30000-40000	30000-40000	30000-40000	30000-40000	30000-40000	30000-40000	30000-40000	30000-40000	1e+05	1e+05	1e+05	1e+05	1e+05	1e+05	1e+05	1e+05	1e+05	500	500	500	500	500	500	500	500	500	0.000	0.0000	0.0000	0.0000	0.0000	0.000	0.000	52977.089	0	0	0	0	0	0	0	0	0	1500	1500	1500	1500	1500	1500	1500	1500	1500	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.9	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.045	1.045	1.045	1.045	1.045	1.045	1.045	1.045	1.045	0.88	0.88	0.88	0.88	0.88	0.88	0.88	0.88	0.88	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	3	3	3	3	3	3	3	3	3	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	-1	-1	0	0	0	0	0	0	1	-1	-1	1.0	1.0	1.0	1.0	1.0	1.0	1.2	-1	-1	0	0	0	0	0	0	-1	-1	1.0	1.0	1.0	1.0	1.0	1.0	1	34	35	36	37	38	39	40	41	42	24-33	34-43	34-43	34-43	34-43	34-43	34-43	34-43	34-43
12236	9	9	9	9	9	9	9	9	9	Single	Single	Single	Single	Single	Single	Single	Single	Single	50	51	52	53	54	55	56	57	58	50-59	50-59	50-59	50-59	50-59	50-59	50-59	50-59	50-59	0-7500	0-7500	0-7500	0-7500	0-7500	0-7500	0-7500	0-7500	0-7500	4	4	4	4	4	4	4	4	4	Medium	Medium	Medium	Medium	Medium	Medium	Medium	Medium	Medium	22600	22600	22600	22600	22600	22600	22600	22600	22600	20000-30000	20000-30000	20000-30000	20000-30000	20000-30000	20000-30000	20000-30000	20000-30000	20000-30000	5e+04	5e+04	5e+04	5e+04	5e+04	5e+04	5e+04	5e+04	5e+04	100	100	100	100	100	100	100	100	100	0.000	0.0000	0.0000	0.0000	0.0000	0.000	0.000	0.000	0	0	0	0	0	0	0	0	0	1500	1500	1500	1500	1500	1500	1500	1500	1500	1.2	1.2	1.2	1.2	1.2	1.2	1.2	1.2	1.2	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.7	0.7	0.7	0.7	0.7	0.7	0.7	0.7	0.7	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	0.60	0.60	0.60	0.60	0.60	0.60	0.60	0.60	0.60	1.080	1.080	1.080	1.080	1.080	1.080	1.080	1.080	1.080	2	2	2	2	2	2	2	2	2	0.9	0.9	0.9	0.9	0.9	0.9	0.9	0.9	0.9	-1	-1	0	0	0	0	0	0	0	-1	-1	1.0	1.0	1.0	1.0	1.0	1.0	1.0	-1	-1	0	0	0	0	0	0	-1	-1	1.0	1.0	1.0	1.0	1.0	1.0	1	35	36	37	38	39	40	41	42	43	34-43	34-43	34-43	34-43	34-43	34-43	34-43	34-43	34-43
14398	9	9	9	9	9	9	9	9	9	Single	Single	Single	Single	Single	Single	Single	Single	Single	47	48	49	50	51	52	53	54	55	40-49	40-49	40-49	50-59	50-59	50-59	50-59	50-59	50-59	0-7500	0-7500	0-7500	0-7500	0-7500	0-7500	0-7500	0-7500	0-7500	3	3	3	3	3	3	3	3	3	Medium	Medium	Medium	Medium	Medium	Medium	Medium	Medium	Medium	28950	28950	28950	28950	28950	28950	28950	28950	28950	20000-30000	20000-30000	20000-30000	20000-30000	20000-30000	20000-30000	20000-30000	20000-30000	20000-30000	5e+04	5e+04	5e+04	5e+04	5e+04	5e+04	5e+04	5e+04	5e+04	1000	1000	1000	1000	1000	1000	1000	1000	1000	0.000	0.0000	0.0000	0.0000	0.0000	0.000	0.000	0.000	0	0	0	0	0	0	0	0	0	1500	1500	1500	1500	1500	1500	1500	1500	1500	1.2	1.2	1.2	1.2	1.2	1.2	1.2	1.2	1.2	0.9	0.9	0.9	0.8	0.8	0.8	0.8	0.8	0.8	0.7	0.7	0.7	0.7	0.7	0.7	0.7	0.7	0.7	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	0.60	0.60	0.60	0.60	0.60	0.60	0.60	0.60	0.60	0.935	0.935	0.935	0.935	0.935	0.935	0.935	0.935	0.935	1	1	1	1	1	1	1	1	1	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	-1	-1	0	0	0	0	0	0	0	-1	-1	1.0	1.0	1.0	1.0	1.0	1.0	1.0	-1	-1	0	0	0	0	0	0	-1	-1	1.0	1.0	1.0	1.0	1.0	1.0	1	32	33	34	35	36	37	38	39	40	24-33	24-33	24-33	34-43	34-43	34-43	34-43	34-43	34-43
6386	10	10	10	10	10	10	10	10	10	Single	Single	Single	Single	Single	Single	Single	Single	Single	16	17	18	19	20	21	22	23	24	16-19	16-19	16-19	16-19	20-24	20-24	20-24	20-24	20-24	7500-10000	7500-10000	7500-10000	7500-10000	7500-10000	7500-10000	7500-10000	7500-10000	7500-10000	2	2	2	2	2	2	2	2	2	Low	Low	Low	Low	Low	Low	Low	Low	Low	1020	1020	1020	1020	1020	1020	1020	1020	1020	0-10000	0-10000	0-10000	0-10000	0-10000	0-10000	0-10000	0-10000	0-10000	5e+04	5e+04	5e+04	5e+04	5e+04	5e+04	5e+04	5e+04	5e+04	100	100	100	100	100	100	100	100	100	2440.102	239.7231	6483.2473	2026.9269	220.6801	1897.678	200.273	2659.388	0	0	0	0	0	0	0	0	0	1500	1500	1500	1500	1500	1500	1500	1500	1500	1.2	1.2	1.2	1.2	1.2	1.2	1.2	1.2	1.2	3.0	3.0	3.0	3.0	2.0	2.0	2.0	2.0	2.0	0.9	0.9	0.9	0.9	0.9	0.9	0.9	0.9	0.9	0.720	0.720	0.720	0.720	0.720	0.720	0.720	0.720	0.720	0.60	0.60	0.60	0.60	0.60	0.60	0.60	0.60	0.60	1.080	1.080	1.080	1.080	1.080	1.080	1.080	1.080	1.080	1	1	1	1	1	1	1	1	1	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	-1	-1	2	3	3	3	3	3	3	-1	-1	1.4	1.6	1.6	1.6	1.6	1.6	1.6	-1	-1	0	0	0	0	0	0	-1	-1	1.0	1.0	1.0	1.0	1.0	1.0	1	1	2	3	4	5	6	7	8	9	0-3	0-3	0-3	0-3	4-8	4-8	4-8	4-8	4-8
5284	11	11	11	11	11	11	11	11	11	Married	Married	Married	Married	Married	Married	Married	Married	Married	27	28	29	30	31	32	33	34	35	25-29	25-29	25-29	30-39	30-39	30-39	30-39	30-39	30-39	7500-10000	7500-10000	7500-10000	7500-10000	7500-10000	7500-10000	7500-10000	7500-10000	7500-10000	3	3	3	3	3	3	3	3	3	High	High	High	High	High	High	High	High	High	1270	1270	1270	1270	1270	1270	1270	1270	1270	0-10000	0-10000	0-10000	0-10000	0-10000	0-10000	0-10000	0-10000	0-10000	1e+05	1e+05	1e+05	1e+05	1e+05	1e+05	1e+05	1e+05	1e+05	250	250	250	250	250	250	250	250	250	0.000	0.0000	0.0000	0.0000	0.0000	0.000	0.000	0.000	0	3	0	0	1	0	0	1	0	1500	1500	1500	1500	1500	1500	1500	1500	1500	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	1.5	1.5	1.5	1.0	1.0	1.0	1.0	1.0	1.0	0.9	0.9	0.9	0.9	0.9	0.9	0.9	0.9	0.9	0.720	0.720	0.720	0.720	0.720	0.720	0.720	0.720	0.720	0.88	0.88	0.88	0.88	0.88	0.88	0.88	0.88	0.88	1.045	1.045	1.045	1.045	1.045	1.045	1.045	1.045	1.045	1	1	1	1	1	1	1	1	1	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	-1	-1	0	0	0	0	0	0	0	-1	-1	1.0	1.0	1.0	1.0	1.0	1.0	1.0	-1	-1	1	1	1	1	1	0	-1	-1	1.2	1.2	1.2	1.2	1.2	1.0	1	12	13	14	15	16	17	18	19	20	9-13	9-13	9-13	14-23	14-23	14-23	14-23	14-23	14-23
999	12	12	12	12	12	12	12	12	12	Married	Married	Married	Married	Married	Married	Married	Married	Married	65	66	67	68	69	70	71	72	73	60-69	60-69	60-69	60-69	60-69	70-79	70-79	70-79	70-79	10000-15000	10000-15000	10000-15000	10000-15000	10000-15000	10000-15000	10000-15000	10000-15000	10000-15000	3	3	3	3	3	3	3	3	3	Medium	Medium	Medium	Medium	Medium	Medium	Medium	Medium	Medium	62030	62030	62030	62030	62030	62030	62030	62030	62030	40000+	40000+	40000+	40000+	40000+	40000+	40000+	40000+	40000+	1e+05	1e+05	1e+05	1e+05	1e+05	1e+05	1e+05	1e+05	1e+05	500	500	500	500	500	500	500	500	500	0.000	0.0000	0.0000	0.0000	0.0000	3620.310	0.000	0.000	0	0	0	0	0	0	0	0	0	1500	1500	1500	1500	1500	1500	1500	1500	1500	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.080	1.080	1.080	1.080	1.080	1.080	1.080	1.080	1.080	0.88	0.88	0.88	0.88	0.88	0.88	0.88	0.88	0.88	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1	1	1	1	1	1	1	1	1	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	-1	-1	0	0	0	0	1	1	1	-1	-1	1.0	1.0	1.0	1.0	1.2	1.2	1.2	-1	-1	0	0	0	0	0	0	-1	-1	1.0	1.0	1.0	1.0	1.0	1.0	1	50	51	52	53	54	55	56	57	58	44-53	44-53	44-53	44-53	44-53	54-63	54-63	54-63	54-63
1553	13	13	13	13	13	13	13	13	13	Single	Single	Single	Single	Single	Single	Single	Single	Single	37	38	39	40	41	42	43	44	45	30-39	30-39	30-39	40-49	40-49	40-49	40-49	40-49	40-49	15000+	15000+	15000+	15000+	15000+	15000+	15000+	15000+	15000+	2	2	2	2	2	2	2	2	2	High	High	High	High	High	High	High	High	High	39430	39430	39430	39430	39430	39430	39430	39430	39430	30000-40000	30000-40000	30000-40000	30000-40000	30000-40000	30000-40000	30000-40000	30000-40000	30000-40000	3e+05	3e+05	3e+05	3e+05	3e+05	3e+05	3e+05	3e+05	3e+05	500	500	500	500	500	500	500	500	500	0.000	0.0000	0.0000	0.0000	0.0000	0.000	0.000	0.000	0	0	0	0	0	0	0	0	0	1500	1500	1500	1500	1500	1500	1500	1500	1500	1.2	1.2	1.2	1.2	1.2	1.2	1.2	1.2	1.2	1.0	1.0	1.0	0.9	0.9	0.9	0.9	0.9	0.9	1.2	1.2	1.2	1.2	1.2	1.2	1.2	1.2	1.2	1.045	1.045	1.045	1.045	1.045	1.045	1.045	1.045	1.045	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1	1	1	1	1	1	1	1	1	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	-1	-1	0	0	0	0	0	0	0	-1	-1	1.0	1.0	1.0	1.0	1.0	1.0	1.0	-1	-1	0	0	0	0	0	0	-1	-1	1.0	1.0	1.0	1.0	1.0	1.0	1	22	23	24	25	26	27	28	29	30	14-23	14-23	14-23	24-33	24-33	24-33	24-33	24-33	24-33
8480	14	14	14	14	14	14	14	14	14	Single	Single	Single	Single	Single	Single	Single	Single	Single	20	21	22	23	24	25	26	27	28	20-24	20-24	20-24	20-24	20-24	25-29	25-29	25-29	25-29	7500-10000	7500-10000	7500-10000	7500-10000	7500-10000	7500-10000	7500-10000	7500-10000	7500-10000	3	3	3	3	3	3	3	3	3	High	High	High	High	High	High	High	High	High	23570	23570	23570	23570	23570	23570	23570	23570	23570	20000-30000	20000-30000	20000-30000	20000-30000	20000-30000	20000-30000	20000-30000	20000-30000	20000-30000	5e+04	5e+04	5e+04	5e+04	5e+04	5e+04	5e+04	5e+04	5e+04	100	100	100	100	100	100	100	100	100	0.000	0.0000	0.0000	236.8179	0.0000	0.000	0.000	0.000	0	1	0	0	0	0	0	0	0	1500	1500	1500	1500	1500	1500	1500	1500	1500	1.2	1.2	1.2	1.2	1.2	1.2	1.2	1.2	1.2	2.0	2.0	2.0	2.0	2.0	1.5	1.5	1.5	1.5	0.9	0.9	0.9	0.9	0.9	0.9	0.9	0.9	0.9	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000	0.60	0.60	0.60	0.60	0.60	0.60	0.60	0.60	0.60	1.080	1.080	1.080	1.080	1.080	1.080	1.080	1.080	1.080	2	2	2	2	2	2	2	2	2	0.9	0.9	0.9	0.9	0.9	0.9	0.9	0.9	0.9	-1	-1	0	0	1	1	1	0	0	-1	-1	1.0	1.0	1.2	1.2	1.2	1.0	1.0	-1	-1	0	0	0	0	0	0	-1	-1	1.0	1.0	1.0	1.0	1.0	1.0	1	5	6	7	8	9	10	11	12	13	4-8	4-8	4-8	4-8	4-8	9-13	9-13	9-13	9-13
10430	14	14	14	14	14	14	14	14	14	Single	Single	Single	Single	Single	Single	Single	Single	Single	51	52	53	54	55	56	57	58	59	50-59	50-59	50-59	50-59	50-59	50-59	50-59	50-59	50-59	10000-15000	10000-15000	10000-15000	10000-15000	10000-15000	10000-15000	10000-15000	10000-15000	10000-15000	2	2	2	2	2	2	2	2	2	High	High	High	High	High	High	High	High	High	11020	11020	11020	11020	11020	11020	11020	11020	11020	10000-20000	10000-20000	10000-20000	10000-20000	10000-20000	10000-20000	10000-20000	10000-20000	10000-20000	1e+05	1e+05	1e+05	1e+05	1e+05	1e+05	1e+05	1e+05	1e+05	250	250	250	250	250	250	250	250	250	0.000	0.0000	0.0000	0.0000	0.0000	0.000	0.000	0.000	0	0	0	0	0	1	0	0	0	1500	1500	1500	1500	1500	1500	1500	1500	1500	1.2	1.2	1.2	1.2	1.2	1.2	1.2	1.2	1.2	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	0.880	0.880	0.880	0.880	0.880	0.880	0.880	0.880	0.880	0.88	0.88	0.88	0.88	0.88	0.88	0.88	0.88	0.88	1.045	1.045	1.045	1.045	1.045	1.045	1.045	1.045	1.045	1	1	1	1	1	1	1	1	1	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	-1	-1	0	0	0	0	0	0	0	-1	-1	1.0	1.0	1.0	1.0	1.0	1.0	1.0	-1	-1	1	1	1	0	0	0	-1	-1	1.2	1.2	1.2	1.0	1.0	1.0	1	36	37	38	39	40	41	42	43	44	34-43	34-43	34-43	34-43	34-43	34-43	34-43	34-43	34-43

From the display of tbl.wider[1:20,], we can see that many columns are redundant. Before we remove any of these columns, this provides critical information for us as actuaries. Because we are trying to create a prospective underwriting guideline, we want to understand the data that go into our models.

Deleting Repeated Columns

# k <- 2 # counting index
keep <- c(1,2) # columns to keep
for (i in 3:(length(names(tbl.wider)) ) ) {
  compare <- prod( tbl.wider[i-1] == tbl.wider[i] )
  if ( is.na(compare) ) { compare <- TRUE }
  # print(diff)
  if ( !as.logical(compare)  ) { # if not exact match
    keep <- c(keep, i)
  }
}
tbl.cleaned <- tbl.wider[keep]
# View(tbl.cleaned, title = "Cleaned Data Table")
tbl.cleaned[1:20,] %>% qkable()

Vehicle Number	Policy Number PY2010	Marital Status PY2010	Driver Age PY2010	Driver Age PY2011	Driver Age PY2012	Driver Age PY2013	Driver Age PY2014	Driver Age PY2015	Driver Age PY2016	Driver Age PY2017	Driver Age PY2018	Driver Age Band PY2010	Driver Age Band PY2011	Driver Age Band PY2012	Driver Age Band PY2013	Driver Age Band PY2014	Driver Age Band PY2015	Driver Age Band PY2016	Driver Age Band PY2017	Driver Age Band PY2018	Annual Mileage PY2010	Territory PY2010	Credit Score PY2010	Car Value PY2010	Car Value Band PY2010	Liability Limit PY2010	Physical Damage Deductible PY2010	Reported Losses PY2011	Reported Losses PY2012	Reported Losses PY2013	Reported Losses PY2014	Reported Losses PY2015	Reported Losses PY2016	Reported Losses PY2017	Reported Losses PY2018	Late Fees PY2011	Late Fees PY2012	Late Fees PY2013	Conviction Points PY2010	Conviction Points PY2011	Conviction Points PY2012	Conviction Points PY2013	Conviction Points PY2014	Conviction Points PY2015	Base Pure Premium PY2010	Marital Status Relativity PY2010	Driver Age Relativity PY2010	Driver Age Relativity PY2011	Driver Age Relativity PY2012	Driver Age Relativity PY2013	Driver Age Relativity PY2014	Driver Age Relativity PY2015	Driver Age Relativity PY2016	Driver Age Relativity PY2017	Driver Age Relativity PY2018	Annual Mileage Relativity PY2010	Car Value Relativity PY2010	Liability Limit Relativity PY2010	Physical Damage Deductible Relativity PY2010	Multi-Car PY2010	Multi-Car Relativity PY2010	Accident Points (AP) last 3 years PY2010	Accident Points (AP) last 3 years PY2011	Accident Points (AP) last 3 years PY2012	Accident Points (AP) last 3 years PY2013	Accident Points (AP) last 3 years PY2014	Accident Points (AP) last 3 years PY2015	Accident Points (AP) last 3 years PY2016	Accident Points (AP) last 3 years PY2017	Accident Points (AP) last 3 years PY2018	AP Relativity PY2010	AP Relativity PY2011	AP Relativity PY2012	AP Relativity PY2013	AP Relativity PY2014	AP Relativity PY2015	AP Relativity PY2016	AP Relativity PY2017	AP Relativity PY2018	Conviction Points (CP) last 3 years PY2013	Conviction Points (CP) last 3 years PY2014	Conviction Points (CP) last 3 years PY2015	Conviction Points (CP) last 3 years PY2016	Conviction Points (CP) last 3 years PY2017	CP Relativity PY2010	CP Relativity PY2012	CP Relativity PY2013	CP Relativity PY2014	CP Relativity PY2015	CP Relativity PY2016	CP Relativity PY2017	CP Relativity PY2018	Driver Experience PY2010	Driver Experience PY2011	Driver Experience PY2012	Driver Experience PY2013	Driver Experience PY2014	Driver Experience PY2015	Driver Experience PY2016	Driver Experience PY2017	Driver Experience PY2018	Driver Experience Band PY2010	Driver Experience Band PY2011	Driver Experience Band PY2012	Driver Experience Band PY2013	Driver Experience Band PY2014	Driver Experience Band PY2015	Driver Experience Band PY2016	Driver Experience Band PY2017	Driver Experience Band PY2018
6125	1	Single	18	19	20	21	22	23	24	25	26	16-19	16-19	20-24	20-24	20-24	20-24	20-24	25-29	25-29	0-7500	4	High	3220	0-10000	5e+04	100	0.000	0.0000	200.0692	0.0000	0.0000	12602.418	0.000	0.000	0	0	0	1	1	0	0	0	0	1500	1.2	3.0	3.0	2.0	2.0	2.0	2.0	2.0	1.5	1.5	0.7	0.720	0.60	1.080	2	0.9	-1	-1	0	1	1	1	1	1	1	-1	-1	1.0	1.2	1.2	1.2	1.2	1.2	1.2	1	0	0	0	0	-1	1.4	1.2	1.0	1.0	1.0	1.0	1	3	4	5	6	7	8	9	10	11	0-3	0-3	4-8	4-8	4-8	4-8	4-8	9-13	9-13
10332	1	Married	45	46	47	48	49	50	51	52	53	40-49	40-49	40-49	40-49	40-49	50-59	50-59	50-59	50-59	7500-10000	3	High	20090	20000-30000	5e+05	250	0.000	0.0000	0.0000	0.0000	0.0000	0.000	0.000	0.000	0	0	0	0	0	0	0	1	0	1500	0.8	0.9	0.9	0.9	0.9	0.9	0.8	0.8	0.8	0.8	0.9	1.000	1.12	1.045	1	1.0	-1	-1	0	0	0	0	0	0	0	-1	-1	1.0	1.0	1.0	1.0	1.0	1.0	1.0	0	1	1	1	0	-1	1.0	1.0	1.2	1.2	1.2	1.0	1	30	31	32	33	34	35	36	37	38	24-33	24-33	24-33	24-33	24-33	34-43	34-43	34-43	34-43
1965	2	Married	54	55	56	57	58	59	60	61	62	50-59	50-59	50-59	50-59	50-59	50-59	60-69	60-69	60-69	15000+	1	Medium	13810	10000-20000	1e+05	500	0.000	0.0000	0.0000	0.0000	0.0000	0.000	0.000	0.000	0	0	0	0	0	0	0	0	0	1500	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	1.2	0.880	0.88	1.000	2	0.9	-1	-1	0	0	0	0	0	0	0	-1	-1	1.0	1.0	1.0	1.0	1.0	1.0	1.0	0	0	0	0	0	-1	1.0	1.0	1.0	1.0	1.0	1.0	1	39	40	41	42	43	44	45	46	47	34-43	34-43	34-43	34-43	34-43	34-43	44-53	44-53	44-53
14130	2	Married	49	50	51	52	53	54	55	56	57	40-49	50-59	50-59	50-59	50-59	50-59	50-59	50-59	50-59	10000-15000	1	High	37060	30000-40000	1e+05	100	0.000	0.0000	0.0000	0.0000	0.0000	0.000	0.000	0.000	0	0	0	1	0	0	0	0	0	1500	0.8	0.9	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	1.0	1.045	0.88	1.080	1	1.0	-1	-1	0	0	0	0	0	0	0	-1	-1	1.0	1.0	1.0	1.0	1.0	1.0	1.0	0	0	0	0	0	-1	1.2	1.0	1.0	1.0	1.0	1.0	1	34	35	36	37	38	39	40	41	42	24-33	34-43	34-43	34-43	34-43	34-43	34-43	34-43	34-43
2976	3	Single	31	32	33	34	35	36	37	38	39	30-39	30-39	30-39	30-39	30-39	30-39	30-39	30-39	30-39	7500-10000	4	High	20860	20000-30000	5e+04	250	0.000	0.0000	0.0000	0.0000	0.0000	0.000	0.000	0.000	0	0	0	0	0	0	0	0	0	1500	1.2	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	0.9	1.000	0.60	1.045	1	1.0	-1	-1	0	0	0	0	0	0	0	-1	-1	1.0	1.0	1.0	1.0	1.0	1.0	1.0	0	0	0	0	0	-1	1.0	1.0	1.0	1.0	1.0	1.0	1	16	17	18	19	20	21	22	23	24	14-23	14-23	14-23	14-23	14-23	14-23	14-23	14-23	14-23
76	4	Married	53	54	55	56	57	58	59	60	61	50-59	50-59	50-59	50-59	50-59	50-59	50-59	60-69	60-69	15000+	2	High	80850	40000+	5e+04	100	0.000	0.0000	0.0000	0.0000	0.0000	0.000	0.000	0.000	0	2	0	0	0	0	0	0	0	1500	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	1.2	1.080	0.60	1.080	1	1.0	-1	-1	0	0	0	0	0	0	0	-1	-1	1.0	1.0	1.0	1.0	1.0	1.0	1.0	0	0	0	0	0	-1	1.0	1.0	1.0	1.0	1.0	1.0	1	38	39	40	41	42	43	44	45	46	34-43	34-43	34-43	34-43	34-43	34-43	34-43	44-53	44-53
8571	5	Single	21	22	23	24	25	26	27	28	29	20-24	20-24	20-24	20-24	25-29	25-29	25-29	25-29	25-29	0-7500	3	Low	5610	0-10000	1e+05	500	0.000	0.0000	10121.7588	0.0000	0.0000	0.000	0.000	0.000	0	0	0	0	0	0	1	0	0	1500	1.2	2.0	2.0	2.0	2.0	1.5	1.5	1.5	1.5	1.5	0.7	0.720	0.88	1.000	1	1.0	-1	-1	0	1	1	1	0	0	0	-1	-1	1.0	1.2	1.2	1.2	1.0	1.0	1.0	1	1	1	0	0	-1	1.0	1.2	1.2	1.2	1.0	1.0	1	6	7	8	9	10	11	12	13	14	4-8	4-8	4-8	4-8	9-13	9-13	9-13	9-13	9-13
8530	6	Single	28	29	30	31	32	33	34	35	36	25-29	25-29	30-39	30-39	30-39	30-39	30-39	30-39	30-39	7500-10000	2	High	20000	20000-30000	5e+04	250	0.000	0.0000	28602.5937	0.0000	0.0000	0.000	0.000	70200.000	2	0	1	0	0	0	1	0	1	1500	1.2	1.5	1.5	1.0	1.0	1.0	1.0	1.0	1.0	1.0	0.9	1.000	0.60	1.045	1	1.0	-1	-1	0	1	1	1	0	0	1	-1	-1	1.0	1.2	1.2	1.2	1.0	1.0	1.2	1	1	2	1	1	-1	1.0	1.2	1.2	1.4	1.2	1.2	1	13	14	15	16	17	18	19	20	21	9-13	9-13	14-23	14-23	14-23	14-23	14-23	14-23	14-23
6104	7	Single	33	34	35	36	37	38	39	40	41	30-39	30-39	30-39	30-39	30-39	30-39	30-39	40-49	40-49	0-7500	1	High	13020	10000-20000	5e+04	500	0.000	0.0000	0.0000	0.0000	0.0000	0.000	0.000	0.000	0	0	0	0	0	0	0	0	0	1500	1.2	1.0	1.0	1.0	1.0	1.0	1.0	1.0	0.9	0.9	0.7	0.880	0.60	1.000	2	0.9	-1	-1	0	0	0	0	0	0	0	-1	-1	1.0	1.0	1.0	1.0	1.0	1.0	1.0	0	0	0	0	0	-1	1.0	1.0	1.0	1.0	1.0	1.0	1	18	19	20	21	22	23	24	25	26	14-23	14-23	14-23	14-23	14-23	14-23	14-23	24-33	24-33
12468	7	Single	27	28	29	30	31	32	33	34	35	25-29	25-29	25-29	30-39	30-39	30-39	30-39	30-39	30-39	0-7500	2	High	26350	20000-30000	1e+05	250	0.000	0.0000	0.0000	0.0000	0.0000	0.000	0.000	0.000	0	0	0	0	1	0	1	1	0	1500	1.2	1.5	1.5	1.5	1.0	1.0	1.0	1.0	1.0	1.0	0.7	1.000	0.88	1.045	1	1.0	-1	-1	0	0	0	0	0	0	0	-1	-1	1.0	1.0	1.0	1.0	1.0	1.0	1.0	2	2	2	1	0	-1	1.2	1.4	1.4	1.4	1.2	1.0	1	12	13	14	15	16	17	18	19	20	9-13	9-13	9-13	14-23	14-23	14-23	14-23	14-23	14-23
1547	8	Married	52	53	54	55	56	57	58	59	60	50-59	50-59	50-59	50-59	50-59	50-59	50-59	50-59	60-69	0-7500	4	Low	39180	30000-40000	5e+05	1000	0.000	0.0000	0.0000	0.0000	0.0000	0.000	0.000	0.000	2	0	0	0	0	0	0	0	0	1500	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.7	1.045	1.12	0.935	1	1.0	-1	-1	0	0	0	0	0	0	0	-1	-1	1.0	1.0	1.0	1.0	1.0	1.0	1.0	0	0	0	0	0	-1	1.0	1.0	1.0	1.0	1.0	1.0	1	37	38	39	40	41	42	43	44	45	34-43	34-43	34-43	34-43	34-43	34-43	34-43	34-43	44-53
736	9	Married	49	50	51	52	53	54	55	56	57	40-49	50-59	50-59	50-59	50-59	50-59	50-59	50-59	50-59	10000-15000	4	Medium	30150	30000-40000	1e+05	500	0.000	0.0000	0.0000	0.0000	0.0000	0.000	0.000	52977.089	0	0	0	0	0	0	0	0	0	1500	0.8	0.9	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	1.0	1.045	0.88	1.000	3	0.8	-1	-1	0	0	0	0	0	0	1	-1	-1	1.0	1.0	1.0	1.0	1.0	1.0	1.2	0	0	0	0	0	-1	1.0	1.0	1.0	1.0	1.0	1.0	1	34	35	36	37	38	39	40	41	42	24-33	34-43	34-43	34-43	34-43	34-43	34-43	34-43	34-43
12236	9	Single	50	51	52	53	54	55	56	57	58	50-59	50-59	50-59	50-59	50-59	50-59	50-59	50-59	50-59	0-7500	4	Medium	22600	20000-30000	5e+04	100	0.000	0.0000	0.0000	0.0000	0.0000	0.000	0.000	0.000	0	0	0	0	0	0	0	0	0	1500	1.2	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.7	1.000	0.60	1.080	2	0.9	-1	-1	0	0	0	0	0	0	0	-1	-1	1.0	1.0	1.0	1.0	1.0	1.0	1.0	0	0	0	0	0	-1	1.0	1.0	1.0	1.0	1.0	1.0	1	35	36	37	38	39	40	41	42	43	34-43	34-43	34-43	34-43	34-43	34-43	34-43	34-43	34-43
14398	9	Single	47	48	49	50	51	52	53	54	55	40-49	40-49	40-49	50-59	50-59	50-59	50-59	50-59	50-59	0-7500	3	Medium	28950	20000-30000	5e+04	1000	0.000	0.0000	0.0000	0.0000	0.0000	0.000	0.000	0.000	0	0	0	0	0	0	0	0	0	1500	1.2	0.9	0.9	0.9	0.8	0.8	0.8	0.8	0.8	0.8	0.7	1.000	0.60	0.935	1	1.0	-1	-1	0	0	0	0	0	0	0	-1	-1	1.0	1.0	1.0	1.0	1.0	1.0	1.0	0	0	0	0	0	-1	1.0	1.0	1.0	1.0	1.0	1.0	1	32	33	34	35	36	37	38	39	40	24-33	24-33	24-33	34-43	34-43	34-43	34-43	34-43	34-43
6386	10	Single	16	17	18	19	20	21	22	23	24	16-19	16-19	16-19	16-19	20-24	20-24	20-24	20-24	20-24	7500-10000	2	Low	1020	0-10000	5e+04	100	2440.102	239.7231	6483.2473	2026.9269	220.6801	1897.678	200.273	2659.388	0	0	0	0	0	0	0	0	0	1500	1.2	3.0	3.0	3.0	3.0	2.0	2.0	2.0	2.0	2.0	0.9	0.720	0.60	1.080	1	1.0	-1	-1	2	3	3	3	3	3	3	-1	-1	1.4	1.6	1.6	1.6	1.6	1.6	1.6	0	0	0	0	0	-1	1.0	1.0	1.0	1.0	1.0	1.0	1	1	2	3	4	5	6	7	8	9	0-3	0-3	0-3	0-3	4-8	4-8	4-8	4-8	4-8
5284	11	Married	27	28	29	30	31	32	33	34	35	25-29	25-29	25-29	30-39	30-39	30-39	30-39	30-39	30-39	7500-10000	3	High	1270	0-10000	1e+05	250	0.000	0.0000	0.0000	0.0000	0.0000	0.000	0.000	0.000	0	3	0	0	1	0	0	1	0	1500	0.8	1.5	1.5	1.5	1.0	1.0	1.0	1.0	1.0	1.0	0.9	0.720	0.88	1.045	1	1.0	-1	-1	0	0	0	0	0	0	0	-1	-1	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1	1	1	1	0	-1	1.2	1.2	1.2	1.2	1.2	1.0	1	12	13	14	15	16	17	18	19	20	9-13	9-13	9-13	14-23	14-23	14-23	14-23	14-23	14-23
999	12	Married	65	66	67	68	69	70	71	72	73	60-69	60-69	60-69	60-69	60-69	70-79	70-79	70-79	70-79	10000-15000	3	Medium	62030	40000+	1e+05	500	0.000	0.0000	0.0000	0.0000	0.0000	3620.310	0.000	0.000	0	0	0	0	0	0	0	0	0	1500	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	1.0	1.080	0.88	1.000	1	1.0	-1	-1	0	0	0	0	1	1	1	-1	-1	1.0	1.0	1.0	1.0	1.2	1.2	1.2	0	0	0	0	0	-1	1.0	1.0	1.0	1.0	1.0	1.0	1	50	51	52	53	54	55	56	57	58	44-53	44-53	44-53	44-53	44-53	54-63	54-63	54-63	54-63
1553	13	Single	37	38	39	40	41	42	43	44	45	30-39	30-39	30-39	40-49	40-49	40-49	40-49	40-49	40-49	15000+	2	High	39430	30000-40000	3e+05	500	0.000	0.0000	0.0000	0.0000	0.0000	0.000	0.000	0.000	0	0	0	0	0	0	0	0	0	1500	1.2	1.0	1.0	1.0	0.9	0.9	0.9	0.9	0.9	0.9	1.2	1.045	1.00	1.000	1	1.0	-1	-1	0	0	0	0	0	0	0	-1	-1	1.0	1.0	1.0	1.0	1.0	1.0	1.0	0	0	0	0	0	-1	1.0	1.0	1.0	1.0	1.0	1.0	1	22	23	24	25	26	27	28	29	30	14-23	14-23	14-23	24-33	24-33	24-33	24-33	24-33	24-33
8480	14	Single	20	21	22	23	24	25	26	27	28	20-24	20-24	20-24	20-24	20-24	25-29	25-29	25-29	25-29	7500-10000	3	High	23570	20000-30000	5e+04	100	0.000	0.0000	0.0000	236.8179	0.0000	0.000	0.000	0.000	0	1	0	0	0	0	0	0	0	1500	1.2	2.0	2.0	2.0	2.0	2.0	1.5	1.5	1.5	1.5	0.9	1.000	0.60	1.080	2	0.9	-1	-1	0	0	1	1	1	0	0	-1	-1	1.0	1.0	1.2	1.2	1.2	1.0	1.0	0	0	0	0	0	-1	1.0	1.0	1.0	1.0	1.0	1.0	1	5	6	7	8	9	10	11	12	13	4-8	4-8	4-8	4-8	4-8	9-13	9-13	9-13	9-13
10430	14	Single	51	52	53	54	55	56	57	58	59	50-59	50-59	50-59	50-59	50-59	50-59	50-59	50-59	50-59	10000-15000	2	High	11020	10000-20000	1e+05	250	0.000	0.0000	0.0000	0.0000	0.0000	0.000	0.000	0.000	0	0	0	0	0	1	0	0	0	1500	1.2	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	1.0	0.880	0.88	1.045	1	1.0	-1	-1	0	0	0	0	0	0	0	-1	-1	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1	1	0	0	0	-1	1.2	1.2	1.2	1.0	1.0	1.0	1	36	37	38	39	40	41	42	43	44	34-43	34-43	34-43	34-43	34-43	34-43	34-43	34-43	34-43

We see here in tbl.cleaned all the unique columns, with all repetitions removed. To emphasize this fact, we keep the ...PY2010 suffix in the column names.

The factors that are constant are listed below, along with the years for which they are repeated:

Constant 2010-2018

Marital Status
Annual Mileage
Territory
Credit Score
Car Value (and Car Value Band)
Liability Limit
Physical Damage Deductible
Multi-Car

Constant 2014-2018

Late Fees

Constant 2016-2018

Conviction Points

From this list, we have reason to believe that either the computer system is broken or there was a serious error in the data reporting.

Because our filed relativity is based on metrics rolling over 3 years, for our project we are interested in modeling based on experience from policy years 2013 through 2016. We want to use Conviction Points to drive our GLM, and this variable for years 2017 and 2018 is not credible.

2. Understanding the Premium Structure

We are told that Cal Insurance suffered large losses over the past 6 years, and that the Chief Actuary believes this may be due to adverse selection. Notably, our dataset only contains a cohort of policyholders who are retained through the years 2010 through 2018. That is, we have no information on newly acquired insureds or loss of customers. This makes it difficult to determine the presence of adverse selection.

However, to get a better intuition on this, we would like to visualize the premium data over the past 6 years. To start, here is a boxplot to demonstrate the distribution of the overall premium structure, as well as separated by different rating factors.

select(prems, Premium, `Policy Year`, Territory)  %>%  ggplot(aes(group =`Policy Year`, y=Premium)) + geom_boxplot(aes(group=`Policy Year`), outlier.color = "lightblue", outlier.shape = 13) + ggtitle("Premium Per Vehicle: Separated by Policy Year") + theme(axis.text.x = element_blank(), axis.ticks.x = element_blank())  # dont know how to change the x axis back to the years

# separated by territory
select(prems, Premium, `Policy Year`, Territory)  %>%  ggplot(aes(group =`Policy Year`, y=Premium)) + geom_boxplot(aes(group=`Policy Year`), outlier.color = "lightblue", outlier.shape = 13) + facet_grid(. ~ Territory) + ggtitle("Premium Per Vehicle: Separated by Territory") + theme(axis.text.x = element_blank(), axis.ticks.x = element_blank())

# separated by mileage 
select(prems, Premium, `Policy Year`, `Annual Mileage`)  %>%  ggplot(aes(group =`Policy Year`, y=Premium)) + geom_boxplot(aes(group=`Annual Mileage`), outlier.color = "lightblue", outlier.shape = 13) + facet_grid(. ~ `Annual Mileage`) + ggtitle("Premium Per Vehicle: Separated by Annual Mileage") + theme(axis.text.x = element_blank(), axis.ticks.x = element_blank())

In the following plots of average premiums and policyholder counts from 2013 through 2018, we see that average premiums are decreasing yearly in both single and married populations. From our data validation, we found that none of the customers in the database change between married and single in our experience period.

# marital status 
select(prems, Premium, `Policy Year`, `Marital Status`) %>% ggplot(aes(x = `Policy Year`)) + geom_bar( aes(fill=`Policy Year`), stat = "count") + facet_wrap(~`Marital Status`) + ggtitle("Policyholder Count (Frequency) by Marital Status") + theme(legend.position = "bottom")

select(prems, Premium, `Policy Year`, `Marital Status`) %>% ggplot(aes(x = `Policy Year`, y = `Premium`)) + geom_bar( aes(fill=`Policy Year`), stat = "summary", fun.y="mean") + facet_wrap(~`Marital Status`) + ggtitle("Average Premium Charged by Marital Status") + theme(legend.position= "bottom")

There is approximately a 50/50 split between single and married policyholders. We’ve established that no individual changes Marital Status through the experience period, as is also shown above. However, it is remarkable that the average premium is monotonically decreasing as years progress. Under the same rating system, with no changes to policies, we see that on average, policyholders are being charged cheaper rates. This is especially evident among single policyholders.

The Age Structure

Here are a few exhibits to understand the distribution about the driver age band. The plots below again show that the overall premium is decreasing each year, at least from the subset of policyholders in our data.

# driver age band

prems[, c("Premium", "Policy Year", "Driver Experience Band")] %>% ggplot(aes(x = `Policy Year`, y = `Premium`)) + geom_bar( aes(fill=`Driver Experience Band`), stat = "identity", position="stack") + ggtitle("Total Premium by Driver Experience Band") + theme(legend.position = "bottom")

prems[, c("Premium", "Policy Year", "Driver Experience Band")] %>% ggplot(aes(x = `Policy Year`, y = `Premium`)) + geom_bar( aes(fill=`Driver Experience Band`), stat = "identity", position="dodge") + ggtitle("Total Premium by Driver Experience Band") + theme(legend.position = "bottom")

prems[, c("Premium", "Policy Year", "Driver Experience Band")] %>% ggplot(aes(x = `Policy Year`, y = `Premium`)) + geom_bar( aes(fill=`Policy Year`), stat = "identity", show.legend = TRUE)  + facet_grid(. ~ `Driver Experience Band`)  + theme(legend.position = "bottom", axis.text.x = element_blank(), axis.ticks.x = element_blank()) + ggtitle("Total Premium by Driver Experience Band") + xlab("Policy Year")

There is very surprising total premium dropoff in driver experience years 4-8 (this is the band of ages 20-24). The plot for the 0-3 band makes sense because we follow a single cohort starting 2010, and only plot starts at 2013 (so there will only be one bar for 2013, and for future years, these individuals are in the next band). The above charts help us understand the proportions of total premiums, but we’ll also want to normalize across the population. We’ll break this down into the average premiums and policyholder count for each group.

To gain more insight on the premium structure and how it may correspond with the age structure and progression over time, we’ll break down into frequency (policyholder counts) and severity (premiums charged).

select(prems, Premium, `Policy Year`, `Driver Age Band`) %>% ggplot(aes(x = `Policy Year`)) + geom_bar( aes(fill=`Driver Age Band`), stat = "count", position="stack") + ggtitle("Frequency: Distribution of Policyholder Age")

select(prems, Premium, `Policy Year`, `Driver Age Band`) %>% ggplot(aes(x = `Policy Year`, y = `Premium`)) + geom_bar( aes(fill=`Driver Age Band`), stat = "summary", fun.y = "mean", position="stack") + ggtitle("Average Premium Charged by Driver Age Band")

These show the age-structure progressing each year; however, the plots are not illuminating. Instead of a stacked bar graph, let’s try position = "dodge".

select(prems, Premium, `Policy Year`, `Driver Age Band`) %>% ggplot(aes(x = `Policy Year`)) + geom_bar( aes(fill=`Driver Age Band`), stat = "count", position="dodge") + ggtitle("Distribution of Policyholder Driver Age")

select(prems, Premium, `Policy Year`, `Driver Age Band`) %>% ggplot(aes(x = `Policy Year`, y = `Premium`)) + geom_bar( aes(fill=`Driver Age Band`), stat = "summary", fun.y = "mean", position="dodge") + ggtitle("Average Premium Charged by Driver Age Band")

The above frequency plot directly shows the age structure shifting each year, and the average premium charged seems relatively stable (with the exception of the highest few age bands 80-89 and 90+).

select(prems, Premium, `Policy Year`, `Driver Age Band`) %>% ggplot(aes(x = `Policy Year`)) + geom_bar( aes(fill=`Driver Age Band`), stat = "count", show.legend = TRUE)  + facet_grid(. ~ `Driver Age Band`)  + theme(legend.position = "bottom", axis.text.x = element_blank(), axis.ticks.x = element_blank()) + ggtitle("Distribution of Driver Age Across Policy Years 2013-2018") + xlab("Policy Year (2013-2018)") + ylab("Average Premium Charged")

select(prems, Premium, `Policy Year`, `Driver Age Band`) %>% ggplot(aes(x = `Policy Year`, y = `Premium`)) + geom_bar( aes(fill=`Driver Age Band`), stat = "summary", fun.y = "mean", show.legend = TRUE)  + facet_grid(. ~ `Driver Age Band`)  + theme(legend.position = "bottom", axis.text.x = element_blank(), axis.ticks.x = element_blank()) + ggtitle("Average Premium Charged to Each Driver Age Band \nAcross Policy Years 2013-2018") + xlab("Policy Year (2013-2018)") + ylab("Average Premium Charged")

These plots show the direct comparisons within each age band. In terms of pricing and rating, these two plots may be the most informative (or at least the most intuitive to utilize).

The Independence Assumption: Reasons for Tweedie Modelling

Traditional models take the assumption that individual risks are independent. In our present case, we have multi-car policies that introduce a dependence, where marital status or multi-car policy may mitigate the collective risk among the policy’s assets. Further, we do not have information regarding the claims process, and we do not know if a policy year consolidates multiple claims in that given year.

Hence we will model the Pure Premium in our Generalized Linear Model. Before this, we may be interested in the historical premiums charged to the different levels of Multi-Car policies:

# policyholder distribution
select(prems, Premium, `Driver Experience Band`, `Multi-Car`) %>% ggplot(aes(x = `Driver Experience Band`)) + geom_bar( aes(fill=`Driver Experience Band`), stat = "count", show.legend = TRUE) + theme(legend.position = "bottom", axis.text.x = element_blank(), axis.ticks.x = element_blank())  + facet_grid(. ~ `Multi-Car`) + ggtitle("Distribution of Driver Experience\n (Separated by Multi-Car Policy)") + scale_y_continuous(trans='log10')

# average premium
# select(prems, Premium, `Driver Experience Band`, `Multi-Car`) %>% ggplot(aes(x = `Driver Experience Band`, y = `Premium`)) + geom_bar( aes(fill=`Driver Experience Band`), stat = "summary", fun.y = "mean", show.legend = TRUE) + theme(legend.position= "bottom", axis.text.x = element_blank(), axis.ticks.x = element_blank())  + facet_grid(. ~ `Multi-Car`) + ggtitle("Average Premium per Vehicle \n(Separated by Multi-Car Policy)")  

# distribution of policies across the annual mileage bands
  # select(prems, Premium, `Annual Mileage`, `Multi-Car`) %>% ggplot(aes(x = `Annual Mileage`)) + geom_bar( aes(fill=`Multi-Car`), stat = "count", show.legend = FALSE) + theme(axis.text.x = element_blank(), axis.ticks.x = element_blank())  + facet_grid(. ~ `Multi-Car`) + ggtitle("Vehicle Count by Multi-Car Policy") + scale_y_continuous(trans='log10') # not very informative


# better plot of average premium
select(prems, Premium, `Annual Mileage`, `Multi-Car`) %>% ggplot(aes(x = `Annual Mileage`, y = `Premium`)) + geom_bar( aes(fill=`Annual Mileage`), stat = "summary", fun.y = "mean", show.legend = TRUE) + theme(axis.text.x = element_blank(), axis.ticks.x = element_blank(), legend.position = "bottom")  + facet_grid(. ~ `Multi-Car`) + ggtitle("Average Premium Charged by Annual Mileage (Separated by Multi-Car Policy)")  # 4th has an odd trend

From these charts, it is clear that charged premiums are generally discounted for multi-car policies (in average after including other factors). There is an exception in the monotonicity of premium charged in Annual Mileage = 7500-10000, 10000-15000 and Multi-Car = 4.

Investigating Credit Score vs Charged Premiums

In California Private Passenger Automobile insurance, we do not use credit score for rating and underwriting considerations. However, this factor may still be of interest to us.

In particular, recall that we did not use Credit Score as a factor in our multiplicative rating algorithm. However, there is a clear monotonic trend where those with higher credit score pay lower premiums than do those with lower credit score.

This is very intriguing and calls for special investigation; however for this task we will not pursue this further, as we cannot use Credit Score as a part of our underwriting guidelines. If one were to seek after this, it would be wise to seek proxies for Credit Score via a combination of other variables.

prems$`Credit Score`<- factor(prems$`Credit Score`, levels = c("Low", "Medium","High")) # set plotting order


select(prems, Premium, `Policy Year`, `Credit Score`) %>% ggplot(aes(x = `Policy Year`, y = `Premium`)) + geom_bar( aes(fill=`Credit Score`), stat = "summary", fun.y = "mean", position="stack") + ggtitle("Average Premium by Credit Score")

select(prems, Premium, `Policy Year`, `Credit Score`) %>% ggplot(aes(x = `Policy Year`, y = `Premium`)) + geom_bar( aes(fill=`Credit Score`), stat = "summary", fun.y = "mean", position="dodge") + ggtitle("Average Premium by Credit Score")

select(prems, Premium, `Policy Year`, `Credit Score`) %>% ggplot(aes(x = `Policy Year`, y = `Premium`)) + geom_bar( aes(fill=`Policy Year`), stat = "summary", fun.y = "mean", show.legend = TRUE)  + facet_grid(. ~ `Credit Score`) + ggtitle("Average Premium by Credit Score") + theme(legend.position = "bottom", axis.text.x = element_blank())

It appears that historical premiums are well correlated with credit score (by comparing the graphs of different colors). Additionally, by aggregating by policy year, the average premium in each group has dropped.

3. Understanding the Reported Loss

Here we’ll have a better look into our data and form assumptions to help with modeling. While we are certainly interested in how we have historically charged policyholders and their resulting losses, our ratemaking algorithm and underwriting guidelines must be prospective. This is because customers are free to shop around for coverage, and an insurer’s intent to recoup past losses from particular individuals may be useless. The individual can simply switch to a competitor insurer that offers cheaper rates.

Let’s take a look at the distribution of claim severity. For an exhibit, we’ll look at our data for Policy Year 2013.

qloss <- select(tbl.cleaned, `Vehicle Number`, `Reported Losses PY2013`) 
pos.loss <- qloss$`Reported Losses PY2013` > 0

This first plot below shows the overall distribution of claim severity, where (as we expect) the bulk (91%) of policyholders file no claims. In fact, 95% of insureds have a reported loss of less than $1,000 in 2013. We call this distribution “zero-inflated,” as there is a very large amount of “zero-severity” claims (no claims filed).

qloss[pos.loss,] %>% ggplot(aes(x = `Reported Losses PY2013`)) + geom_histogram(bins = 15, fill = "lightblue", color = "lightyellow") + ggtitle("Distribution of Claims by Severity")

To have a better look at the tail, we scale the $x$-axis by log10(). This eliminates zero-severity claims from our plot (as $\log_{10} 0 = - \infty$), and groups higher severity claims together.

qloss[pos.loss,] %>% ggplot(aes(x = `Reported Losses PY2013`)) + geom_histogram(bins = 15, fill = "lightblue", color = "lightyellow") + scale_x_log10() + ggtitle("Distribution of Claims by Log Severity")

This appears like a typical loss distribution, where we can fit this histogram to a Gamma or Tweedie distribution.

We may want to cap the losses for our model if we expect that the few high severity claims will adversely affect our model.

For our predictive model, we must choose whether to model true reported losses or the incurred losses after adjusting to deductible and liability limits. Although it may appear beneficial to capture the underlying data via the raw, unadjusted reported losses, we must note that there is a substantial likelihood that policyholders with a high deductible do not report a small-cost claim, whether to avoid the hassle or to not adversely affect their record when there is no benefit or payout.

Now this leaves us to expect that there are some low-amount losses that are incurred but will not be reported. Because this is a natural (and often desired as it helps lower adjusting costs) mechanism of the deductible, we choose to model to adjusted loss data. This will naturally put a cap on the high reported losses, capped at the maximum liability limit for the policy.

Adjusting the Losses to Liability Limit Caps and Deductible Minimums

In our data cleaning, we notice that some filed premiums are high (above $4000), but many of these also incur high losses in our experience period. To evaluate claims by their impact on Cal Insurance’s finances, we want to normalize the losses by first applying the liability limits and deductibles.

n <- length(tbl$`Reported Losses`)

tmp <- matrix(data = NA, nrow = n )

# adjust the losses to deductible and liability limit
for (i in 1:n) {
 tmp[i] <-  max( min(tbl$`Liability Limit`[i], tbl$`Reported Losses`[i]) - tbl$`Physical Damage Deductible`[i], 0 ) 
  # take minimum of limit and the loss, and 
  # then take maximum of 0 and the difference to the deductible
}

# View(adj.loss)

loss <- tbl %>% mutate(`Adjusted Loss` = tmp) # append adjusted loss

loss  %>% ggplot(aes(x = `Adjusted Loss`)) + geom_histogram(bins = 15, fill = "lightblue", color = "lightyellow") + ggtitle("Log-Distribution of Nonzero Claims by Severity") + scale_y_log10()

loss  %>% ggplot(aes(x = `Adjusted Loss`)) + geom_histogram(bins = 15, fill = "lightblue", color = "lightyellow") + scale_x_log10()  + ggtitle("Distribution of Nonzero Claims by Log-Severity")

To gain some insight on the data after applying the deductible and liability limits, we’ll look at some distribution plots.

loss %>% ggplot(aes(x = `Credit Score`, y = `Adjusted Loss`)) + geom_bar(aes(fill = `Credit Score`), stat = "summary", fun.y = "mean", show.legend = TRUE) + theme(legend.position = "bottom", axis.text.x = element_blank(), axis.ticks = element_blank()) + ggtitle("Average Adjusted Loss by Credit Score and Marital Status") + facet_grid(. ~ `Marital Status`)

From this above plot, we see that Credit Score and Marital Status are indeed very strong indicators of expected loss. This validates the significantly lower premiums charged to married policyholders with high credit scores.

Let’s take a look at the average adjusted loss for Annual Mileage and Driver Experience Band, two variables that are heavily influenced by sequential analysis in compliance with California’s Proposition 103.

loss %>% ggplot(aes(x = `Annual Mileage`, y = `Adjusted Loss`)) + geom_bar(aes(fill = `Annual Mileage`), stat = "summary", fun.y = "mean", show.legend = TRUE) + theme(legend.position = "bottom", axis.text.x = element_blank()) + ggtitle("Average Adjusted Loss", subtitle = "by Annual Mileage and Marital Status") + facet_grid(. ~ `Marital Status`)

loss %>% ggplot(aes(x = `Driver Experience Band`, y = `Adjusted Loss`)) + geom_bar(aes(fill = `Driver Experience Band`), stat = "summary", fun.y = "mean", show.legend = TRUE) + theme(legend.position = "bottom", axis.text.x = element_blank(), axis.ticks = element_blank()) + ggtitle("Average Adjusted Loss by Driver Experience Band and Territory") + facet_grid(. ~ `Territory`)

# loss %>% ggplot(aes(x = `Territory`, y = `Adjusted Loss`)) + geom_bar(aes(fill = `Territory`), stat = "identity", show.legend = TRUE) + facet_grid(. ~ `Marital Status`) + theme(legend.position = "bottom")  + ggtitle("Total loss by Territory and Marital Status") 

loss %>% ggplot(aes(x = `Territory`, y = `Adjusted Loss`)) + geom_bar(aes(fill = `Territory`), stat = "summary", fun.y = "mean", show.legend = TRUE) + facet_grid(. ~ `Marital Status`) + theme(legend.position = "bottom", axis.text.x = element_blank())  + ggtitle("Average Loss by Territory and Marital Status")

The total and average losses by aggregating by Marital Status and Territory appears to be very similar. We can check the counts and see that they are very closely uniform across the territories:

loss %>% ggplot(aes(x = `Territory`)) + geom_bar(aes(fill = `Territory`), stat = "count", show.legend = FALSE) + facet_grid(. ~ `Marital Status`) + theme(legend.position = "bottom")  + ggtitle("Distribution of Policyholders by Territory and Marital Status")

loss %>% ggplot(aes(x = `Policy Year`, y = `Adjusted Loss`)) + geom_bar(aes(fill = `Policy Year`), stat = "summary", fun.y = "mean", show.legend = TRUE) + facet_grid(. ~ `Marital Status`) + theme(legend.position = "bottom", axis.text.x = element_blank())  + ggtitle("Average loss by Policy Year, Comparing Marital Status")

Without specific data on the loss-related expenses, we take the simplifying assumption that loss related expenses are 20% of the adjusted loss. That is, we assume \[ \begin{align*} \text{Pure Premium} &= \text{Losses} + \text{Loss Related Expenses} \\ &= 1.20 \times \text{Losses}. \end{align*}\] We verify that this assumption is asymptotically sound in that low-severity claims under the deductible have no loss related expenses, while large severity claims may involve attorney fees that scale with the size of the claim. Because we are training on the years 2013-2015, we assume that there has been sufficient time (3~6 years) for losses to develop to ultimate.

# loss %>% ggplot(aes(x = `Driver Experience Band`, y = `Adjusted Loss`)) + geom_histogram(aes(fill = `Driver Experience Band`), stat = "summary", fun.y = "mean", show.legend = TRUE) + facet_grid(. ~ `Marital Status`) + theme(legend.position = "bottom", axis.text.x = element_blank())  + ggtitle("Average loss by Policy Year and Marital Status")


loss <- loss %>% mutate(`Pure Premium` = 1.20 * `Adjusted Loss`)
  
df.loss <- filter(loss, `Policy Year` >= 2013, `Policy Year` <= 2015 ) %>% select(`Policy Number`, `Vehicle Number`,  `Pure Premium`, `Conviction Points (CP) last 3 years`, `Accident Points (AP) last 3 years`, `Annual Mileage`, `Driver Experience Band`, `Marital Status`,   `Territory`, `Driver Age`, `Credit Score`, `Late Fees`, `Liability Limit` ) # bring credit score for cross-validation of proxy later


df.loss[1:100,] %>% qkable()

Policy Number	Vehicle Number	Pure Premium	Conviction Points (CP) last 3 years	Accident Points (AP) last 3 years	Annual Mileage	Driver Experience Band	Marital Status	Territory	Driver Age	Credit Score	Late Fees	Liability Limit
1	6125	120.0830	1	1	0-7500	4-8	Single	4	21	High	0	5e+04
1	10332	0.0000	0	0	7500-10000	24-33	Married	3	48	High	0	5e+05
2	1965	0.0000	0	0	15000+	34-43	Married	1	57	Medium	0	1e+05
2	14130	0.0000	0	0	10000-15000	34-43	Married	1	52	High	0	1e+05
3	2976	0.0000	0	0	7500-10000	14-23	Single	4	34	High	0	5e+04
4	76	0.0000	0	0	15000+	34-43	Married	2	56	High	0	5e+04
5	8571	11546.1106	1	1	0-7500	4-8	Single	3	24	Low	0	1e+05
6	8530	34023.1125	1	1	7500-10000	14-23	Single	2	31	High	1	5e+04
7	6104	0.0000	0	0	0-7500	14-23	Single	1	36	High	0	5e+04
7	12468	0.0000	2	0	0-7500	14-23	Single	2	30	High	0	1e+05
8	1547	0.0000	0	0	0-7500	34-43	Married	4	55	Low	0	5e+05
9	736	0.0000	0	0	10000-15000	34-43	Married	4	52	Medium	0	1e+05
9	12236	0.0000	0	0	0-7500	34-43	Single	4	53	Medium	0	5e+04
9	14398	0.0000	0	0	0-7500	34-43	Single	3	50	Medium	0	5e+04
10	6386	7659.8968	0	3	7500-10000	0-3	Single	2	19	Low	0	5e+04
11	5284	0.0000	1	0	7500-10000	14-23	Married	3	30	High	0	1e+05
12	999	0.0000	0	0	10000-15000	44-53	Married	3	68	Medium	0	1e+05
13	1553	0.0000	0	0	15000+	24-33	Single	2	40	High	0	3e+05
14	8480	0.0000	0	0	7500-10000	4-8	Single	3	23	High	0	5e+04
14	10430	0.0000	1	0	10000-15000	34-43	Single	2	54	High	0	1e+05
15	5609	0.0000	2	0	7500-10000	34-43	Married	4	52	Low	0	5e+05
16	5679	0.0000	0	0	10000-15000	14-23	Single	1	31	High	0	3e+05
16	14610	122.8126	0	1	7500-10000	34-43	Married	1	51	High	0	5e+05
17	3462	0.0000	0	0	0-7500	34-43	Single	1	54	High	3	3e+05
17	12553	63413.4231	0	1	10000-15000	14-23	Single	2	37	Low	0	1e+05
18	5397	0.0000	0	0	15000+	34-43	Married	1	54	High	2	3e+05
19	2344	0.0000	0	0	0-7500	24-33	Single	3	41	High	0	3e+05
20	8792	0.0000	1	0	0-7500	14-23	Single	4	36	Medium	0	5e+05
21	4380	0.0000	0	0	10000-15000	9-13	Single	1	27	Medium	0	3e+05
21	12703	120.0024	0	1	10000-15000	4-8	Single	3	24	Low	0	5e+04
22	9614	0.0000	1	0	7500-10000	24-33	Single	3	41	High	0	3e+05
23	7817	0.0000	0	0	7500-10000	14-23	Single	3	34	Low	0	5e+05
24	4802	0.0000	0	0	10000-15000	24-33	Single	1	41	Low	0	1e+05
24	11025	0.0000	0	0	7500-10000	44-53	Married	4	67	High	0	3e+05
25	2795	0.0000	0	0	10000-15000	9-13	Single	4	27	Low	1	1e+05
25	11584	0.0000	1	0	0-7500	4-8	Single	1	22	Low	0	1e+05
26	2611	0.0000	0	0	10000-15000	14-23	Single	3	31	Low	0	5e+04
27	6005	0.0000	1	0	0-7500	14-23	Single	4	31	Low	0	5e+04
28	3107	0.0000	0	0	0-7500	9-13	Single	4	27	High	0	1e+05
28	10304	0.0000	0	0	15000+	14-23	Married	3	39	High	0	5e+04
28	11879	0.0000	1	0	7500-10000	44-53	Married	1	67	High	0	5e+04
29	9910	0.0000	0	0	10000-15000	34-43	Single	4	54	Low	0	5e+04
30	5177	0.0000	0	1	0-7500	9-13	Single	2	29	Low	0	5e+04
30	14568	0.0000	0	0	15000+	34-43	Married	4	59	High	0	1e+05
31	9230	0.0000	0	0	15000+	4-8	Single	2	22	High	0	3e+05
32	1665	0.0000	1	0	15000+	9-13	Single	3	29	Medium	0	1e+05
33	4652	0.0000	1	0	15000+	34-43	Single	2	51	High	0	5e+04
34	3222	0.0000	0	0	0-7500	24-33	Married	4	41	High	0	5e+04
34	10923	0.0000	2	0	0-7500	34-43	Single	3	52	Medium	0	1e+05
34	12380	0.0000	0	0	0-7500	9-13	Single	2	25	Medium	0	1e+05
34	13859	0.0000	1	0	10000-15000	44-53	Married	2	68	High	0	1e+05
35	9666	0.0000	1	0	7500-10000	24-33	Married	4	47	High	0	1e+05
36	6180	0.0000	1	0	0-7500	64-73	Married	4	85	High	0	5e+05
37	6273	0.0000	2	0	0-7500	44-53	Married	1	69	Medium	0	1e+05
37	11273	0.0000	0	0	15000+	44-53	Married	2	65	Medium	0	5e+05
38	7200	0.0000	0	0	15000+	4-8	Single	2	22	High	0	5e+04
39	1753	0.0000	1	1	7500-10000	9-13	Single	1	26	Low	0	1e+05
40	4931	0.0000	1	0	7500-10000	34-43	Single	2	56	Medium	0	1e+05
41	2560	0.0000	0	0	10000-15000	9-13	Single	2	25	High	0	3e+05
42	644	1331.1593	3	1	7500-10000	44-53	Married	1	63	Low	0	5e+04
43	2991	0.0000	1	1	7500-10000	14-23	Single	4	30	High	0	1e+05
44	9914	0.0000	0	0	0-7500	9-13	Single	3	27	High	0	5e+04
44	12279	0.0000	0	0	7500-10000	24-33	Married	2	47	Medium	0	1e+05
45	7013	0.0000	0	0	10000-15000	24-33	Married	1	43	Medium	0	3e+05
45	10173	458.2196	0	1	0-7500	9-13	Single	1	28	High	0	5e+04
45	10767	0.0000	1	0	0-7500	44-53	Married	2	65	High	0	5e+04
46	4662	0.0000	0	0	15000+	24-33	Married	2	43	High	0	5e+04
46	11794	0.0000	0	1	0-7500	34-43	Married	2	56	Low	0	5e+05
46	12190	0.0000	0	0	15000+	44-53	Married	2	67	High	1	3e+05
47	9509	0.0000	0	0	0-7500	54-63	Married	4	71	High	0	5e+04
47	10134	0.0000	0	0	15000+	24-33	Married	4	40	Medium	1	3e+05
48	9985	0.0000	1	0	15000+	24-33	Married	2	43	Medium	0	3e+05
48	11131	0.0000	1	0	7500-10000	24-33	Married	4	41	Medium	0	1e+05
48	11320	0.0000	0	0	15000+	34-43	Married	3	59	High	0	3e+05
48	14055	0.0000	1	0	10000-15000	24-33	Married	1	47	High	0	1e+05
49	7219	0.0000	0	0	0-7500	14-23	Married	1	36	High	0	5e+05
50	6263	0.0000	0	0	0-7500	24-33	Married	1	42	High	0	1e+05
50	13926	1869.7136	0	1	0-7500	14-23	Single	2	38	High	0	3e+05
51	7260	0.0000	0	0	15000+	44-53	Married	2	67	Medium	0	3e+05
52	6243	0.0000	1	0	7500-10000	14-23	Single	2	31	Medium	0	5e+05
53	7866	0.0000	1	0	0-7500	14-23	Single	1	33	High	0	5e+04
53	11892	0.0000	0	0	0-7500	24-33	Single	2	40	Low	0	5e+05
54	7	0.0000	0	1	15000+	4-8	Single	3	24	High	0	3e+05
55	3650	0.0000	0	0	0-7500	4-8	Single	2	21	Low	0	1e+05
56	6369	0.0000	0	0	10000-15000	44-53	Married	1	69	High	0	5e+05
57	9857	0.0000	1	0	10000-15000	44-53	Married	3	67	Medium	0	5e+05
58	395	0.0000	0	0	10000-15000	34-43	Married	2	56	Low	0	5e+05
59	5637	0.0000	0	0	10000-15000	14-23	Married	3	39	Medium	0	3e+05
59	12228	0.0000	1	0	15000+	4-8	Single	4	21	Low	0	3e+05
59	14572	0.0000	0	1	7500-10000	34-43	Married	3	51	Medium	0	3e+05
60	5079	0.0000	0	0	0-7500	44-53	Married	3	62	High	0	3e+05
61	6131	0.0000	0	1	15000+	24-33	Married	4	44	High	0	5e+04
62	8742	0.0000	0	1	0-7500	9-13	Single	3	27	High	0	5e+04
62	12257	0.0000	0	0	0-7500	34-43	Single	1	52	High	1	5e+05
62	14614	0.0000	0	0	10000-15000	44-53	Married	2	67	Low	0	5e+04
63	9104	0.0000	1	0	7500-10000	24-33	Married	2	40	High	0	5e+04
63	14213	0.0000	0	0	7500-10000	24-33	Single	3	42	Low	1	3e+05
64	7515	0.0000	0	0	7500-10000	24-33	Married	2	42	High	0	1e+05
64	10697	0.0000	0	0	0-7500	9-13	Single	3	25	Medium	0	5e+05
65	4023	0.0000	0	0	15000+	14-23	Single	1	38	Medium	0	3e+05

As we generally expect, the average loss (severity) is highest for inexperienced and over-experienced drivers (where old age effects come into account). Interestingly, the old age single drivers and young married drivers tend to not have high losses.

df.loss %>%
  ggplot(aes(x = `Accident Points (AP) last 3 years`, y = `Pure Premium`)) + geom_bar(aes(fill = `Conviction Points (CP) last 3 years` ), stat = "summary", fun.y = "mean", show.legend = TRUE)  + facet_grid(. ~ `Conviction Points (CP) last 3 years`, labeller = label_parsed) + theme(legend.position = "bottom") + ggtitle("Average Pure Premium by 3-Year AP and CP")

filter(df.loss, `Accident Points (AP) last 3 years` == 1, `Conviction Points (CP) last 3 years` == 3) %>% qkable(height = "240px")

Policy Number	Vehicle Number	Pure Premium	Conviction Points (CP) last 3 years	Accident Points (AP) last 3 years	Annual Mileage	Driver Experience Band	Marital Status	Territory	Driver Age	Credit Score	Liability Limit
42	644	1331.159	3	1	7500-10000	44-53	Married	1	63	Low	5e+04
795	11667	0.000	3	1	15000+	34-43	Married	1	57	Medium	5e+05
968	11412	46363.502	3	1	10000-15000	34-43	Married	2	52	Medium	5e+05
1462	6432	11873.345	3	1	10000-15000	34-43	Single	2	54	High	1e+05
2138	14961	66620.400	3	1	10000-15000	4-8	Single	2	23	Medium	3e+05
6411	4113	78368.346	3	1	7500-10000	24-33	Single	3	41	Medium	3e+05
6411	4113	0.000	3	1	7500-10000	24-33	Single	3	42	Medium	3e+05
6471	5023	6269.003	3	1	7500-10000	34-43	Married	2	58	High	1e+05

Very oddly, in the 2015 data above, we see an anomaly. The combination of 3 conviction points in the last 3 years and precisely 1 accident in the last 3 years appears to have a high average loss severity (and pure premium). Although this is only a sample of 6, this may be an indication to reject this category of drivers with these specifications.

4. Building the Predictive Model

“Unfortunately, Cal Insurance’s pricing model was already filed with the Department of Insurance and cannot be changed for another two years.”

Although this is unfortunate, this affords us with two years to research and develop models to inform a better set of underwriting guidelines.

We will use a Generalized Linear Model (GLM) with target variable Pure Premium (dollars of loss per exposure) for pricing, where exposure is per vehicle insured.

For a response variable $y$, our generalized linear model is given by

\[\begin{align*} f(y) = c(y, \phi) e^{\left( \frac{y \theta - a (\theta) }{\phi} \right)} , \quad g(\mu) = x' \beta, \end{align*}\] where the second equation is the generalization of the linear model. We take our link $g(\mu)$ to be $\log$ to align with our desired multiplicative rating system. Then by considering the average count $\mu/n$, we have \[ \begin{align*} \log\left( \frac{\mu}{n} \right) = x' \beta \implies \log \mu = \log n + x' \beta \implies \mu = n e^{x' \beta}. \end{align*}\] where $\log n$ is our offset.

Now the Maximum Likelihood Estimate (MLE) of $\beta$ and $\phi$ are solved numerically (computationally as opposed to analytically) via iterative methods and a non-positive definite Hessian matrix to indicate the maximum.

As mentioned earlier in this document,

“Traditional models take the assumption that individual risks are independent. In our present case, we have multi-car policies that introduce a dependence, where marital status or multi-car policy may mitigate the collective risk among the policy’s assets. Further, we do not have information regarding the claims process, and we do not know if a policy year consolidates multiple claims in that given year.”

To not assume that frequency and severity are independent, we use a Tweedie distribution. Recall that a Poisson$(\lambda)$ and Gamma($\alpha, \theta$) distribution has expected values $\lambda$ and $\alpha \dot \theta$ respectively. Correspondingly, Tweedie distribution has expected value \[ \mu = \lambda \cdot \alpha \cdot \theta, \] where $\lambda$ is the expected frequency (modeled via Poisson) and $\alpha \theta$ is the expected severity (modeled via Gamma). Hence we think of the Tweedie distribution as a Poisson sum (number of) Gamma-severity claims. The power $p$ is given by \[ p = \frac{\alpha + 2}{\alpha + 1}, \] and the Tweedie dispersion parameter $\phi$ is given by \[ \phi = \frac{\lambda^{1 - p} (\alpha \theta )^{2 - p}}{2 - p}. \] We have special cases of the normal distribution $(p = 0)$, the Poisson distribution $(p = 1, \phi = 1)$, the Gamma distribution $(p=2)$, and the inverse Gaussian $(p = 3)$.

# X <- select(loss, `Driver Age`, `Marital Status`)

pp <- df.loss$`Pure Premium` # response variable; 

x.conviction <- df.loss$`Conviction Points (CP) last 3 years`
x.mileage <- df.loss$`Annual Mileage`
x.experience <- df.loss$`Driver Experience Band`
x.accident <- df.loss$`Accident Points (AP) last 3 years`
x.marital <- df.loss$`Marital Status`
x.territory <- df.loss$Territory

Selecting $p$-value for Tweedie via Gamma Fitting

# determine p from gamma glm, given by Glenn Meyers 
# https://dsury.com/tweedie-distribution-on-the-generalized-linear-model/
posi <- pp > 0
glm.sev <- glm(pp[posi] ~ x.conviction[posi] + x.mileage[posi] + x.experience[posi] + x.accident[posi] + x.marital[posi] + x.territory[posi], 
               family = Gamma(link="log"))
tmp <- summary(glm.sev)
phi.sev <- tmp$dispersion
alpha1 <- 1 / phi.sev 
p.hat <- (2 + alpha1) / (1 + alpha1) 
print(paste0("The p-value given by Gamma fitting is:  ",p.hat))

## [1] "The p-value given by Gamma fitting is:  1.7894905804437"

Compute negative log-likelihood

Using the Gamma-fitted GLM parameters, we initialize a log-linked tweedie GLM fit with the same $\hat p$ parameter.

x.vec <- c(x.conviction, x.mileage, x.experience, x.accident, x.marital, x.territory) 

# initial fit using p.hat = 1.7916
glm.init <- glm(pp ~ x.conviction + x.mileage + x.experience + x.accident + x.marital + x.territory, family = tweedie(var.power = p.hat, link.power = 0)) # 0 for log-link

We would like to fine-tune the $p$ parameter and we do this using the tglm function, with output suppressed as it normally prints pages of iterations.

# use as start into tglm
glm.fisher <- tglm(pp ~ x.conviction + x.mileage + x.experience + x.accident + x.marital + x.territory, data = df.loss, inits = glm.init$coefficients)

Here we’ll use the value of $p$ from our last result to drive our glm. We use the coefficients from glm.init$coefficients to start the iterative optimization process. The details for the Tweedie GLM fit are given by summary(glm.tweedie) below.

# glm with tweedie family, using p from last result
# p <- glm.fisher$coef[["p"]]
glm.tweedie <- glm(formula = pp ~ x.conviction + x.mileage + x.experience + x.accident + x.marital + x.territory, family = tweedie(var.power = p.hat, link.power = 0), start = glm.init$coefficients, data = df.loss)

summary(glm.tweedie)

## 
## Call:
## glm(formula = pp ~ x.conviction + x.mileage + x.experience + 
##     x.accident + x.marital + x.territory, family = tweedie(var.power = p.hat, 
##     link.power = 0), data = df.loss, start = glm.init$coefficients)
## 
## Deviance Residuals: 
##    Min      1Q  Median      3Q     Max  
## -8.915  -0.069  -0.069  -0.069  32.651  
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     -2.29287    0.24540  -9.343  < 2e-16 ***
## x.conviction.L   0.71134    0.28402   2.504  0.01227 *  
## x.conviction.Q   0.40416    0.21764   1.857  0.06332 .  
## x.conviction.C   0.09275    0.11873   0.781  0.43472    
## x.mileage.L      0.06565    0.03266   2.010  0.04443 *  
## x.mileage.Q      0.02614    0.03190   0.819  0.41254    
## x.mileage.C     -0.05908    0.03127  -1.889  0.05884 .  
## x.experience.L  -0.15900    0.27703  -0.574  0.56601    
## x.experience.Q  -0.06377    0.26988  -0.236  0.81320    
## x.experience.C  -0.74950    0.24005  -3.122  0.00180 ** 
## x.experience^4  -0.25593    0.19409  -1.319  0.18730    
## x.experience^5  -0.47085    0.14853  -3.170  0.00153 ** 
## x.experience^6  -0.74376    0.11560  -6.434 1.25e-10 ***
## x.experience^7  -0.46117    0.09189  -5.019 5.22e-07 ***
## x.experience^8  -0.20726    0.06825  -3.037  0.00239 ** 
## x.experience^9  -0.15517    0.05114  -3.034  0.00241 ** 
## x.accident.L    32.05088    0.56879  56.349  < 2e-16 ***
## x.accident.Q   -23.59221    0.42401 -55.640  < 2e-16 ***
## x.accident.C    10.39852    0.19138  54.333  < 2e-16 ***
## x.marital.L     -0.18222    0.04278  -4.260 2.05e-05 ***
## x.territory2    -0.04984    0.04165  -1.197  0.23148    
## x.territory3    -0.04758    0.04402  -1.081  0.27973    
## x.territory4    -0.14142    0.04563  -3.099  0.00194 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for Tweedie family taken to be 13.35685)
## 
##     Null deviance: 2293547  on 44999  degrees of freedom
## Residual deviance:  386865  on 44977  degrees of freedom
## AIC: NA
## 
## Number of Fisher Scoring iterations: 11

print(paste("The AIC with this Tweedie fit is: ", AICtweedie(glm.tweedie))) # aic in glm is unsupported for tweedie, so use this value

## [1] "The AIC with this Tweedie fit is:  113072.018195223"

# confint(glm.tweedie) # run if confidence interval is desired; this is cpu and time-intensive

print(paste("The Log-Likelihood is: ",logLiktweedie(glm.tweedie)))

## [1] "The Log-Likelihood is:  -56512.0090976116"

We’d like to compare the observed and predicted pure premiums.

pp.hat <- predict(glm.tweedie, type="response")

# compare pure premiums
compare.pp <- df.loss %>% mutate(`Predicted Pure Premium` =  floor(pp.hat) ) 
compare.pp <- compare.pp %>% select(1:3, 14, 4:13)

We can take a look at two sides of the model: (1) the individuals who have higher Pure Premiums than predicted (we want to consider these for rejection via UW guidelines) and (2) those who incur less loss (at least in experience) than predicted. We show these below.

compare.pp %>% filter(`Pure Premium` > `Predicted Pure Premium`) %>% slice(1:40) %>% qkable() # type 1: higher observed than predicted

Policy Number	Vehicle Number	Pure Premium	Predicted Pure Premium	Conviction Points (CP) last 3 years	Accident Points (AP) last 3 years	Annual Mileage	Driver Experience Band	Marital Status	Territory	Driver Age	Credit Score	Late Fees	Liability Limit
5	8571	11546.111	8911	1	1	0-7500	4-8	Single	3	24	Low	0	1e+05
6	8530	34023.112	6311	1	1	7500-10000	14-23	Single	2	31	High	1	5e+04
17	12553	63413.423	7057	0	1	10000-15000	14-23	Single	2	37	Low	0	1e+05
71	6110	45661.666	10682	0	2	15000+	9-13	Single	2	27	Low	0	5e+05
73	10790	24235.851	6845	1	1	0-7500	9-13	Single	3	26	Low	0	3e+05
100	4979	30921.584	10707	0	2	15000+	9-13	Single	3	27	Low	0	5e+04
126	10770	36485.179	6519	0	1	7500-10000	9-13	Single	2	28	Medium	0	5e+05
138	9746	119880.000	9924	0	1	15000+	24-33	Single	2	40	High	0	1e+05
144	10613	167697.445	15197	1	3	15000+	4-8	Single	1	24	Low	0	3e+05
155	6927	61615.862	8655	0	1	15000+	4-8	Single	4	22	Medium	0	5e+05
222	7400	13467.457	9351	0	1	0-7500	24-33	Single	3	40	Low	0	1e+05
222	12590	59700.000	14333	0	3	0-7500	4-8	Single	1	20	Low	1	5e+04
253	3009	195796.493	9485	0	1	15000+	4-8	Single	2	23	Low	0	3e+05
342	11869	102554.379	7669	0	1	15000+	24-33	Married	2	48	High	1	5e+05
359	12495	29606.490	13667	0	3	0-7500	4-8	Single	3	23	Low	0	5e+05
366	11846	150178.152	9374	0	1	0-7500	4-8	Single	1	23	Low	0	3e+05
391	2093	9763.145	6439	0	1	10000-15000	14-23	Single	4	33	Low	0	1e+05
429	11233	36016.321	5949	0	1	7500-10000	9-13	Single	4	29	Medium	0	5e+05
459	3839	119880.000	12442	0	3	0-7500	4-8	Single	4	24	Low	0	1e+05
466	6452	15951.110	14503	0	3	15000+	4-8	Single	2	22	Low	0	5e+04
484	10925	40784.553	8460	1	1	7500-10000	4-8	Single	2	24	Low	1	5e+05
542	385	81434.919	9332	0	1	7500-10000	24-33	Single	1	45	High	0	5e+05
569	1682	102256.288	7054	1	1	15000+	14-23	Single	2	37	Low	0	1e+05
569	11376	135318.705	6534	0	1	7500-10000	9-13	Single	3	26	High	1	3e+05
579	9501	7942.275	4937	0	1	0-7500	54-63	Married	2	70	Medium	0	5e+05
591	6143	10921.049	7076	0	1	15000+	14-23	Single	2	37	High	0	1e+05
630	2661	79833.405	8486	0	1	7500-10000	4-8	Single	2	22	Medium	0	5e+05
632	266	119700.000	19067	0	2	10000-15000	0-3	Single	3	19	High	3	1e+05
638	12439	56539.803	11679	0	2	7500-10000	34-43	Married	1	53	High	0	5e+04
653	11742	9970.465	6251	0	1	0-7500	9-13	Single	4	27	Medium	0	3e+05
661	10676	44546.224	7869	0	1	0-7500	44-53	Married	3	65	Medium	0	5e+04
679	4235	26765.813	13681	0	2	7500-10000	24-33	Single	1	49	Low	1	1e+05
685	2454	27305.808	8302	1	1	10000-15000	44-53	Married	2	61	Medium	3	5e+04
719	5937	21149.783	19997	0	2	10000-15000	0-3	Single	1	19	Medium	0	5e+04
793	6776	198037.554	6534	0	1	7500-10000	9-13	Single	3	29	Low	0	3e+05
806	3380	59880.000	19879	1	3	15000+	0-3	Single	3	19	Low	0	5e+04
856	8207	36108.439	6877	0	1	7500-10000	24-33	Married	3	48	High	2	3e+05
881	1686	15909.689	10397	0	2	15000+	14-23	Single	3	30	High	0	1e+05
883	11809	20614.581	8655	0	1	15000+	4-8	Single	4	21	Low	0	5e+04
898	10744	5508.839	4892	0	1	7500-10000	14-23	Married	2	37	High	0	3e+05

compare.pp %>% filter(`Pure Premium` < `Predicted Pure Premium`, `Pure Premium` > 0) %>% slice(1:40) %>% qkable() # type 2 : lower observed than predicted

Policy Number	Vehicle Number	Pure Premium	Predicted Pure Premium	Conviction Points (CP) last 3 years	Accident Points (AP) last 3 years	Annual Mileage	Driver Experience Band	Marital Status	Territory	Driver Age	Credit Score	Late Fees	Liability Limit
1	6125	120.083050	8112	1	1	0-7500	4-8	Single	4	21	High	0	5e+04
10	6386	7659.896762	17800	0	3	7500-10000	0-3	Single	2	19	Low	0	5e+04
16	14610	122.812605	7966	0	1	7500-10000	34-43	Married	1	51	High	0	5e+05
21	12703	120.002350	9481	0	1	10000-15000	4-8	Single	3	24	Low	0	5e+04
42	644	1331.159272	21258	3	1	7500-10000	44-53	Married	1	63	Low	0	5e+04
45	10173	458.219589	7201	0	1	0-7500	9-13	Single	1	28	High	0	5e+04
50	13926	1869.713603	6653	0	1	0-7500	14-23	Single	2	38	High	0	3e+05
67	14663	4721.120736	12404	1	3	0-7500	4-8	Single	4	23	Low	0	5e+04
72	4694	3238.283113	11111	0	2	7500-10000	34-43	Married	2	50	Medium	0	5e+04
134	10731	170.466932	8879	0	1	7500-10000	24-33	Single	2	41	Low	0	5e+04
160	5309	5059.700585	13868	0	2	10000-15000	4-8	Single	2	20	Medium	1	1e+05
160	11547	9556.861052	13639	0	3	7500-10000	4-8	Single	1	23	Low	0	1e+05
170	1998	77.453846	14571	1	2	15000+	4-8	Single	1	23	Medium	0	3e+05
185	176	65.444578	8252	0	1	0-7500	44-53	Married	1	65	Low	0	5e+04
188	8759	124.945101	6439	0	1	10000-15000	14-23	Single	4	37	Medium	0	3e+05
227	13876	2374.628316	5949	0	1	7500-10000	9-13	Single	4	26	High	0	1e+05
228	9054	1554.679772	12688	0	2	15000+	4-8	Single	4	21	Low	0	5e+05
229	9047	236.542783	6851	0	1	0-7500	9-13	Single	2	27	Medium	0	3e+05
239	11550	236.838725	7212	0	1	7500-10000	24-33	Married	1	45	High	0	5e+04
242	4193	7927.919848	8347	0	1	10000-15000	44-53	Married	3	68	High	0	5e+04
245	12361	93.473388	8372	0	1	0-7500	34-43	Married	1	59	Medium	0	3e+05
255	12575	195.377965	17066	0	2	7500-10000	0-3	Single	2	19	Low	0	5e+04
263	11482	121.608025	10364	1	2	15000+	14-23	Single	3	33	High	1	1e+05
284	250	156.448694	8891	1	1	0-7500	4-8	Single	2	21	Low	0	1e+05
287	8863	2045.819190	7659	0	1	15000+	9-13	Single	1	27	Medium	0	3e+05
295	7144	182.375381	9943	0	1	10000-15000	4-8	Single	1	21	Low	0	3e+05
296	6859	2929.094250	6853	0	1	7500-10000	9-13	Single	1	25	High	0	1e+05
322	2562	127.074275	15112	0	2	7500-10000	34-43	Single	1	53	Low	1	5e+04
362	8086	1162.610422	8605	1	1	10000-15000	4-8	Single	4	23	High	0	1e+05
370	7186	120.379670	11107	1	3	15000+	9-13	Single	2	29	Low	0	5e+04
379	4132	4.918854	10046	0	2	7500-10000	9-13	Single	1	26	Low	0	1e+05
383	7407	58.551625	8853	1	1	10000-15000	34-43	Married	1	56	High	0	3e+05
388	12099	69.613962	11930	0	2	0-7500	4-8	Single	4	24	Medium	0	1e+05
413	14921	1415.149733	8754	0	1	10000-15000	44-53	Married	1	65	High	0	3e+05
422	432	174.921748	8347	0	1	10000-15000	44-53	Married	3	63	Medium	0	5e+04
425	2623	654.456802	13639	0	3	7500-10000	4-8	Single	1	21	Low	2	1e+05
427	14101	11064.581506	14532	1	2	10000-15000	4-8	Single	1	24	Medium	0	5e+04
458	8477	1800.937360	9970	0	1	15000+	4-8	Single	1	20	Low	0	5e+04
463	1179	6975.193925	9507	0	1	15000+	4-8	Single	3	22	Low	0	1e+05
476	4442	6376.173124	7659	0	1	15000+	9-13	Single	1	26	High	0	5e+04

We can see that some rows (individuals) are fit quite closely by our model, whereas some are quite a way off. Perhaps we can get a better fit by capping high severity claims at $100,000. Then predictions of high severities should be interpreted as possibly higher severity.

Re-constructing the Model with Capped Severity

pp.capped <- df.loss[["Pure Premium"]]
tmp <- pp.capped > 100000
pp.capped[tmp] <- 100000 # assign cap of $100,000 in PP

df.loss <- df.loss %>% mutate(`PP Capped` =  pp.capped) 
# %>% select(1:2, 11, 3:10)


# glm tweedie capped (glm tw c)
glm.tw.c <- glm(formula = pp.capped ~ x.conviction + x.mileage + x.experience + x.accident + x.marital + x.territory, family = tweedie(var.power = p.hat, link.power = 0), start = glm.init$coefficients, data = df.loss)
summary(glm.tw.c)

## 
## Call:
## glm(formula = pp.capped ~ x.conviction + x.mileage + x.experience + 
##     x.accident + x.marital + x.territory, family = tweedie(var.power = p.hat, 
##     link.power = 0), data = df.loss, start = glm.init$coefficients)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -8.9497  -0.0694  -0.0694  -0.0694  14.9911  
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     -2.34197    0.19260 -12.160  < 2e-16 ***
## x.conviction.L   0.83367    0.22252   3.746 0.000180 ***
## x.conviction.Q   0.49735    0.17073   2.913 0.003580 ** 
## x.conviction.C   0.22521    0.09381   2.401 0.016369 *  
## x.mileage.L      0.03690    0.02603   1.418 0.156295    
## x.mileage.Q      0.03138    0.02542   1.234 0.217170    
## x.mileage.C     -0.09932    0.02493  -3.983  6.8e-05 ***
## x.experience.L  -0.26469    0.21897  -1.209 0.226748    
## x.experience.Q  -0.12543    0.21235  -0.591 0.554738    
## x.experience.C  -0.58121    0.18888  -3.077 0.002092 ** 
## x.experience^4  -0.07659    0.15416  -0.497 0.619323    
## x.experience^5  -0.24826    0.11989  -2.071 0.038391 *  
## x.experience^6  -0.45401    0.09381  -4.840  1.3e-06 ***
## x.experience^7  -0.23625    0.07384  -3.199 0.001378 ** 
## x.experience^8  -0.07872    0.05444  -1.446 0.148146    
## x.experience^9  -0.07951    0.04078  -1.950 0.051213 .  
## x.accident.L    32.05443    0.44615  71.848  < 2e-16 ***
## x.accident.Q   -23.48979    0.33259 -70.628  < 2e-16 ***
## x.accident.C    10.32694    0.15015  68.777  < 2e-16 ***
## x.marital.L     -0.12760    0.03410  -3.742 0.000183 ***
## x.territory2    -0.06745    0.03322  -2.030 0.042313 *  
## x.territory3    -0.08151    0.03516  -2.318 0.020435 *  
## x.territory4    -0.10372    0.03628  -2.859 0.004257 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for Tweedie family taken to be 8.216501)
## 
##     Null deviance: 2213257  on 44999  degrees of freedom
## Residual deviance:  367501  on 44977  degrees of freedom
## AIC: NA
## 
## Number of Fisher Scoring iterations: 11

AICtweedie(glm.tw.c) # aic in glm is unsupported for tweedie, so use this value

## [1] 112712.7

# confint(glm.tweedie) # run if needed
logLiktweedie(glm.tw.c)

## [1] -56332.37

pp.cap.hat <- predict(glm.tw.c, type="response")

# compare pure premiums
compare.pp.capped <- compare.pp %>% mutate(`PP Capped` = floor(pp.capped), `Predicted PP Capped` = floor(pp.cap.hat), `Pure Premium` = floor(`Pure Premium`) ) %>% as_tibble()
compare.pp.capped <- compare.pp.capped %>% select(1:2, 15:16, 3:14)


# compare.pp.capped %>% filter(`Pure Premium` > `Predicted Pure Premium`) %>% slice(1:40) %>% qkable()

# compare.pp.capped %>% filter(`Pure Premium` < `Predicted Pure Premium`, `Pure Premium` > 0) %>% slice(1:40) %>% qkable()

compare.pp.capped %>% filter( abs(`PP Capped` - `Predicted PP Capped`) < 4000, `Pure Premium` > 0) %>% select(`PP Capped`, `Predicted PP Capped`, `Driver Age`, `Annual Mileage`, `Marital Status`, `Territory`, `Credit Score`, `Late Fees`) %>% qkable()

PP Capped	Predicted PP Capped	Driver Age	Annual Mileage	Marital Status	Territory	Credit Score	Late Fees
11546	7604	24	0-7500	Single	3	Low	0
1869	5768	38	0-7500	Single	2	High	0
9556	12084	23	7500-10000	Single	1	Low	0
2374	5019	26	7500-10000	Single	4	High	0
7927	6597	68	10000-15000	Married	3	High	0
2929	5567	25	7500-10000	Single	1	High	0
9763	5824	33	10000-15000	Single	4	Low	0
11064	13963	24	10000-15000	Single	1	Medium	0
6975	7077	22	15000+	Single	3	Low	0
15951	12594	22	15000+	Single	2	Low	0
6376	6207	26	15000+	Single	1	High	0
4023	7177	21	15000+	Single	2	High	1
7942	4877	70	0-7500	Married	2	Medium	0
14146	12937	20	10000-15000	Single	3	Low	0
13229	12411	21	15000+	Single	1	Low	0
9229	9131	25	7500-10000	Single	2	Medium	0
8885	9084	26	7500-10000	Single	2	High	0
7917	9105	19	7500-10000	Single	1	Medium	0
3219	5955	36	10000-15000	Single	3	Medium	0
4633	6229	35	0-7500	Single	2	High	0
6161	8752	30	7500-10000	Single	4	Low	0
5508	4341	37	7500-10000	Married	2	High	0
4976	7373	21	10000-15000	Single	3	Medium	0
7690	8208	19	7500-10000	Single	4	Low	0
5943	6422	61	15000+	Married	2	High	0
5698	7999	23	10000-15000	Single	1	Low	0
8278	5562	37	7500-10000	Single	1	High	0
5642	6887	24	7500-10000	Single	1	Low	0
3380	5768	38	0-7500	Single	2	High	0
8840	5797	33	15000+	Single	2	High	0
7957	9180	50	10000-15000	Single	3	High	0
12897	15338	19	15000+	Single	2	High	0
10656	13472	20	15000+	Single	1	Medium	0
9180	7373	22	10000-15000	Single	3	Medium	0
7513	6461	32	10000-15000	Single	1	Low	0
2481	6162	60	0-7500	Married	4	Medium	0
3471	7097	58	10000-15000	Married	3	High	0
2211	5199	39	7500-10000	Single	2	High	0
2811	6170	32	0-7500	Single	1	High	0
6970	6162	61	0-7500	Married	4	High	0
7503	9151	19	15000+	Single	4	Medium	0
8394	6045	26	10000-15000	Single	2	High	0
5688	5824	30	10000-15000	Single	4	Medium	0
9430	6652	48	10000-15000	Married	2	High	0
6180	6201	30	15000+	Single	1	Low	0
9189	5199	33	7500-10000	Single	2	Medium	0
10002	12298	48	0-7500	Single	2	High	0
2460	6348	23	7500-10000	Single	3	High	0
7445	6859	48	7500-10000	Single	2	High	0
3963	7141	21	0-7500	Single	2	Low	0
5843	6348	24	7500-10000	Single	3	High	0
13963	11601	22	15000+	Single	2	High	0
3477	6670	27	0-7500	Single	1	Medium	0
17985	16480	19	0-7500	Single	2	Medium	0
6426	5768	34	0-7500	Single	2	Medium	0
7582	6039	36	10000-15000	Single	2	High	0
2951	6922	20	15000+	Single	4	Low	0
7460	10552	25	10000-15000	Single	2	Low	0
11482	12930	21	10000-15000	Single	1	Medium	0
9210	6704	28	15000+	Single	1	Low	0
3672	5036	76	10000-15000	Married	3	Low	0
7964	6133	66	7500-10000	Married	3	Medium	0
7722	7157	66	10000-15000	Married	1	High	0
2737	6032	26	7500-10000	Single	2	High	0
5088	6688	66	15000+	Married	4	High	0
6543	9634	25	10000-15000	Single	3	High	2
7870	8208	19	7500-10000	Single	4	Low	0
9732	7177	22	15000+	Single	2	Medium	0
8896	6332	62	15000+	Married	3	High	0
10600	7541	48	15000+	Single	3	High	0
2659	6559	48	10000-15000	Married	3	Medium	0
6709	6631	25	15000+	Single	3	Medium	0
9395	11381	21	0-7500	Single	3	Medium	0
8810	7116	44	10000-15000	Married	1	Low	0
8917	5562	31	0-7500	Single	4	Low	0
7274	6012	28	7500-10000	Single	1	Low	0
7116	5999	65	7500-10000	Married	4	High	0
6978	10405	21	7500-10000	Single	2	Low	0
11663	11601	21	15000+	Single	2	Low	0
9834	9634	25	10000-15000	Single	3	Low	0
7793	10453	28	10000-15000	Single	1	Low	0
5941	7141	24	0-7500	Single	2	Medium	0
4665	7116	48	10000-15000	Married	1	High	0
9971	8807	57	0-7500	Single	1	High	0
5639	6952	22	7500-10000	Single	2	Low	0
5087	6835	62	0-7500	Married	1	Medium	0
6951	5415	33	7500-10000	Single	4	Medium	0
7233	7639	21	0-7500	Single	1	Medium	2
11909	11917	21	10000-15000	Single	3	Medium	0
2134	5773	27	0-7500	Single	2	Medium	0
6135	5415	34	7500-10000	Single	4	Medium	0
7160	4772	38	15000+	Married	3	Medium	0
5613	6941	58	10000-15000	Married	4	Medium	0
8149	6385	48	15000+	Married	2	Medium	0
7278	10260	21	7500-10000	Single	3	Medium	0
6246	10033	29	15000+	Single	1	Low	0
2987	6045	26	10000-15000	Single	2	Medium	0
10444	8412	29	7500-10000	Single	2	Medium	0
2588	6039	33	10000-15000	Single	2	Medium	0
2254	6039	31	10000-15000	Single	2	Medium	0
9430	5692	25	0-7500	Single	3	Low	0
11385	7773	57	10000-15000	Married	2	Medium	0
6268	6332	62	15000+	Married	3	High	0
5538	6234	28	0-7500	Single	2	Medium	0
8709	11439	23	15000+	Single	3	Medium	0
6185	6941	50	10000-15000	Married	4	High	0
7911	6663	31	0-7500	Single	1	Medium	0
3673	5955	31	10000-15000	Single	3	High	0
2479	5721	28	15000+	Single	3	Medium	0
3311	7197	58	10000-15000	Married	2	High	0
9124	6461	38	10000-15000	Single	1	Medium	2
9562	12411	22	15000+	Single	1	Low	0
10894	10453	26	10000-15000	Single	1	Low	0
6103	8112	29	7500-10000	Single	4	Low	0
9051	10891	29	15000+	Single	1	Low	0
10071	8259	40	15000+	Single	2	Low	0
6845	5199	35	7500-10000	Single	2	Medium	0
9180	6909	52	15000+	Married	2	Medium	0
6643	6126	47	0-7500	Married	4	High	0
5520	8143	40	15000+	Single	3	Low	0
14315	13410	22	15000+	Single	3	Low	0
6068	6812	58	15000+	Married	3	Medium	0
3818	6234	25	0-7500	Single	2	Low	0
12904	14725	19	7500-10000	Single	3	High	0
9321	6461	34	10000-15000	Single	1	High	0
8878	5542	28	7500-10000	Single	3	Low	0
14774	11542	20	0-7500	Single	2	High	0
5950	8292	24	15000+	Single	1	Low	0
6151	5824	34	10000-15000	Single	4	Low	0
8210	7353	56	0-7500	Married	1	High	0
9471	9709	36	0-7500	Single	4	Medium	0
8324	6422	64	15000+	Married	2	Low	0
5382	3167	90	10000-15000	Married	4	Medium	0
7291	6629	53	7500-10000	Married	1	High	0
10780	9201	26	0-7500	Single	3	Low	0
3555	5802	29	15000+	Single	2	Low	0
7459	7041	21	0-7500	Single	3	Medium	0
19488	17346	19	10000-15000	Single	2	Low	0
6005	6039	36	10000-15000	Single	2	Low	0
4242	5590	36	15000+	Single	4	Medium	0
9374	7375	47	15000+	Single	4	High	0
8223	11764	21	7500-10000	Single	4	Low	0
12869	10405	24	7500-10000	Single	2	Low	0
7251	8314	51	10000-15000	Single	4	Low	0
3250	5942	33	7500-10000	Single	3	High	0
15066	11131	22	7500-10000	Single	1	Low	0
8756	7319	52	0-7500	Married	3	Medium	0
2839	5178	39	15000+	Married	1	Low	0
5721	9322	31	0-7500	Single	2	Low	0
5649	6461	32	10000-15000	Single	1	Low	0
1827	5132	27	7500-10000	Single	3	Low	0
7221	6110	58	7500-10000	Married	3	High	0
6575	6984	28	10000-15000	Single	1	Low	0
3077	6629	54	7500-10000	Married	1	Medium	0
10546	7376	41	15000+	Married	1	High	0
6374	5768	38	0-7500	Single	2	High	0
6657	3024	93	7500-10000	Married	1	Low	0
13249	11656	23	10000-15000	Single	4	Low	0
9654	11656	24	10000-15000	Single	4	Low	0
5053	6170	36	0-7500	Single	1	Medium	0
11685	11828	51	7500-10000	Single	3	Medium	0
11085	13120	20	10000-15000	Single	2	Low	0
9915	6873	50	0-7500	Married	2	High	0
11231	12145	21	15000+	Single	4	Low	0
9887	7195	59	15000+	Married	4	High	0
6431	8574	53	7500-10000	Single	1	High	0
14612	11131	20	7500-10000	Single	1	Low	0
3592	6437	24	7500-10000	Single	2	High	0
7436	5127	33	7500-10000	Single	3	High	0
4229	7225	66	10000-15000	Married	2	High	0
3345	5132	27	7500-10000	Single	3	Low	0
6300	6037	32	15000+	Single	4	Medium	0
3491	5132	29	7500-10000	Single	3	Medium	0
4432	7041	22	0-7500	Single	3	Low	0
3570	7391	59	15000+	Married	1	Medium	0
2621	6264	43	0-7500	Married	3	Medium	0
5439	5955	33	10000-15000	Single	3	High	0
13863	12937	20	10000-15000	Single	3	Medium	0
5395	7338	47	0-7500	Single	4	Low	0
8599	5445	36	10000-15000	Married	2	High	0
14026	12653	24	10000-15000	Single	4	Low	0
1838	5596	29	15000+	Single	4	High	0
5214	7963	23	10000-15000	Single	3	Low	0
4676	5132	28	7500-10000	Single	3	Low	0
5494	5204	26	7500-10000	Single	2	Low	0
3050	5692	25	0-7500	Single	3	Low	0
9590	12587	23	10000-15000	Single	4	Low	0
17089	13776	42	10000-15000	Single	1	Low	0
7797	8936	55	15000+	Single	2	Low	0
4105	6461	31	10000-15000	Single	1	Medium	0
2650	5014	39	7500-10000	Single	4	Medium	0
10952	13410	20	15000+	Single	3	Low	0
3842	6126	46	7500-10000	Married	1	Medium	0
14867	12594	21	15000+	Single	2	Low	0
4093	5199	37	7500-10000	Single	2	Medium	0
3953	5692	25	0-7500	Single	3	Low	0
5536	5802	27	15000+	Single	2	High	0
1864	5019	26	7500-10000	Single	4	Medium	0
8533	12082	24	15000+	Single	4	Medium	0
8772	9534	19	10000-15000	Single	4	Low	0
12926	10995	26	15000+	Single	2	High	0
7971	5961	27	10000-15000	Single	3	Medium	0
2742	6348	21	7500-10000	Single	3	Low	0
9426	9771	28	10000-15000	Single	2	Medium	0
5546	5522	41	7500-10000	Married	4	High	0
4384	7137	44	15000+	Married	4	Medium	0
3268	6348	20	7500-10000	Single	3	Low	0
4053	6812	53	15000+	Married	3	Low	0
8882	9331	28	0-7500	Single	2	Medium	0
15991	15158	23	10000-15000	Single	1	Low	0
3146	5721	28	15000+	Single	3	Low	0
3228	6670	27	0-7500	Single	1	High	0
10282	10181	25	15000+	Single	2	Low	0
8293	6830	45	15000+	Married	1	Low	0
9050	7375	47	15000+	Single	4	High	0
4401	7188	30	15000+	Single	1	Low	0
10255	7177	23	15000+	Single	2	High	0
2633	6157	41	15000+	Married	4	Medium	0
9439	6184	41	7500-10000	Married	2	High	0
7457	7338	48	7500-10000	Single	1	Low	0
10416	7647	43	15000+	Single	2	Medium	0
4629	6012	29	0-7500	Single	4	Medium	0
878	4186	38	7500-10000	Married	4	Medium	0
5051	6126	45	7500-10000	Married	1	Low	0
1149	4748	39	0-7500	Married	3	High	0
4756	6126	46	0-7500	Married	4	Medium	0
7685	6887	24	7500-10000	Single	1	Low	0
6579	6870	63	15000+	Married	1	High	0
5882	6859	46	7500-10000	Single	2	Medium	0
9569	12594	23	15000+	Single	2	Low	0
7661	5824	35	10000-15000	Single	4	Low	0
7813	7391	52	15000+	Married	1	High	0
10786	8250	21	0-7500	Single	1	Low	0
1227	5199	31	7500-10000	Single	2	Medium	0
2573	5019	26	7500-10000	Single	4	Medium	0
12762	13410	20	15000+	Single	3	Low	0
7320	8990	37	7500-10000	Single	1	Medium	0
2257	5567	29	7500-10000	Single	1	High	0
6077	9988	29	0-7500	Single	3	Low	0
4386	8143	42	15000+	Single	3	High	0
5310	6012	29	7500-10000	Single	1	Low	0
2106	6043	28	15000+	Single	4	Low	0
6980	5204	26	7500-10000	Single	2	Medium	0
5184	6528	27	10000-15000	Single	2	High	0
15494	12348	22	0-7500	Single	1	Low	0
12350	12355	20	0-7500	Single	3	Low	0
9966	12145	21	15000+	Single	4	Medium	0
1465	4397	73	7500-10000	Married	2	High	0
3287	6296	46	15000+	Married	3	Low	0
8604	7478	24	10000-15000	Single	2	Low	0
2886	6196	53	7500-10000	Married	2	Low	0
16991	13120	20	10000-15000	Single	2	Low	0
3089	6207	29	15000+	Single	1	Low	0
5619	4834	71	15000+	Married	3	High	0
4945	6922	21	15000+	Single	4	Low	0
7105	5218	70	0-7500	Married	1	High	0
9857	6348	22	7500-10000	Single	3	Low	0
13379	10033	29	15000+	Single	1	High	0
6675	6039	36	10000-15000	Single	2	Medium	0
6690	6045	25	10000-15000	Single	2	Low	0
10385	13600	23	15000+	Single	2	Low	0
2821	6196	54	7500-10000	Married	2	High	0
10743	8811	51	15000+	Single	3	High	0
5159	6012	28	7500-10000	Single	1	Low	0
11236	12145	23	15000+	Single	4	Low	0
6308	8819	41	0-7500	Single	2	High	0
10428	6692	58	7500-10000	Married	2	Medium	0
4003	5647	45	7500-10000	Married	3	High	0
14799	12870	20	10000-15000	Single	3	Low	0
7273	7647	44	15000+	Single	2	Low	0
5842	6162	63	0-7500	Married	4	Low	0
4859	7141	21	0-7500	Single	2	Medium	0
16353	12594	21	15000+	Single	2	Medium	0
1017	4877	74	0-7500	Married	2	Low	0
8877	5679	65	7500-10000	Married	3	Medium	0
2700	5773	25	0-7500	Single	2	Low	0
6406	7604	23	0-7500	Single	3	Medium	0
7619	6855	23	7500-10000	Single	3	Low	0
5670	6629	53	7500-10000	Married	1	Low	0
3973	7437	24	7500-10000	Single	1	Low	0
2392	5797	34	15000+	Single	2	Medium	0
6468	5955	33	10000-15000	Single	3	Low	0
5800	6389	66	0-7500	Married	2	High	0
5556	6922	21	15000+	Single	4	High	0
4918	6264	47	0-7500	Married	3	Medium	0
7008	6704	26	15000+	Single	1	Low	0
7005	7211	24	10000-15000	Single	4	Low	0
1759	5692	25	0-7500	Single	3	Low	0
1927	5036	71	10000-15000	Married	3	High	0
10811	7211	22	10000-15000	Single	4	Low	0
6337	6928	43	10000-15000	Married	4	Medium	0
14421	11295	22	7500-10000	Single	2	Low	0
15539	12421	41	10000-15000	Married	1	High	0
7277	9370	33	15000+	Single	2	Low	0
4585	5726	40	7500-10000	Married	2	High	0
5194	7177	22	15000+	Single	2	Low	0
5308	6201	32	15000+	Single	1	Medium	0
2118	5687	37	0-7500	Single	3	Low	0
3327	5567	26	7500-10000	Single	1	Medium	0
7294	6173	35	15000+	Single	3	Medium	0
9857	6220	63	7500-10000	Married	2	High	0
4593	8045	52	10000-15000	Married	4	Medium	0
6727	10405	23	7500-10000	Single	2	Low	0
11651	13600	23	15000+	Single	2	Low	0
12001	10552	29	10000-15000	Single	2	Medium	0
3416	5824	38	10000-15000	Single	4	Low	0
8344	6437	26	10000-15000	Single	3	Low	0
5228	6039	35	10000-15000	Single	2	High	0
1808	5773	27	0-7500	Single	2	Medium	0
7524	7077	22	15000+	Single	3	Medium	0
13726	13120	22	10000-15000	Single	2	Low	0
4416	5204	28	7500-10000	Single	2	Medium	0
9372	5590	31	15000+	Single	4	Low	0
8982	11188	24	15000+	Single	4	Low	0
4291	7225	63	10000-15000	Married	2	High	0
13016	12418	24	15000+	Single	3	Medium	0
3751	6173	37	15000+	Single	3	High	0
18872	14877	41	10000-15000	Single	1	High	0
6119	5204	25	7500-10000	Single	2	High	0
11355	10837	21	7500-10000	Single	4	Low	0
7350	7903	54	7500-10000	Single	3	Medium	0
2164	5596	26	15000+	Single	4	Medium	0
6986	6522	36	10000-15000	Single	2	Medium	0
4642	7211	21	10000-15000	Single	4	Medium	0
9763	6266	25	15000+	Single	2	Low	0
7209	6652	40	10000-15000	Married	2	High	0
4094	6452	63	10000-15000	Married	4	High	0
5810	9423	29	10000-15000	Single	4	Low	0
11915	13120	24	10000-15000	Single	2	Low	0
5499	6332	66	15000+	Married	3	Medium	0
13633	15615	21	15000+	Single	1	Low	0
13632	11295	21	7500-10000	Single	2	Medium	0
3629	5721	26	15000+	Single	3	High	0
2193	5955	34	10000-15000	Single	3	High	0
3026	6870	61	15000+	Married	1	Low	0
12948	12493	62	10000-15000	Married	1	Low	0
2759	6196	52	7500-10000	Married	2	Medium	0
1591	5567	29	0-7500	Single	4	Low	0
11654	13472	24	15000+	Single	1	Low	0
11843	11946	56	15000+	Married	1	Medium	0
9376	10770	30	0-7500	Single	1	Low	0
11373	12086	21	10000-15000	Single	2	Low	0
14037	13403	22	15000+	Single	1	High	0
2304	6179	27	15000+	Single	3	Low	0
14879	12348	20	0-7500	Single	1	Low	0
9020	5961	25	10000-15000	Single	3	High	0
10342	6922	23	15000+	Single	4	High	0
9325	12348	22	0-7500	Single	1	Low	0
8732	12653	24	10000-15000	Single	4	Medium	0
6904	6629	50	7500-10000	Married	1	Medium	0
4275	7712	24	0-7500	Single	2	Medium	0
5877	6690	64	10000-15000	Married	2	Medium	0
9348	5768	31	0-7500	Single	2	Low	0
6906	6296	47	15000+	Married	3	Low	0
2446	5415	33	7500-10000	Single	4	Low	0
8630	8484	41	10000-15000	Single	3	High	0
3684	7197	51	10000-15000	Married	2	Low	0
6572	7683	44	10000-15000	Single	4	Medium	0
8949	12587	24	10000-15000	Single	4	Low	0
3249	6629	52	0-7500	Married	4	Low	0
8030	5562	35	0-7500	Single	4	High	0
220	3010	102	7500-10000	Married	3	Medium	0
5973	6162	63	0-7500	Married	4	High	0
15324	12930	22	10000-15000	Single	1	Low	0
9080	5797	35	15000+	Single	2	High	0
3305	6007	31	0-7500	Single	4	Medium	0
7750	5127	39	7500-10000	Single	3	Medium	0
1102	4727	71	15000+	Married	4	Low	0
12797	12418	21	15000+	Single	3	Medium	0
3634	6110	50	7500-10000	Married	3	Low	0
5527	6437	28	10000-15000	Single	3	Low	0
13142	15158	21	10000-15000	Single	1	Medium	0
3341	6290	32	10000-15000	Single	4	Medium	0
3672	7376	46	15000+	Married	1	Medium	0
1785	5615	35	7500-10000	Single	2	High	0
8479	5768	34	0-7500	Single	2	High	0
8063	7077	21	15000+	Single	3	Low	0
3949	6685	34	0-7500	Single	2	Medium	0
4862	6763	42	7500-10000	Single	3	Medium	0
10170	12908	54	15000+	Married	3	Low	0
4947	7116	48	10000-15000	Married	1	Low	0
5133	8412	25	7500-10000	Single	2	Low	0
9558	6763	46	7500-10000	Single	3	High	0
4223	7177	23	15000+	Single	2	Low	0
6702	5797	38	15000+	Single	2	Medium	0
4094	7437	21	0-7500	Single	4	Low	0
9859	10176	25	10000-15000	Single	4	Low	0
4667	4186	38	7500-10000	Married	4	High	0
11804	14320	22	0-7500	Single	3	Low	0
5493	9045	27	15000+	Single	4	Low	0
5820	6461	34	10000-15000	Single	1	Low	0
4937	4335	70	7500-10000	Married	3	High	0
9703	6007	33	7500-10000	Single	1	Medium	0
6600	7678	24	15000+	Single	1	High	0
11743	11439	23	15000+	Single	3	Low	0
5584	6126	43	0-7500	Married	4	High	0
4653	6348	22	7500-10000	Single	3	Low	0
9714	8835	41	15000+	Single	1	High	0
16316	13600	20	15000+	Single	2	Low	0
10368	8118	55	0-7500	Single	3	Medium	0
11196	12354	21	15000+	Single	3	Medium	0
1790	5716	32	15000+	Single	3	High	0
1800	5768	34	0-7500	Single	2	Low	0
10895	8181	44	15000+	Single	1	Medium	0
10709	12594	22	15000+	Single	2	Low	0
4974	6290	39	10000-15000	Single	4	Medium	0
4029	6830	47	15000+	Married	1	High	0
10428	8915	76	10000-15000	Married	2	High	0
7531	5132	29	7500-10000	Single	3	High	0
8535	11601	24	15000+	Single	2	Low	0
11567	9379	28	15000+	Single	2	High	0
4479	6170	32	0-7500	Single	1	High	0
8848	10835	25	15000+	Single	1	Low	0
6402	6207	27	15000+	Single	1	Medium	0
5857	6663	30	0-7500	Single	1	Low	0
8094	8112	27	7500-10000	Single	4	Medium	0
9812	6352	41	0-7500	Married	2	High	0
9948	10068	31	0-7500	Single	2	Low	0
11010	7647	49	15000+	Single	2	High	0
3445	6649	47	15000+	Married	4	Medium	0
9811	6196	52	7500-10000	Married	2	Low	0
905	4644	38	7500-10000	Married	1	Medium	0
2137	5773	27	0-7500	Single	2	Medium	0
12019	10995	26	15000+	Single	2	Low	0
12845	10033	29	15000+	Single	1	Low	0
6338	5721	26	15000+	Single	3	Low	0
8897	6348	23	7500-10000	Single	3	Medium	0
10050	7678	24	15000+	Single	1	High	0
3582	6528	28	10000-15000	Single	2	Low	0
12548	10891	26	15000+	Single	1	Low	0
5351	6654	61	7500-10000	Married	1	Low	0
7497	7382	69	0-7500	Married	1	Medium	0
7187	10181	25	15000+	Single	2	Low	0
14118	10405	21	7500-10000	Single	2	Low	0
5136	6902	33	10000-15000	Single	3	Medium	0
12974	11630	22	7500-10000	Single	4	High	0
9646	12084	23	7500-10000	Single	1	Low	0
14221	14549	22	15000+	Single	1	Low	0
14379	11601	24	15000+	Single	2	Medium	0
8820	6704	24	7500-10000	Single	4	Medium	0
1778	5590	39	15000+	Single	4	Medium	0
3817	7097	56	10000-15000	Married	3	Medium	0
14548	12084	21	7500-10000	Single	1	Medium	0
2334	5537	34	7500-10000	Single	3	Medium	0
8212	6812	59	15000+	Married	3	High	0
12189	10033	25	15000+	Single	1	High	0
4296	6870	65	15000+	Married	1	Medium	0
9252	5562	37	7500-10000	Single	1	High	0
14413	12355	21	0-7500	Single	3	Low	0
7519	10260	24	7500-10000	Single	3	Low	0
9412	10405	22	7500-10000	Single	2	Low	0
2501	5647	48	7500-10000	Married	3	Low	0
11084	11336	38	10000-15000	Single	1	Low	0
2257	5961	28	10000-15000	Single	3	Medium	0
12892	10405	24	7500-10000	Single	2	Low	0
649	4397	76	7500-10000	Married	2	Medium	0
8976	5797	34	15000+	Single	2	High	0
13626	11946	53	15000+	Married	1	Medium	0
3802	6110	53	7500-10000	Married	3	High	0
3111	4877	71	0-7500	Married	2	High	0
2798	5824	34	10000-15000	Single	4	High	0
4888	6629	58	0-7500	Married	4	Medium	0
7772	5721	26	15000+	Single	3	Low	0
2600	5679	65	7500-10000	Married	3	Low	0
5267	8899	21	15000+	Single	1	Medium	0
7692	6615	43	7500-10000	Single	4	Low	0
1783	5542	28	7500-10000	Single	3	High	0
4416	8404	30	7500-10000	Single	2	High	0
11534	8523	44	10000-15000	Single	1	High	0
7765	7391	55	15000+	Married	1	Low	0
3692	7373	24	10000-15000	Single	3	Low	0
6378	10181	26	15000+	Single	2	Low	0
5379	5824	31	10000-15000	Single	4	Low	0
4542	4748	70	7500-10000	Married	2	High	0
9173	7319	59	0-7500	Married	3	High	0
5982	5961	29	10000-15000	Single	3	Medium	0
7426	9634	26	10000-15000	Single	3	High	0
8728	6201	32	15000+	Single	1	Low	0
8884	5797	30	15000+	Single	2	Low	0
14202	11455	25	10000-15000	Single	2	Medium	0
6189	7141	21	0-7500	Single	2	Low	0
9045	5955	30	10000-15000	Single	3	High	0
8683	7373	23	10000-15000	Single	3	Low	0
8300	10024	32	15000+	Single	1	Low	0
7417	9771	27	10000-15000	Single	2	Low	0
7173	5773	28	0-7500	Single	2	Low	0
10944	14036	21	10000-15000	Single	1	Medium	0
10373	6690	65	10000-15000	Married	2	Medium	0
6808	6007	31	0-7500	Single	4	Low	0
4650	6208	24	7500-10000	Single	4	Medium	0
4610	5797	34	15000+	Single	2	Low	0
5782	6179	25	15000+	Single	3	High	0
2365	5716	39	15000+	Single	3	Low	0
7412	11219	50	10000-15000	Married	4	Medium	0
7523	9625	34	10000-15000	Single	3	Medium	0
9101	9625	34	10000-15000	Single	3	Low	0
2236	5596	27	15000+	Single	4	Medium	0
6011	6415	46	10000-15000	Married	4	Medium	0
15702	12411	22	15000+	Single	1	High	0
4083	5687	31	0-7500	Single	3	High	0
5007	6697	36	15000+	Single	1	Medium	0
8133	9973	31	0-7500	Single	1	Low	0
3950	7683	44	10000-15000	Single	4	High	0
5689	5687	36	0-7500	Single	3	Low	0
12724	11080	22	7500-10000	Single	3	Low	0
2740	6045	28	10000-15000	Single	2	Medium	0
8598	10825	33	15000+	Single	1	Low	0
8428	6528	27	10000-15000	Single	2	Medium	0
8210	7373	23	10000-15000	Single	3	Medium	0
9719	7391	51	15000+	Married	1	High	0
3045	5679	64	7500-10000	Married	3	Low	0
10914	13349	40	15000+	Single	2	High	0
2638	6385	48	15000+	Married	2	Medium	0
5077	6037	32	15000+	Single	4	Medium	0
2370	6045	26	10000-15000	Single	2	Medium	0
8010	6777	56	0-7500	Married	3	High	0
7660	6290	32	10000-15000	Single	4	Low	0
3203	6039	39	10000-15000	Single	2	Medium	0
3209	6176	25	0-7500	Single	1	Low	0
6691	9959	66	7500-10000	Married	1	Low	0
6140	4925	70	10000-15000	Married	4	Medium	0
3014	6830	48	15000+	Married	1	High	0
3638	5590	33	15000+	Single	4	Low	0
16351	12594	24	15000+	Single	2	Low	0
3834	6804	66	0-7500	Married	3	High	0
3914	7319	56	0-7500	Married	3	Medium	0
11763	9201	28	0-7500	Single	3	Low	0
2940	6922	24	15000+	Single	4	Low	0
8316	6012	29	0-7500	Single	4	Medium	0
6692	5976	52	7500-10000	Married	4	High	0
10842	7924	40	7500-10000	Single	1	Low	0
3115	5768	30	0-7500	Single	2	Medium	0
10871	12084	23	7500-10000	Single	1	Low	0
8356	6855	23	7500-10000	Single	3	Low	0
9693	6296	44	15000+	Married	3	High	0
9184	8523	41	10000-15000	Single	1	Low	0
3499	5687	36	0-7500	Single	3	Medium	0
6783	6812	58	15000+	Married	3	High	0
14074	10172	37	15000+	Single	2	Low	0
6535	6855	24	7500-10000	Single	3	Low	0
10026	6201	34	15000+	Single	1	Medium	0
1765	5679	61	7500-10000	Married	3	Low	0
7725	5824	39	10000-15000	Single	4	High	0
2178	5716	31	15000+	Single	3	Low	0
5696	6461	39	10000-15000	Single	1	Low	0
9429	11502	42	10000-15000	Married	1	Low	0
4091	5562	34	0-7500	Single	4	Low	0
3969	6900	69	0-7500	Married	2	Medium	0
8014	6045	25	10000-15000	Single	2	Low	0
7483	7939	59	0-7500	Single	4	Medium	0
4244	6045	28	10000-15000	Single	2	Medium	0
13266	13472	21	15000+	Single	1	Medium	0
9223	7700	58	10000-15000	Married	1	High	0
2391	5692	25	0-7500	Single	3	High	0
7907	10542	37	10000-15000	Single	2	Medium	0
7454	10034	21	7500-10000	Single	4	Low	0
8464	12348	22	0-7500	Single	1	Low	0
1975	5687	34	0-7500	Single	3	Low	0
6386	6812	50	15000+	Married	3	High	0
12317	13963	21	10000-15000	Single	1	Low	0
3039	6352	44	0-7500	Married	2	Low	0
11570	9036	30	15000+	Single	4	Low	0
8099	12084	21	7500-10000	Single	1	Low	0
10095	9370	39	15000+	Single	2	Medium	0
2509	6332	60	15000+	Married	3	Low	0
6298	8999	25	7500-10000	Single	1	Medium	0
6329	6796	42	0-7500	Married	1	Low	0
3807	7373	22	10000-15000	Single	3	Medium	0
6209	6629	53	0-7500	Married	4	High	0
11899	14036	22	10000-15000	Single	1	Low	0
2743	5199	33	7500-10000	Single	2	Medium	0
3757	7373	24	10000-15000	Single	3	Low	0
10482	10260	21	7500-10000	Single	3	High	0
9427	8999	25	7500-10000	Single	1	Medium	0
1655	5567	29	7500-10000	Single	1	High	0
10337	9762	30	10000-15000	Single	2	Medium	0
7408	5567	27	7500-10000	Single	1	Low	0
940	4704	71	0-7500	Married	4	High	0
8243	6170	30	0-7500	Single	1	Low	0
7432	6461	37	10000-15000	Single	1	High	0
2702	5199	34	7500-10000	Single	2	Low	0
8667	7856	48	10000-15000	Single	3	High	0
7791	6625	31	15000+	Single	3	Medium	0
7221	10714	53	0-7500	Married	4	Low	0
2907	4644	39	7500-10000	Married	1	Medium	0
9392	9423	26	10000-15000	Single	4	Low	0
2606	5132	29	7500-10000	Single	3	Medium	0
3590	6467	25	10000-15000	Single	1	Medium	0
4403	8159	51	15000+	Single	3	Medium	0
6538	6922	21	15000+	Single	4	Low	0
10098	9322	35	0-7500	Single	2	High	0
10774	7177	23	15000+	Single	2	Medium	0
3381	5802	27	15000+	Single	2	Medium	0
11485	10176	26	10000-15000	Single	4	Low	0
11882	10405	22	7500-10000	Single	2	Low	0
9709	6763	40	7500-10000	Single	3	Low	0
6409	6859	49	7500-10000	Single	2	Medium	0
2569	6296	44	15000+	Married	3	Medium	0
8462	10453	29	10000-15000	Single	1	Low	0
7573	10033	29	15000+	Single	1	Medium	0
16698	12870	24	10000-15000	Single	3	Medium	0
6486	5830	29	10000-15000	Single	4	Low	0
15437	12198	22	7500-10000	Single	2	Medium	0
6872	5014	33	7500-10000	Single	4	Low	0
1874	5768	35	0-7500	Single	2	Medium	0
8699	11131	24	0-7500	Single	4	High	0
1504	5127	31	7500-10000	Single	3	Medium	0
6370	6039	32	10000-15000	Single	2	Low	0
8319	7609	40	0-7500	Single	2	Medium	0
13508	10607	29	10000-15000	Single	2	High	0
1538	5132	26	7500-10000	Single	3	Low	0
3700	7188	36	15000+	Single	1	Low	0
5977	9768	25	15000+	Single	4	Medium	0
9254	5961	28	10000-15000	Single	3	Medium	0
9214	7195	56	15000+	Married	4	Medium	0
5014	6385	49	15000+	Married	2	High	0
5352	6461	35	10000-15000	Single	1	High	0
7073	10039	26	15000+	Single	3	Low	0
2526	6332	67	15000+	Married	3	High	0
5063	5567	25	7500-10000	Single	1	Medium	0
8764	7647	48	15000+	Single	2	High	0
5952	8412	28	7500-10000	Single	2	Low	0
5699	7177	24	15000+	Single	2	Low	0
1080	4682	76	7500-10000	Married	3	Low	0
2752	6260	31	15000+	Single	2	Low	0
12208	8523	44	10000-15000	Single	1	Medium	0
14639	11455	27	10000-15000	Single	2	Low	0
8560	8807	50	0-7500	Single	1	Medium	0
3766	7502	44	0-7500	Single	3	Low	0
8530	8999	25	7500-10000	Single	1	Medium	0
6281	6467	27	10000-15000	Single	1	High	0
10969	13472	23	15000+	Single	1	Medium	0
8780	6909	54	15000+	Married	2	High	0
1689	5596	25	15000+	Single	4	Medium	0
5111	6649	47	15000+	Married	4	Low	0
7050	7751	24	15000+	Single	2	High	0
3206	6110	54	7500-10000	Married	3	High	0
2973	6690	65	10000-15000	Married	2	High	0
6506	6201	37	15000+	Single	1	Low	0
3838	6234	29	0-7500	Single	2	Low	0
12993	9709	32	0-7500	Single	4	Low	0
3768	7478	24	10000-15000	Single	2	Low	0
5346	6704	23	7500-10000	Single	4	High	0
6260	5199	38	7500-10000	Single	2	Low	0
4677	6461	32	10000-15000	Single	1	Medium	0
5961	6007	30	0-7500	Single	4	Low	0
7622	5760	64	7500-10000	Married	2	Low	0
15558	13258	21	15000+	Single	3	Low	0
10947	11439	22	15000+	Single	3	Low	0
6496	7496	58	10000-15000	Married	4	High	0
11582	9978	34	15000+	Single	3	Medium	0
9343	7678	23	15000+	Single	1	Low	0
7725	5590	34	15000+	Single	4	High	0
5216	6201	35	15000+	Single	1	High	0
5022	5900	72	10000-15000	Married	1	High	0
6551	6812	54	15000+	Married	3	Low	0
6776	5687	35	0-7500	Single	3	Low	0
4578	6352	46	0-7500	Married	2	Medium	0
4545	8275	54	15000+	Single	2	Low	0
4149	4335	72	7500-10000	Married	3	Medium	0
3230	5768	38	0-7500	Single	2	High	0
3311	5199	33	7500-10000	Single	2	Low	0
10488	11439	24	15000+	Single	3	Medium	0
7233	7924	45	7500-10000	Single	1	Low	0
3758	5716	38	15000+	Single	3	High	0
8287	5802	29	15000+	Single	2	Medium	0
7666	7353	53	0-7500	Married	1	Medium	0
7814	7400	41	15000+	Married	2	Medium	0
3027	6690	60	10000-15000	Married	2	Medium	0
9501	6835	60	0-7500	Married	1	Medium	0

This looks like a much better fit. However, we don’t worry about our fit not being perfect–we’re interested in this model generalizing well for future observations and know that we avoid overfitting to data. Our GLM is tuned to minimize the deviation between observed and expected Pure Premiums and so generalizes to other experience data.

5. Interpreting the Model

Given the low credibility of our data as representative of the entire population of Cal Insurance’s policyholders, we will focus on the interpretation of the GLM. Individuals “below” the GLM have a lower historical loss cost than expected.

The overall goal here is balancing compliance with California’s ratemaking regulations, where our models must be equitable. However, using sequential analysis with the allowed factors can lead us to a weak classification of risk, leading to adverse selection where low-risk individuals prefer competitors with lower rates, and higher-risk individuals (who may have been rejected from competitors’ underwriting guidelines) may seek coverage from Cal Insurance (but incur high losses).

We consider two selections of individuals below: sel1 and sel2. The subset sel1 contains individuals who historically incur higher losses than average (as predicted by the GLM). This does not necessarily mean these are the individuals we want to reject via underwriting guidelines (if anything, we would like to legally charge them higher premiums), but we can expect to gain a lot of insight here.

The subset sel2 contains individuals who historically in 2013-2015 have significantly lower incurred losses than estimated by the GLM. Although this is not a causal relationship between the combination of factors and fewer incurred losses, there may be interesting insights to gain.

# selections of individuals for analysis
sel1 <- compare.pp.capped %>% filter(`Pure Premium` > 2 * `Predicted Pure Premium`) 

sel2 <- compare.pp.capped %>% filter(`Pure Premium` * 2 < `Predicted Pure Premium`, `Pure Premium` > 0)


# compare.pp.capped %>% ggplot(aes(x = compare.pp.capped$`Pure Premium`)) + geom_histogram(bins = 10, fill = "lightblue", color = "lightyellow") + ggtitle("Distribution of Observed Pure Premiums") + scale_x_log10()


# compare.pp.capped %>% ggplot(aes(x = compare.pp.capped$`Predicted PP Capped`)) + geom_histogram(bins = 20, fill = "lightblue", color = "lightyellow") + ggtitle("Distribution of Projected Pure Premiums") + scale_x_log10()  


sel2 %>% ggplot(aes(x = sel2$`Pure Premium`)) + geom_histogram(bins = 10, fill = "lightblue", color = "lightyellow") +  ggtitle("Distribution of Observed Pure Premiums")

# + scale_x_log10()


sel2 %>% ggplot(aes(x = sel2$`Predicted PP Capped`)) + geom_histogram(bins = 20, fill = "lightblue", color = "lightyellow") + ggtitle("Distribution of Projected Pure Premiums")

compare.pp.capped %>% ggplot(aes(x = `Annual Mileage`, y = `Predicted PP Capped`)) + geom_bar(aes(fill = `Annual Mileage`), stat = "summary", fun.y = "mean", show.legend = TRUE) + facet_grid(. ~ `Driver Experience Band`) + theme(legend.position = "bottom", axis.text.x = element_blank(), axis.ticks.x = element_blank()) + ggtitle("Average Predicted Pure Premium \nby Driver Experience Years")

compare.pp.capped %>% ggplot(aes(x = `Driver Experience Band`, y = `Predicted PP Capped`)) + geom_bar(aes(fill = `Driver Experience Band`), stat = "summary", fun.y = "mean", show.legend = TRUE) + facet_grid(. ~ `Annual Mileage`) + theme(legend.position = "bottom", axis.text.x = element_blank(), axis.ticks.x = element_blank()) + ggtitle("Average Predicted Pure Premium \nby Annual Mileage")

# loss %>% ggplot(aes(x = `Territory`, y = `Adjusted Loss`)) + geom_bar(aes(fill = `Territory`), stat = "identity", show.legend = TRUE) + facet_grid(. ~ `Marital Status`) + theme(legend.position = "bottom")  + ggtitle("Total loss by Territory and Marital Status")

The predicted Pure Premiums are generally monotonic as Annual Mileage increases, with the exception of the third mileage band, where it appears that low-experience drivers with this mileage are expected to incur a relatively high average loss. This may be due to a tradeoff between lower mileage corresponding to less road-time and exposure to risk, versus high mileage (150,000+) corresponding to more skilled drivers, despite fewer years of experience.

GLM factors as a proxy for `Credit Score`

compare.pp.capped %>% ggplot(aes(x = `Driver Experience Band`, y = `Predicted PP Capped`)) + geom_bar(aes(fill = `Driver Experience Band`), stat = "summary", fun.y = "mean", show.legend = TRUE) + facet_grid(. ~ `Credit Score`) + theme(legend.position = "bottom", axis.text.x = element_blank(), axis.ticks.x = element_blank()) + ggtitle("Average Predicted Pure Premium by Credit Score")

compare.pp.capped %>% ggplot(aes(x = `Annual Mileage`, y = `Predicted PP Capped`)) + geom_bar(aes(fill = `Annual Mileage`), stat = "summary", fun.y = "mean", show.legend = TRUE) + facet_grid(. ~ `Credit Score`) + theme(legend.position = "bottom", axis.text.x = element_blank(), axis.ticks.x = element_blank()) + ggtitle("Average Predicted Pure Premium by Credit Score")

compare.pp.capped %>% ggplot(aes(x = `Territory`, y = `Predicted PP Capped`)) + geom_bar(aes(fill = `Territory`), stat = "summary", fun.y = "mean", show.legend = TRUE) + facet_grid(. ~ `Credit Score`) + theme(legend.position = "bottom", axis.text.x = element_blank(), axis.ticks.x = element_blank()) + ggtitle("Average Predicted Pure Premium by Credit Score")

The past filed relativities for territory (1.2, 1.1, 0.9, 0.8) appear to be insufficient to distinguish the expected loss from each territory.

# compound poisson from zhang
glm.cp <- cpglm(formula = pp ~ x.conviction + x.mileage + x.experience + x.accident + x.marital + x.territory, link = 0, data = df.loss)
#  does not converge; do not use

# brute force "optimize" approach; # NOT USED

start <- c(glm.tweedie$coefficients/2, glm.tweedie$coefficients/2)

# compute negative log likelihood (nll)
nll <- function(param){
  # f0, s0 for offset
  f0 <- param[1]
  f1 <- param[2]
  f2 <- param[3]
  f3 <- param[4]
  f4 <- param[5]
  f5 <- param[6]
  f6 <- param[7]
  
  s0 <- param[1]
  s1 <- param[2]
  s2 <- param[3]
  s3 <- param[4]
  s4 <- param[5]
  s5 <- param[6]
  s6 <- param[7]
  
  # lambda <- exp(sum( c(f0, f1, f2, f3, f4, f5, f6) * c(1, x.vec) ))
  lambda <- exp(f0 + f1*x.conviction + f2*x.mileage + f3*x.experience + f4*x.accident + f5*x.marital + f6*x.territory)
  
  # theta <- exp(sum( c(s0, s1, s2, s3, s4, s5, s6) * c(1, x.vec) ))
  theta <- exp(s0 + s1*x.conviction + s2*x.mileage + s3*x.experience + s4*x.accident + s5*x.marital + s6*x.territory)
  
  tau <- alpha1 * theta
  p <- (alpha1 + 2) / (alpha1 + 1)
  mu <- lambda * tau 
  print(p) # debug
  phi <- abs( lambda^(1-p) * tau^(2-p) / (2-p) )
  
  #log-likelihood 
  ll <- log(dtweedie(pp, p, mu, phi))
  return(-sum(ll))
}

bfmle <- optim(start, nll)
bfmle

Now because we hand-select the factors to include into our GLM (as opposed to randomized subsetting), a $k$-fold cross-validation of data would not be effective. We trained our data on the experience years 2013-2015, reasoning that four years experience captures a good amount of the underlying policyholder risk behavior.

6. Creating Underwriting Guidelines

From our exhibits above and GLM, we want to essentially reject drivers with the following specifications, given in the table below. Of course, in the process, we can expect to unfortunately reject individuals who are falsely projected to incur high losses.

rej <- compare.pp.capped %>% filter(`Predicted Pure Premium` > 12000)

rej %>% qkable() # reject these

Policy Number	Vehicle Number	PP Capped	Predicted PP Capped	Pure Premium	Predicted Pure Premium	Conviction Points (CP) last 3 years	Accident Points (AP) last 3 years	Annual Mileage	Driver Experience Band	Marital Status	Territory	Driver Age	Credit Score	Late Fees	Liability Limit
10	6386	7659	14934	7659	17800	0	3	7500-10000	0-3	Single	2	19	Low	0	5e+04
42	644	1331	20855	1331	21258	3	1	7500-10000	44-53	Married	1	63	Low	0	5e+04
67	14663	4721	13049	4721	12404	1	3	0-7500	4-8	Single	4	23	Low	0	5e+04
144	10613	100000	14549	167697	15197	1	3	15000+	4-8	Single	1	24	Low	0	3e+05
160	5309	5059	12086	5059	13868	0	2	10000-15000	4-8	Single	2	20	Medium	1	1e+05
160	11547	9556	12084	9556	13639	0	3	7500-10000	4-8	Single	1	23	Low	0	1e+05
170	1998	77	13403	77	14571	1	2	15000+	4-8	Single	1	23	Medium	0	3e+05
222	12590	59700	13404	59700	14333	0	3	0-7500	4-8	Single	1	20	Low	1	5e+04
228	9054	1554	11188	1554	12688	0	2	15000+	4-8	Single	4	21	Low	0	5e+05
255	12575	195	13757	195	17066	0	2	7500-10000	0-3	Single	2	19	Low	0	5e+04
311	2430	0	11131	0	13077	0	2	7500-10000	4-8	Single	1	20	Low	0	1e+05
322	2562	127	12833	127	15112	0	2	7500-10000	34-43	Single	1	53	Low	1	5e+04
359	12495	29606	12355	29606	13667	0	3	0-7500	4-8	Single	3	23	Low	0	5e+05
425	2623	654	12084	654	13639	0	3	7500-10000	4-8	Single	1	21	Low	2	1e+05
427	14101	11064	13963	11064	14532	1	2	10000-15000	4-8	Single	1	24	Medium	0	5e+04
459	3839	100000	12083	119880	12442	0	3	0-7500	4-8	Single	4	24	Low	0	1e+05
466	6452	15951	12594	15951	14503	0	3	15000+	4-8	Single	2	22	Low	0	5e+04
507	5816	0	11131	0	13077	0	2	7500-10000	4-8	Single	1	22	Low	0	5e+04
549	2165	0	10196	0	12196	1	1	0-7500	0-3	Single	2	19	Medium	0	3e+05
580	9359	0	9202	0	15957	1	1	0-7500	64-73	Married	2	86	Medium	0	3e+05
581	12571	120	14512	120	14579	1	2	10000-15000	34-43	Single	4	57	Low	0	5e+04
584	14769	14146	12937	14146	14497	0	3	10000-15000	4-8	Single	3	20	Low	0	1e+05
601	9459	0	10430	0	12155	2	2	7500-10000	9-13	Single	1	25	Low	0	5e+04
601	11555	189	11295	189	12976	0	3	7500-10000	4-8	Single	2	24	Low	0	5e+04
608	6741	13229	12411	13229	14616	0	2	15000+	4-8	Single	1	21	Low	0	1e+05
622	12734	0	9441	0	12234	0	1	0-7500	0-3	Single	2	19	Low	1	5e+05
632	266	100000	15756	119700	19067	0	2	10000-15000	0-3	Single	3	19	High	3	1e+05
660	13300	4070	13472	4070	15244	0	3	15000+	4-8	Single	1	21	Low	0	3e+05
663	3618	120	12145	120	13234	0	3	15000+	4-8	Single	4	24	Low	0	3e+05
674	7410	9920	33070	9920	28841	3	2	10000-15000	9-13	Single	2	29	Low	0	5e+04
679	4235	26765	11860	26765	13681	0	2	7500-10000	24-33	Single	1	49	Low	1	1e+05
696	8004	0	11188	0	12688	0	2	15000+	4-8	Single	4	21	Low	0	5e+04
719	5937	21149	17094	21149	19997	0	2	10000-15000	0-3	Single	1	19	Medium	0	5e+04
756	8498	1043	13116	1043	13193	1	3	15000+	4-8	Single	4	24	Low	0	5e+04
788	9747	7917	9105	7917	12236	0	1	7500-10000	0-3	Single	1	19	Medium	0	3e+05
795	11667	0	25014	0	24104	3	1	15000+	34-43	Married	1	57	Medium	0	5e+05
806	3380	59880	17730	59880	19879	1	3	15000+	0-3	Single	3	19	Low	0	5e+04
830	9367	0	9886	0	12977	0	1	10000-15000	0-3	Single	2	19	Low	1	3e+05
852	1798	5629	12028	5629	12965	1	3	7500-10000	4-8	Single	3	23	Medium	0	5e+04
908	5522	35374	12411	35374	14616	0	2	15000+	4-8	Single	1	23	High	0	3e+05
959	5589	120	12411	120	14616	0	2	15000+	4-8	Single	1	21	Medium	0	1e+05
960	9085	4507	15756	4507	19067	0	2	10000-15000	0-3	Single	3	19	Medium	0	1e+05
962	5826	386	12930	386	14577	0	2	10000-15000	4-8	Single	1	20	Low	0	5e+04
968	11412	46363	24360	46363	22872	3	1	10000-15000	34-43	Married	2	52	Medium	0	5e+05
992	5507	2236	17730	2236	19879	1	3	15000+	0-3	Single	3	19	Medium	1	5e+04
1013	10079	21778	12348	21778	13742	0	2	0-7500	4-8	Single	1	21	Low	0	5e+04
1059	1423	134	12411	134	14616	0	2	15000+	4-8	Single	1	22	Medium	0	1e+05
1095	10470	134	16250	134	17920	1	2	0-7500	0-3	Single	3	19	Low	0	5e+04
1116	2778	0	10932	0	13045	0	2	7500-10000	24-33	Single	3	43	Low	0	3e+05
1121	12043	17451	11086	17451	13016	0	2	7500-10000	24-33	Single	2	41	High	0	1e+05
1123	13141	120	14036	120	15204	0	3	10000-15000	4-8	Single	1	21	Low	0	5e+04
1162	12613	497	11422	497	13598	1	1	10000-15000	0-3	Single	1	19	Low	0	5e+04
1167	75	72567	12145	72567	13234	0	3	15000+	4-8	Single	4	20	Medium	0	3e+05
1176	12198	347	13757	347	17066	0	2	7500-10000	0-3	Single	2	19	Low	0	1e+05
1195	5610	0	11080	0	12430	1	2	7500-10000	4-8	Single	3	21	Low	0	5e+05
1196	4300	427	8923	427	16979	0	1	10000-15000	64-73	Married	2	85	Medium	0	3e+05
1214	5681	142	13049	142	13597	1	3	7500-10000	4-8	Single	1	20	Low	0	5e+04
1215	5923	1237	12145	1237	13234	0	3	15000+	4-8	Single	4	24	Low	3	5e+04
1267	7221	0	12361	0	14548	0	2	15000+	24-33	Single	2	47	High	0	3e+05
1277	2649	448	18733	448	19781	1	3	10000-15000	0-3	Single	2	19	Low	0	5e+04
1312	764	0	10405	0	12441	0	2	7500-10000	4-8	Single	2	22	Low	0	1e+05
1317	8409	0	10260	0	12469	0	2	7500-10000	4-8	Single	3	22	Low	0	5e+04
1332	2437	56584	10260	56584	12469	0	2	7500-10000	4-8	Single	3	21	Low	0	1e+05
1334	3004	4407	12021	4407	13036	1	2	7500-10000	4-8	Single	1	24	High	0	3e+05
1375	4114	0	9357	0	13041	0	1	15000+	0-3	Single	3	19	Low	0	5e+05
1430	4182	0	9441	0	12234	0	1	0-7500	0-3	Single	2	19	Low	0	1e+05
1442	196	11	16418	11	19940	0	3	15000+	0-3	Single	3	19	High	0	1e+05
1462	6432	11873	29178	11873	29595	3	1	10000-15000	34-43	Single	2	54	High	0	1e+05
1464	2561	0	11237	0	12402	1	2	7500-10000	4-8	Single	2	24	Medium	0	1e+05
1543	13719	519	11917	519	13900	0	2	10000-15000	4-8	Single	3	22	Low	0	3e+05
1672	8125	0	13335	0	13699	1	2	0-7500	4-8	Single	1	21	Low	0	1e+05
1678	13775	12897	15338	12897	19075	0	2	15000+	0-3	Single	2	19	High	0	1e+05
1694	7524	0	11656	0	12655	0	2	10000-15000	4-8	Single	4	21	Low	0	1e+05
1716	13708	100000	11131	182708	13077	0	2	7500-10000	4-8	Single	1	24	Low	1	3e+05
1721	11192	2011	17257	2011	18966	1	2	10000-15000	0-3	Single	2	19	Low	0	5e+04
1739	10845	86590	10100	86590	12859	0	1	0-7500	0-3	Single	1	19	Low	0	5e+05
1765	5484	34592	13963	34592	14532	1	2	10000-15000	4-8	Single	1	22	Low	0	3e+05
1807	11300	10656	13472	10656	15244	0	3	15000+	4-8	Single	1	20	Medium	0	5e+04
1829	13317	86946	15979	86946	19024	0	2	10000-15000	0-3	Single	2	19	Low	0	1e+05
1843	9209	313	16057	313	18154	0	3	15000+	0-3	Single	4	19	Low	0	3e+05
1867	8501	100000	9844	159187	16772	1	1	0-7500	64-73	Married	1	84	Low	0	5e+05
1895	12963	0	8445	0	17062	0	1	15000+	64-73	Married	3	85	High	0	5e+04
2008	14190	0	12529	0	13862	1	2	15000+	4-8	Single	2	23	High	0	1e+05
2046	1256	69141	11188	69141	12688	0	2	15000+	4-8	Single	4	24	Low	0	1e+05
2050	8006	3811	13600	3811	14458	1	3	15000+	4-8	Single	2	22	Low	2	3e+05
2069	7881	120	12084	120	13639	0	3	7500-10000	4-8	Single	1	20	Low	0	5e+04
2075	4150	1203	12594	1203	14503	0	3	15000+	4-8	Single	2	24	Low	0	5e+04
2138	14961	66620	25309	66620	25609	3	1	10000-15000	4-8	Single	2	23	Medium	0	3e+05
2195	4739	978	11601	978	13905	0	2	15000+	4-8	Single	2	24	Low	0	1e+05
2209	1479	57116	13120	57116	14465	0	3	10000-15000	4-8	Single	2	20	Low	0	5e+04
2221	510	4897	12411	4897	14616	0	2	15000+	4-8	Single	1	23	Low	0	1e+05
2256	652	10002	12298	10002	13678	0	2	0-7500	24-33	Single	2	48	High	0	5e+04
2342	13622	35384	12145	35384	13234	0	3	15000+	4-8	Single	4	22	Low	0	3e+05
2352	4571	0	7408	0	13898	0	1	7500-10000	64-73	Married	4	85	Low	0	5e+04
2377	11124	0	10527	0	12967	1	1	10000-15000	0-3	Single	3	19	Low	0	5e+04
2385	1659	6418	13404	6418	14333	0	3	0-7500	4-8	Single	1	21	Low	1	5e+04
2391	7753	0	9105	0	12236	0	1	7500-10000	0-3	Single	1	19	High	0	1e+05
2419	1040	20636	13120	20636	14465	0	3	10000-15000	4-8	Single	2	20	Low	0	1e+05
2430	8616	0	8217	0	16009	0	1	7500-10000	64-73	Married	1	85	Low	0	1e+05
2439	9308	0	9441	0	12234	0	1	0-7500	0-3	Single	2	19	Low	0	1e+05
2514	2666	100000	11131	161465	13077	0	2	7500-10000	4-8	Single	1	24	High	0	3e+05
2534	597	13963	11601	13963	13905	0	2	15000+	4-8	Single	2	22	High	0	5e+04
2569	5574	17985	16480	17985	17879	1	2	0-7500	0-3	Single	2	19	Medium	0	1e+05
2580	8202	0	12086	0	13868	0	2	10000-15000	4-8	Single	2	22	Low	1	5e+04
2607	11909	83351	15979	83351	19024	0	2	10000-15000	0-3	Single	2	19	Medium	0	3e+05
2663	1983	55344	15158	55344	15157	1	3	10000-15000	4-8	Single	1	21	Medium	0	5e+04
2672	5138	11482	12930	11482	14577	0	2	10000-15000	4-8	Single	1	21	Medium	0	5e+04
2695	9013	1186	18557	1186	20856	0	3	10000-15000	0-3	Single	1	19	Medium	0	1e+05
2703	2156	7828	17346	7828	19842	0	3	10000-15000	0-3	Single	2	19	Low	0	5e+05
2742	9117	0	10607	0	14366	2	1	15000+	0-3	Single	4	19	Medium	0	5e+04
2747	5175	259	10576	259	13640	0	1	10000-15000	0-3	Single	1	19	Medium	1	1e+05
2750	11370	8657	16408	8657	20050	0	2	15000+	0-3	Single	1	19	Medium	0	1e+05
2781	12112	125	12188	125	14581	0	2	15000+	24-33	Single	3	48	Low	0	1e+05
2794	12111	919	12529	919	13862	1	2	15000+	4-8	Single	2	20	Medium	0	1e+05
2799	10404	1619	11131	1619	13077	0	2	7500-10000	4-8	Single	1	22	Low	0	5e+04
2805	8348	4499	14169	4499	14420	1	3	10000-15000	4-8	Single	2	20	Low	0	5e+04
2813	14580	48898	13120	48898	14465	0	3	10000-15000	4-8	Single	2	20	High	0	1e+05
2835	500	1572	12145	1572	13234	0	3	15000+	4-8	Single	4	21	Low	0	1e+05
2837	7811	5739	12930	5739	14577	0	2	10000-15000	4-8	Single	1	23	Low	0	5e+05
2880	2538	61905	15893	61905	17883	1	2	7500-10000	0-3	Single	1	19	Low	0	3e+05
2883	8321	0	11917	0	13900	0	2	10000-15000	4-8	Single	3	21	Low	0	3e+05
2893	13736	0	11656	0	12655	0	2	10000-15000	4-8	Single	4	22	Low	0	1e+05
2934	4897	32317	12418	32317	14536	0	3	15000+	4-8	Single	3	22	Low	1	5e+05
2937	9728	0	12930	0	14577	0	2	10000-15000	4-8	Single	1	22	Low	0	1e+05
2946	270	2195	12198	2195	12936	1	3	7500-10000	4-8	Single	2	24	Low	0	1e+05
2951	8297	123	11381	123	13103	0	2	0-7500	4-8	Single	3	20	Medium	0	5e+04
3039	8516	0	11860	0	13681	0	2	7500-10000	24-33	Single	1	40	Low	0	1e+05
3067	117	120	15382	120	15745	1	3	0-7500	34-43	Single	3	50	Medium	0	5e+04
3220	11693	120	13049	120	13597	1	3	7500-10000	4-8	Single	1	21	Medium	0	5e+04
3259	2938	9395	11381	9395	13103	0	2	0-7500	4-8	Single	3	21	Medium	0	1e+05
3260	12920	0	13052	0	13826	1	2	10000-15000	4-8	Single	2	24	Medium	0	5e+04
3271	10132	2473	15756	2473	19067	0	2	10000-15000	0-3	Single	3	19	Low	0	5e+05
3314	6202	5752	14549	5752	15197	1	3	15000+	4-8	Single	1	24	Medium	0	5e+04
3351	11006	1468	12930	1468	14577	0	2	10000-15000	4-8	Single	1	21	Low	0	1e+05
3359	5342	0	16250	0	17920	1	2	0-7500	0-3	Single	3	19	Medium	0	1e+05
3361	13104	100000	13052	158223	13826	1	2	10000-15000	4-8	Single	2	23	Low	1	5e+05
3399	11887	1396	13565	1396	17105	0	2	7500-10000	0-3	Single	3	19	Medium	0	3e+05
3408	14848	0	15893	0	17883	1	2	7500-10000	0-3	Single	1	19	Low	0	5e+05
3452	11557	0	11131	0	13077	0	2	7500-10000	4-8	Single	1	20	Low	0	3e+05
3459	439	332	14169	332	14420	1	3	10000-15000	4-8	Single	2	22	Low	0	5e+04
3478	10667	0	11618	0	13193	2	2	15000+	14-23	Single	1	31	Low	1	5e+04
3493	10012	218	12937	218	14497	0	3	10000-15000	4-8	Single	3	23	Low	0	5e+04
3504	1133	0	10100	0	12859	0	1	0-7500	0-3	Single	1	19	Low	0	1e+05
3508	9009	5926	14036	5926	15204	0	3	10000-15000	4-8	Single	1	22	Low	0	3e+05
3530	14261	1595	12198	1595	12936	1	3	7500-10000	4-8	Single	2	23	Low	0	1e+05
3552	4206	6978	10405	6978	12441	0	2	7500-10000	4-8	Single	2	21	Low	0	5e+04
3553	13983	11663	11601	11663	13905	0	2	15000+	4-8	Single	2	21	Low	0	3e+05
3556	8072	6107	12937	6107	14497	0	3	10000-15000	4-8	Single	3	20	Low	0	5e+04
3571	4321	37345	14476	37345	14289	1	3	0-7500	4-8	Single	1	24	Low	0	5e+04
3578	8492	168	12291	168	13063	1	2	0-7500	4-8	Single	3	24	Low	0	1e+05
3599	13195	0	8874	0	14560	1	1	0-7500	64-73	Married	4	82	Medium	0	5e+05
3611	4939	3765	11917	3765	13900	0	2	10000-15000	4-8	Single	3	20	High	0	5e+04
3662	6891	28895	11237	28895	12402	1	2	7500-10000	4-8	Single	2	20	Medium	0	5e+04
3682	13487	0	10100	0	12859	0	1	0-7500	0-3	Single	1	19	High	0	1e+05
3723	5129	0	8564	0	17024	0	1	15000+	64-73	Married	2	87	Medium	2	1e+05
3748	6740	0	9886	0	12977	0	1	10000-15000	0-3	Single	2	19	Medium	0	5e+05
3753	6383	0	12082	0	12649	1	2	15000+	4-8	Single	4	20	Medium	0	1e+05
3780	1427	1292	12198	1292	12936	1	3	7500-10000	4-8	Single	2	21	Low	0	5e+04
3884	6450	0	11860	0	13681	0	2	7500-10000	24-33	Single	1	41	Low	0	5e+04
3907	7522	159	11601	159	13905	0	2	15000+	4-8	Single	2	24	Low	1	5e+04
3928	11576	71121	13757	71121	17066	0	2	7500-10000	0-3	Single	2	19	Low	0	3e+05
4000	9093	425	10405	425	12441	0	2	7500-10000	4-8	Single	2	22	Low	0	5e+04
4117	1272	6650	12418	6650	14536	0	3	15000+	4-8	Single	3	22	Low	0	5e+04
4125	2457	0	9441	0	12234	0	1	0-7500	0-3	Single	2	19	Low	0	5e+05
4125	10958	0	8402	0	16042	0	1	0-7500	64-73	Married	3	86	Medium	0	5e+04
4167	369	0	13776	0	15251	0	2	10000-15000	24-33	Single	1	43	Low	0	5e+04
4168	8803	34433	13600	34433	14458	1	3	15000+	4-8	Single	2	22	Low	0	3e+05
4174	6845	667	11080	667	12430	1	2	7500-10000	4-8	Single	3	23	High	0	5e+04
4183	11341	0	9886	0	12977	0	1	10000-15000	0-3	Single	2	19	Medium	0	1e+05
4229	898	1765	13472	1765	15244	0	3	15000+	4-8	Single	1	21	Low	0	1e+05
4231	5690	11909	11917	11909	13900	0	2	10000-15000	4-8	Single	3	21	Medium	0	5e+04
4297	4617	120	12084	120	13639	0	3	7500-10000	4-8	Single	1	20	Medium	1	5e+04
4336	5452	956	12348	956	13742	0	2	0-7500	4-8	Single	1	23	Low	1	5e+04
4383	6201	66169	13472	66169	15244	0	3	15000+	4-8	Single	1	20	Low	0	5e+05
4401	5179	538	17722	538	19662	0	3	0-7500	0-3	Single	1	19	Low	0	5e+04
4472	5801	0	11237	0	12402	1	2	7500-10000	4-8	Single	2	24	High	0	5e+04
4483	9338	218	12021	218	13036	1	2	7500-10000	4-8	Single	1	21	Low	0	1e+05
4508	1073	1122	9309	1122	12261	0	1	0-7500	0-3	Single	3	19	Medium	0	1e+05
4508	14369	7278	10260	7278	12469	0	2	7500-10000	4-8	Single	3	21	Medium	0	3e+05
4541	8541	5090	14717	5090	16365	0	2	0-7500	0-3	Single	4	19	Medium	0	1e+05
4605	6611	1846	12348	1846	13742	0	2	0-7500	4-8	Single	1	22	High	0	5e+04
4639	1239	59700	12465	59700	13033	1	2	0-7500	4-8	Single	2	20	Low	0	5e+04
4689	10598	198	11381	198	13103	0	2	0-7500	4-8	Single	3	20	Medium	0	3e+05
4715	14591	4315	16728	4315	18106	0	3	10000-15000	0-3	Single	4	19	Low	0	1e+05
4754	7724	4044	9886	4044	12977	0	1	10000-15000	0-3	Single	2	19	High	0	5e+05
4764	9322	52649	12084	52649	13639	0	3	7500-10000	4-8	Single	1	24	Low	0	3e+05
4786	5468	19316	12465	19316	13033	1	2	0-7500	4-8	Single	2	24	Low	0	5e+04
4790	8389	1336	12529	1336	13862	1	2	15000+	4-8	Single	2	24	Low	0	5e+05
4794	228	88420	12086	88420	13868	0	2	10000-15000	4-8	Single	2	21	Medium	0	1e+05
4841	14397	120	12418	120	14536	0	3	15000+	4-8	Single	3	21	Low	0	5e+04
4873	11193	354	13813	354	16818	2	2	10000-15000	4-8	Single	3	23	Low	0	5e+04
4882	13981	1062	10405	1062	12441	0	2	7500-10000	4-8	Single	2	23	Low	1	1e+05
4889	6305	120	14169	120	14420	1	3	10000-15000	4-8	Single	2	21	Low	0	5e+04
4936	10081	0	8217	0	16009	0	1	7500-10000	64-73	Married	1	85	Medium	0	3e+05
4960	419	286	13258	286	16863	2	2	15000+	4-8	Single	3	23	Low	0	3e+05
4964	12979	104	11188	104	12688	0	2	15000+	4-8	Single	4	23	Low	0	1e+05
4965	9470	0	12529	0	13862	1	2	15000+	4-8	Single	2	23	High	0	1e+05
4972	6998	312	10260	312	12469	0	2	7500-10000	4-8	Single	3	23	Low	0	5e+04
5005	14321	2416	12930	2416	14577	0	2	10000-15000	4-8	Single	1	23	Medium	0	3e+05
5055	9891	192	13472	192	15244	0	3	15000+	4-8	Single	1	20	Medium	0	5e+04
5100	5607	7114	12348	7114	13742	0	2	0-7500	4-8	Single	1	22	High	0	3e+05
5103	10672	523	11917	523	13900	0	2	10000-15000	4-8	Single	3	20	Medium	0	5e+04
5110	4923	8709	11439	8709	13937	0	2	15000+	4-8	Single	3	23	Medium	0	5e+04
5111	4085	2789	11188	2789	12688	0	2	15000+	4-8	Single	4	23	Low	0	1e+05
5124	1262	155	13713	155	14497	1	2	10000-15000	24-33	Single	3	42	Low	0	5e+04
5146	7526	0	11973	0	12976	1	2	7500-10000	24-33	Single	2	44	High	0	5e+04
5148	8114	52811	9879	52811	12588	2	1	10000-15000	24-33	Single	1	40	High	0	1e+05
5193	14919	568	13664	568	13158	1	3	10000-15000	4-8	Single	4	21	Low	0	5e+05
5248	2755	0	11131	0	13077	0	2	7500-10000	4-8	Single	1	24	Medium	0	1e+05
5248	12586	0	10527	0	12967	1	1	10000-15000	0-3	Single	3	19	High	0	1e+05
5269	4392	28970	12901	28970	13013	1	2	15000+	34-43	Married	1	58	High	0	3e+05
5277	6221	24807	12084	24807	13639	0	3	7500-10000	4-8	Single	1	22	Low	0	3e+05
5310	892	50138	16325	50138	18851	0	2	0-7500	0-3	Single	1	19	High	0	3e+05
5410	10087	121	11946	121	13053	0	2	15000+	34-43	Married	1	57	Medium	0	5e+04
5415	11472	46	11131	46	13077	0	2	7500-10000	4-8	Single	1	21	Low	0	1e+05
5462	9445	29569	17812	29569	20912	0	3	15000+	0-3	Single	1	19	Medium	0	5e+04
5476	3788	1124	10576	1124	13640	0	1	10000-15000	0-3	Single	1	19	High	0	1e+05
5497	5881	9562	12411	9562	14616	0	2	15000+	4-8	Single	1	22	Low	0	5e+04
5552	1695	49555	11325	49555	12891	2	2	10000-15000	9-13	Single	2	28	Low	1	1e+05
5574	8878	46	12594	46	14503	0	3	15000+	4-8	Single	2	22	Low	0	1e+05
5593	12713	0	10576	0	13640	0	1	10000-15000	0-3	Single	1	19	High	0	3e+05
5595	12742	2388	13267	2388	15573	0	2	7500-10000	0-3	Single	4	19	Low	0	1e+05
5646	10191	100000	8564	213238	17024	0	1	15000+	64-73	Married	2	86	High	0	3e+05
5675	3865	6629	11542	6629	13074	0	2	0-7500	4-8	Single	2	23	Medium	0	5e+04
5712	6203	2047	13963	2047	14532	1	2	10000-15000	4-8	Single	1	23	Low	0	3e+05
5717	11564	123	12594	123	14503	0	3	15000+	4-8	Single	2	20	Low	0	5e+04
5723	12765	63774	12529	63774	13862	1	2	15000+	4-8	Single	2	22	Low	0	1e+05
5787	8587	51839	10870	51839	12926	2	2	15000+	9-13	Single	2	29	Medium	0	5e+05
5790	13476	1480	13120	1480	14465	0	3	10000-15000	4-8	Single	2	23	Low	0	5e+04
5823	12546	0	11422	0	13598	1	1	10000-15000	0-3	Single	1	19	Low	0	1e+05
5834	2271	100000	17094	161363	19997	0	2	10000-15000	0-3	Single	1	19	Low	0	5e+05
5838	13063	5850	14549	5850	15197	1	3	15000+	4-8	Single	1	20	Low	1	5e+04
5843	3376	391	11439	391	13937	0	2	15000+	4-8	Single	3	22	Low	0	1e+05
5849	2876	0	10405	0	12441	0	2	7500-10000	4-8	Single	2	24	Low	0	5e+05
5856	6237	30591	17104	30591	19887	0	3	10000-15000	0-3	Single	3	19	Low	2	1e+05
5864	727	26479	11295	26479	12976	0	3	7500-10000	4-8	Single	2	20	Medium	0	1e+05
5890	7990	221	11917	221	13900	0	2	10000-15000	4-8	Single	3	24	Low	0	3e+05
5908	12542	35636	14717	35636	17938	0	2	7500-10000	0-3	Single	1	19	Low	0	3e+05
5953	11819	5587	14717	5587	17938	0	2	7500-10000	0-3	Single	1	19	Low	0	3e+05
6005	7451	6739	13472	6739	15244	0	3	15000+	4-8	Single	1	23	Low	0	1e+05
6005	13460	49502	12594	49502	14503	0	3	15000+	4-8	Single	2	24	Low	0	5e+04
6011	10541	2764	11946	2764	13053	0	2	15000+	34-43	Married	1	55	Medium	0	5e+04
6015	13687	15467	11188	15467	12688	0	2	15000+	4-8	Single	4	23	Low	0	1e+05
6041	1992	29149	11131	29149	13077	0	2	7500-10000	4-8	Single	1	23	Medium	0	5e+05
6052	14654	0	12878	0	14509	0	2	10000-15000	24-33	Single	2	40	Low	0	5e+04
6055	13899	121	14549	121	15197	1	3	15000+	4-8	Single	1	21	Low	0	5e+05
6062	2351	71310	15976	71310	18710	0	3	7500-10000	0-3	Single	1	19	Low	0	3e+05
6087	13494	30654	13403	30654	14571	1	2	15000+	4-8	Single	1	21	Low	0	1e+05
6098	4698	42055	13403	42055	14571	1	2	15000+	4-8	Single	1	21	High	0	3e+05
6120	8243	14315	13410	14315	14491	1	3	15000+	4-8	Single	3	22	Low	0	5e+04
6141	7120	0	10100	0	12859	0	1	0-7500	0-3	Single	1	19	Low	0	5e+04
6162	11748	2919	15338	2919	19075	0	2	15000+	0-3	Single	2	19	Medium	0	1e+05
6169	12711	1791	12930	1791	14577	0	2	10000-15000	4-8	Single	1	20	Low	0	3e+05
6176	295	130	13472	130	15244	0	3	15000+	4-8	Single	1	21	Low	0	5e+04
6196	12821	2958	17104	2958	19887	0	3	10000-15000	0-3	Single	3	19	Low	0	5e+04
6217	12059	0	10260	0	12469	0	2	7500-10000	4-8	Single	3	20	High	0	5e+04
6238	5600	12904	14725	12904	17840	0	3	7500-10000	0-3	Single	3	19	High	0	5e+04
6242	9168	70826	12021	70826	13036	1	2	7500-10000	4-8	Single	1	22	Low	0	3e+05
6272	13758	120	9357	120	13041	0	1	15000+	0-3	Single	3	19	High	0	5e+04
6278	5967	121	11917	121	13900	0	2	10000-15000	4-8	Single	3	20	Medium	0	1e+05
6280	14265	5540	11656	5540	12655	0	2	10000-15000	4-8	Single	4	23	Medium	0	5e+04
6288	7510	0	9309	0	12261	0	1	0-7500	0-3	Single	3	19	Medium	0	1e+05
6297	9079	11	13739	11	16063	0	2	10000-15000	34-43	Single	3	51	High	0	3e+05
6304	12219	14774	11542	14774	13074	0	2	0-7500	4-8	Single	2	20	High	0	5e+04
6337	11570	0	9441	0	12234	0	1	0-7500	0-3	Single	2	19	High	0	5e+04
6411	4113	78368	22891	78368	24089	3	1	7500-10000	24-33	Single	3	41	Medium	0	3e+05
6432	10368	51087	11131	51087	13077	0	2	7500-10000	4-8	Single	1	22	Low	0	5e+05
6434	585	0	16408	0	20050	0	2	15000+	0-3	Single	1	19	Medium	0	1e+05
6465	10441	32231	15976	32231	18710	0	3	7500-10000	0-3	Single	1	19	Medium	0	5e+04
6496	4681	0	11601	0	13905	0	2	15000+	4-8	Single	2	24	Medium	0	3e+05
6540	791	24447	11656	24447	12655	0	2	10000-15000	4-8	Single	4	23	Low	0	5e+04
6592	11802	23526	17722	23526	19662	0	3	0-7500	0-3	Single	1	19	Low	0	5e+04
6613	10270	211	8217	211	14605	0	1	0-7500	64-73	Married	4	85	High	0	5e+04
6657	7155	120	11542	120	13074	0	2	0-7500	4-8	Single	2	20	Low	0	5e+05
6686	6166	0	13162	0	14536	1	2	15000+	24-33	Single	3	40	Medium	0	5e+05
6693	424	19488	17346	19488	19842	0	3	10000-15000	0-3	Single	2	19	Low	0	5e+04
6700	7941	0	12348	0	13742	0	2	0-7500	4-8	Single	1	20	Medium	0	5e+04
6727	9705	969	17094	969	19997	0	2	10000-15000	0-3	Single	1	19	Low	0	1e+05
6733	10312	22448	12465	22448	13033	1	2	0-7500	4-8	Single	2	21	Low	0	5e+05
6745	4117	17711	12529	17711	13862	1	2	15000+	4-8	Single	2	23	Low	0	5e+04
6746	6257	1974	12653	1974	13199	0	3	10000-15000	4-8	Single	4	24	Low	0	5e+04
6750	219	12869	10405	12869	12441	0	2	7500-10000	4-8	Single	2	24	Low	0	5e+05
6803	831	0	11080	0	12430	1	2	7500-10000	4-8	Single	3	20	Low	0	1e+05
6811	1602	164	16650	164	19895	0	3	15000+	0-3	Single	2	19	Low	0	5e+04
6846	11697	52914	12411	52914	14616	0	2	15000+	4-8	Single	1	23	Low	0	5e+04
6881	14165	309	10380	309	12241	0	2	15000+	44-53	Married	2	65	High	0	3e+05
6892	7452	15066	11131	15066	13077	0	2	7500-10000	4-8	Single	1	22	Low	0	3e+05
6900	14871	25951	15260	25951	17934	0	2	0-7500	0-3	Single	2	19	Low	0	5e+05
6902	12548	4021	13404	4021	14333	0	3	0-7500	4-8	Single	1	24	Medium	0	5e+04
6933	1131	205	15615	205	18445	2	3	15000+	4-8	Single	1	24	Low	0	1e+05
6935	9680	140	17104	140	19887	0	3	10000-15000	0-3	Single	3	19	Low	0	5e+04
6946	619	3619	12348	3619	13742	0	2	0-7500	4-8	Single	1	23	Low	0	1e+05
6962	9846	294	12411	294	14616	0	2	15000+	4-8	Single	1	24	Low	0	5e+04
6978	11740	0	8899	0	12063	2	1	15000+	4-8	Single	1	20	Low	0	5e+05
6985	11258	161	11131	161	13077	0	2	7500-10000	4-8	Single	1	24	Low	0	5e+04
6997	14301	1156	12145	1156	13234	0	3	15000+	4-8	Single	4	23	Low	0	5e+04
7017	9996	1000	12418	1000	14536	0	3	15000+	4-8	Single	3	20	Medium	0	3e+05
7046	1861	3373	14036	3373	15204	0	3	10000-15000	4-8	Single	1	20	Medium	0	1e+05
7050	2568	129	11917	129	13900	0	2	10000-15000	4-8	Single	3	24	Low	0	1e+05
7064	2000	92081	17720	92081	19988	1	2	15000+	0-3	Single	1	19	Low	0	5e+05
7072	12291	0	8521	0	16006	0	1	0-7500	64-73	Married	2	86	Medium	0	5e+04
7090	8087	40238	12411	40238	14616	0	2	15000+	4-8	Single	1	23	Low	0	3e+05
7099	3962	197	12348	197	13742	0	2	0-7500	4-8	Single	1	24	Low	0	5e+04
7121	12430	0	11131	0	13077	0	2	7500-10000	4-8	Single	1	22	Low	0	5e+04
7130	12123	4936	10908	4936	12819	1	1	0-7500	0-3	Single	1	19	Low	0	5e+04
7140	10714	22940	11188	22940	12688	0	2	15000+	4-8	Single	4	20	Low	0	3e+05
7179	4028	2541	11601	2541	13905	0	2	15000+	4-8	Single	2	22	Low	0	5e+04
7181	7580	13249	11656	13249	12655	0	2	10000-15000	4-8	Single	4	23	Low	0	1e+05
7189	3126	33126	12021	33126	13036	1	2	7500-10000	4-8	Single	1	24	Low	0	1e+05
7191	4509	9654	11656	9654	12655	0	2	10000-15000	4-8	Single	4	24	Low	0	1e+05
7208	14150	5554	17104	5554	19887	0	3	10000-15000	0-3	Single	3	19	Low	0	5e+04
7218	14459	0	10405	0	12441	0	2	7500-10000	4-8	Single	2	20	Low	0	1e+05
7229	9803	3986	11576	3986	12704	2	3	0-7500	9-13	Single	3	26	Medium	0	5e+04
7250	315	495	9545	495	17846	0	1	10000-15000	64-73	Married	1	87	Low	0	5e+04
7251	7356	1746	17057	1746	21705	2	2	7500-10000	0-3	Single	1	19	Medium	0	1e+05
7252	5256	11685	11828	11685	14410	0	2	7500-10000	34-43	Single	3	51	Medium	0	3e+05
7312	9446	681	12354	681	13894	1	2	15000+	4-8	Single	3	23	Low	0	3e+05
7316	5127	5619	12021	5619	13036	1	2	7500-10000	4-8	Single	1	21	Medium	0	1e+05
7362	2346	0	14235	0	15881	0	2	0-7500	34-43	Single	1	50	High	0	5e+04
7363	12882	306	14549	306	15197	1	3	15000+	4-8	Single	1	24	Low	0	5e+04
7377	11567	11085	13120	11085	14465	0	3	10000-15000	4-8	Single	2	20	Low	0	1e+05
7379	14373	3222	12145	3222	13234	0	3	15000+	4-8	Single	4	20	Low	0	5e+04
7391	4191	437	11601	437	13905	0	2	15000+	4-8	Single	2	22	Medium	0	5e+05
7415	4511	2075	13403	2075	14571	1	2	15000+	4-8	Single	1	21	High	0	5e+04
7425	8870	241	17812	241	20912	0	3	15000+	0-3	Single	1	19	Low	0	5e+04
7431	9742	65	14036	65	15204	0	3	10000-15000	4-8	Single	1	20	Low	0	3e+05
7445	12519	179	11295	179	12976	0	3	7500-10000	4-8	Single	2	20	Low	0	5e+04
7452	4558	0	12411	0	14616	0	2	15000+	4-8	Single	1	21	High	0	1e+05
7485	6122	0	11629	0	13586	2	2	15000+	9-13	Single	1	29	High	0	5e+04
7493	3007	1550	13971	1550	14453	1	3	10000-15000	4-8	Single	3	22	Medium	0	1e+05
7503	7825	0	13281	0	13636	1	2	0-7500	24-33	Single	2	44	High	0	5e+04
7511	9964	1506	11188	1506	12688	0	2	15000+	4-8	Single	4	21	Low	0	1e+05
7587	10272	11231	12145	11231	13234	0	3	15000+	4-8	Single	4	21	Low	0	5e+04
7600	2381	102	12587	102	12616	1	2	10000-15000	4-8	Single	4	23	Medium	0	1e+05
7633	14750	120	11891	120	12408	1	2	15000+	34-43	Married	3	53	Low	0	5e+04
7677	8694	0	11656	0	12655	0	2	10000-15000	4-8	Single	4	22	High	0	1e+05
7694	732	0	12529	0	13862	1	2	15000+	4-8	Single	2	20	Low	0	5e+04
7699	7523	0	9441	0	12234	0	1	0-7500	0-3	Single	2	19	Low	0	1e+05
7729	4147	0	7574	0	15265	0	1	7500-10000	64-73	Married	3	80	High	0	5e+05
7756	3638	1590	11080	1590	12430	1	2	7500-10000	4-8	Single	3	23	Low	0	1e+05
7765	2392	330	12348	330	13742	0	2	0-7500	4-8	Single	1	22	Low	0	1e+05
7788	3302	14612	11131	14612	13077	0	2	7500-10000	4-8	Single	1	20	Low	0	1e+05
7789	14978	142	12411	142	14616	0	2	15000+	4-8	Single	1	20	High	0	3e+05
7804	1275	5496	10196	5496	12196	1	1	0-7500	0-3	Single	2	19	Low	0	1e+05
7817	8502	49772	14169	49772	14420	1	3	10000-15000	4-8	Single	2	24	Low	0	5e+05
7862	9438	0	12419	0	13240	0	2	10000-15000	24-33	Single	4	41	Medium	0	5e+04
7988	13134	3143	12354	3143	13894	1	2	15000+	4-8	Single	3	22	Medium	0	1e+05
8007	5492	244	14934	244	17800	0	3	7500-10000	0-3	Single	2	19	Low	0	5e+04
8015	8116	80	18066	80	18050	1	3	10000-15000	0-3	Single	4	19	Low	0	3e+05
8041	177	2589	8899	2589	12063	2	1	15000+	4-8	Single	1	24	High	0	1e+05
8042	12568	100000	12082	118833	12649	1	2	15000+	4-8	Single	4	23	Medium	0	3e+05
8048	14144	605	10260	605	12469	0	2	7500-10000	4-8	Single	3	21	Low	0	1e+05
8063	3226	45361	13342	45361	13625	1	3	0-7500	4-8	Single	3	21	Low	0	3e+05
8066	8446	1644	13404	1644	14333	0	3	0-7500	4-8	Single	1	20	Low	0	5e+04
8075	7377	4900	12086	4900	13868	0	2	10000-15000	4-8	Single	2	23	Low	0	5e+05
8105	4633	7753	12930	7753	14577	0	2	10000-15000	4-8	Single	1	23	Low	0	3e+05
8140	10640	13863	12937	13863	14497	0	3	10000-15000	4-8	Single	3	20	Medium	0	1e+05
8182	2954	3817	16650	3817	19895	0	3	15000+	0-3	Single	2	19	Low	0	1e+05
8252	14926	1360	12291	1360	13063	1	2	0-7500	4-8	Single	3	20	Medium	0	5e+04
8255	13794	100000	15979	352088	19024	0	2	10000-15000	0-3	Single	2	19	Medium	0	3e+05
8293	520	0	9105	0	12236	0	1	7500-10000	0-3	Single	1	19	Medium	0	5e+05
8294	9700	2188	11439	2188	13937	0	2	15000+	4-8	Single	3	24	Low	0	5e+04
8304	1298	45353	11439	45353	13937	0	2	15000+	4-8	Single	3	22	Low	0	5e+04
8317	1261	14026	12653	14026	13199	0	3	10000-15000	4-8	Single	4	24	Low	0	5e+04
8325	1291	132	12901	132	14435	2	2	0-7500	4-8	Single	4	21	Low	0	3e+05
8384	6393	0	9162	0	17894	0	1	15000+	64-73	Married	1	86	High	0	5e+04
8388	3406	9590	12587	9590	12616	1	2	10000-15000	4-8	Single	4	23	Low	0	1e+05
8390	9658	17089	13776	17089	15251	0	2	10000-15000	24-33	Single	1	42	Low	0	3e+05
8440	8052	791	12594	791	14503	0	3	15000+	4-8	Single	2	24	Low	0	3e+05
8476	4203	48	11917	48	13900	0	2	10000-15000	4-8	Single	3	21	Low	0	5e+04
8484	11792	0	10405	0	12441	0	2	7500-10000	4-8	Single	2	20	Low	0	3e+05
8502	156	41558	15338	41558	19075	0	2	15000+	0-3	Single	2	19	Low	0	1e+05
8554	12913	0	13258	0	16863	2	2	15000+	4-8	Single	3	20	Medium	0	5e+04
8600	5979	0	13509	0	15312	2	2	10000-15000	4-8	Single	4	20	High	0	5e+04
8610	14702	7258	12418	7258	14536	0	3	15000+	4-8	Single	3	24	Medium	0	5e+04
8633	4980	10952	13410	10952	14491	1	3	15000+	4-8	Single	3	20	Low	0	1e+05
8641	12114	48747	8798	48747	17017	0	1	10000-15000	64-73	Married	3	85	High	0	5e+04
8690	12685	125	12445	125	13019	0	2	10000-15000	34-43	Married	1	54	Low	0	5e+04
8692	3259	2648	11131	2648	13077	0	2	7500-10000	4-8	Single	1	23	Medium	0	5e+05
8705	3188	4983	13600	4983	14458	1	3	15000+	4-8	Single	2	20	Low	0	1e+05
8709	3620	8208	16333	8208	19059	1	2	15000+	0-3	Single	3	19	Low	0	3e+05
8748	1877	0	9879	0	12588	2	1	10000-15000	24-33	Single	1	43	Medium	0	5e+05
8757	11135	14867	12594	14867	14503	0	3	15000+	4-8	Single	2	21	Low	0	5e+04
8766	14451	43312	12411	43312	14616	0	2	15000+	4-8	Single	1	21	Medium	0	1e+05
8781	5907	1710	12084	1710	13639	0	3	7500-10000	4-8	Single	1	22	Medium	0	1e+05
8811	8022	0	10553	0	14806	2	1	7500-10000	0-3	Single	1	19	High	0	5e+05
8817	4261	31555	10260	31555	12469	0	2	7500-10000	4-8	Single	3	23	Low	0	5e+04
8837	3954	126	11295	126	12976	0	3	7500-10000	4-8	Single	2	20	Medium	0	1e+05
8845	2482	823	16250	823	17920	1	2	0-7500	0-3	Single	3	19	Medium	0	3e+05
8872	11047	168	16728	168	18106	0	3	10000-15000	0-3	Single	4	19	Medium	0	5e+04
8902	5190	0	10815	0	12153	2	2	0-7500	9-13	Single	2	27	Low	0	5e+04
8932	2899	3105	12084	3105	13639	0	3	7500-10000	4-8	Single	1	24	Low	0	3e+05
8944	14946	100000	12021	122399	13036	1	2	7500-10000	4-8	Single	1	24	Low	0	5e+05
8948	3371	155	9879	155	12588	2	1	10000-15000	24-33	Single	1	41	High	0	5e+04
9039	7910	138	11917	138	13900	0	2	10000-15000	4-8	Single	3	20	Low	0	5e+04
9045	14057	4260	15756	4260	19067	0	2	10000-15000	0-3	Single	3	19	Low	0	1e+05
9071	6868	640	12083	640	12442	0	3	0-7500	4-8	Single	4	20	Low	0	5e+04
9090	1308	100000	10963	117192	13635	1	1	15000+	0-3	Single	1	19	Medium	0	3e+05
9111	11778	129	14549	129	15197	1	3	15000+	4-8	Single	1	20	Low	0	1e+05
9133	11486	0	16333	0	19059	1	2	15000+	0-3	Single	3	19	Low	0	1e+05
9135	859	81268	11439	81268	13937	0	2	15000+	4-8	Single	3	20	Low	0	1e+05
9181	12917	4282	12901	4282	13013	1	2	15000+	34-43	Married	1	59	Medium	0	5e+05
9191	8868	51386	13403	51386	14571	1	2	15000+	4-8	Single	1	24	Low	0	5e+05
9241	1134	0	9886	0	12977	0	1	10000-15000	0-3	Single	2	19	High	0	5e+04
9245	2267	8533	12082	8533	12649	1	2	15000+	4-8	Single	4	24	Medium	0	5e+04
9274	4293	386	12465	386	13033	1	2	0-7500	4-8	Single	2	21	Medium	0	5e+04
9279	11598	777	15976	777	18710	0	3	7500-10000	0-3	Single	1	19	Low	0	1e+05
9292	12383	41523	12411	41523	14616	0	2	15000+	4-8	Single	1	21	Low	0	5e+05
9347	3168	56744	11131	56744	13077	0	2	7500-10000	4-8	Single	1	21	High	0	5e+04
9392	8751	120	11885	120	12273	0	2	0-7500	34-43	Married	1	52	Low	0	5e+04
9415	6070	100000	13049	154284	13597	1	3	7500-10000	4-8	Single	1	23	Medium	0	5e+05
9423	1987	419	12411	419	14616	0	2	15000+	4-8	Single	1	20	High	0	1e+05
9441	9025	3652	11542	3652	13074	0	2	0-7500	4-8	Single	2	21	Medium	0	5e+04
9476	12148	0	9441	0	12234	0	1	0-7500	0-3	Single	2	19	Medium	0	5e+05
9580	11269	365	12348	365	13742	0	2	0-7500	4-8	Single	1	24	Low	0	5e+05
9590	4692	898	10105	898	13001	1	1	15000+	0-3	Single	3	19	Low	0	3e+05
9594	12399	95	15047	95	17975	0	2	0-7500	0-3	Single	3	19	Low	0	1e+05
9619	11591	2336	10405	2336	12441	0	2	7500-10000	4-8	Single	2	24	Medium	0	5e+04
9689	742	6675	11237	6675	12402	1	2	7500-10000	4-8	Single	2	20	Medium	0	3e+05
9715	12673	43871	11656	43871	12655	0	2	10000-15000	4-8	Single	4	20	Low	0	3e+05
9742	5064	15991	15158	15991	15157	1	3	10000-15000	4-8	Single	1	23	Low	0	5e+04
9760	1681	1317	13472	1317	15244	0	3	15000+	4-8	Single	1	20	Low	0	3e+05
9774	5269	55828	13963	55828	14532	1	2	10000-15000	4-8	Single	1	22	Low	0	1e+05
9792	5157	1282	12529	1282	13862	1	2	15000+	4-8	Single	2	24	Medium	0	1e+05
9807	13788	0	9357	0	13041	0	1	15000+	0-3	Single	3	19	High	0	5e+05
9812	10772	49534	16334	49534	18748	0	3	0-7500	0-3	Single	3	19	Medium	0	5e+05
9827	10045	18154	13120	18154	14465	0	3	10000-15000	4-8	Single	2	20	Medium	0	5e+04
9863	9165	135	11131	135	13077	0	2	7500-10000	4-8	Single	1	23	Low	0	5e+04
9868	12337	14	10718	14	12955	2	2	15000+	9-13	Single	3	27	Low	0	5e+04
9921	11951	6566	11917	6566	13900	0	2	10000-15000	4-8	Single	3	21	Low	0	1e+05
9940	5132	2776	13472	2776	15244	0	3	15000+	4-8	Single	1	22	Low	0	5e+04
9944	13860	0	11048	0	12097	0	2	0-7500	44-53	Married	1	64	Medium	0	3e+05
9991	8572	0	12086	0	13868	0	2	10000-15000	4-8	Single	2	20	High	0	5e+04
10	6386	2312	11295	2312	12976	0	3	7500-10000	4-8	Single	2	20	Low	0	5e+04
155	6927	2199	12082	2199	12649	1	2	15000+	4-8	Single	4	23	Medium	0	5e+05
160	5309	0	12086	0	13868	0	2	10000-15000	4-8	Single	2	21	Medium	0	1e+05
160	11547	46106	12084	46106	13639	0	3	7500-10000	4-8	Single	1	24	Low	0	1e+05
170	1998	3381	14549	3381	15197	1	3	15000+	4-8	Single	1	24	Medium	0	3e+05
199	8392	62945	13776	62945	15251	0	2	10000-15000	24-33	Single	1	45	Low	0	5e+05
222	12590	43549	13404	43549	14333	0	3	0-7500	4-8	Single	1	21	Low	0	5e+04
228	9054	8137	12145	8137	13234	0	3	15000+	4-8	Single	4	22	Low	0	5e+05
234	13829	48829	13052	48829	13826	1	2	10000-15000	4-8	Single	2	21	Low	0	5e+04
253	3009	2115	11601	2115	13905	0	2	15000+	4-8	Single	2	24	Low	0	3e+05
311	2430	24703	11131	24703	13077	0	2	7500-10000	4-8	Single	1	21	Low	0	1e+05
322	2562	0	12833	0	15112	0	2	7500-10000	34-43	Single	1	54	Low	0	5e+04
359	12495	0	11381	0	13103	0	2	0-7500	4-8	Single	3	24	Low	0	5e+05
425	2623	36750	12084	36750	13639	0	3	7500-10000	4-8	Single	1	22	Low	0	1e+05
458	8477	4458	13403	4458	14571	1	2	15000+	4-8	Single	1	21	Low	0	5e+04
466	6452	9569	12594	9569	14503	0	3	15000+	4-8	Single	2	23	Low	0	5e+04
507	5816	37896	11131	37896	13077	0	2	7500-10000	4-8	Single	1	23	Low	0	5e+04
549	11096	94	11601	94	13905	0	2	15000+	4-8	Single	2	23	Medium	0	5e+04
567	5976	20883	11601	20883	13905	0	2	15000+	4-8	Single	2	22	High	0	1e+05
580	9359	0	9202	0	15957	1	1	0-7500	64-73	Married	2	87	Medium	0	3e+05
581	12571	0	13438	0	14624	0	2	10000-15000	34-43	Single	4	58	Low	0	5e+04
584	14769	0	11917	0	13900	0	2	10000-15000	4-8	Single	3	21	Low	0	1e+05
601	9459	106	10430	106	12155	2	2	7500-10000	9-13	Single	1	26	Low	0	5e+04
608	6741	3241	13472	3241	15244	0	3	15000+	4-8	Single	1	22	Low	0	1e+05
660	13300	0	12411	0	14616	0	2	15000+	4-8	Single	1	22	Low	0	3e+05
696	8004	3909	11188	3909	12688	0	2	15000+	4-8	Single	4	22	Low	0	5e+04
719	5937	0	12930	0	14577	0	2	10000-15000	4-8	Single	1	20	Medium	0	5e+04
788	9747	4987	11131	4987	13077	0	2	7500-10000	4-8	Single	1	20	Medium	0	3e+05
806	3380	12762	13410	12762	14491	1	3	15000+	4-8	Single	3	20	Low	0	5e+04
808	14403	404	11188	404	12688	0	2	15000+	4-8	Single	4	20	Low	0	3e+05
852	1798	0	11080	0	12430	1	2	7500-10000	4-8	Single	3	24	Medium	0	5e+04
883	11809	151	11188	151	12688	0	2	15000+	4-8	Single	4	22	Low	0	5e+04
908	5522	0	12411	0	14616	0	2	15000+	4-8	Single	1	24	High	0	3e+05
959	5589	44420	14549	44420	15197	1	3	15000+	4-8	Single	1	22	Medium	0	1e+05
960	9085	0	12870	0	13857	1	2	10000-15000	4-8	Single	3	20	Medium	0	1e+05
992	5507	869	12418	869	14536	0	3	15000+	4-8	Single	3	20	Medium	0	5e+04
1013	10079	15494	12348	15494	13742	0	2	0-7500	4-8	Single	1	22	Low	0	5e+04
1059	1423	0	12411	0	14616	0	2	15000+	4-8	Single	1	23	Medium	0	1e+05
1095	10470	12350	12355	12350	13667	0	3	0-7500	4-8	Single	3	20	Low	0	5e+04
1121	12043	1206	11086	1206	13016	0	2	7500-10000	24-33	Single	2	42	High	0	1e+05
1123	13141	128	14036	128	15204	0	3	10000-15000	4-8	Single	1	22	Low	0	5e+04
1162	12613	535	12930	535	14577	0	2	10000-15000	4-8	Single	1	20	Low	0	5e+04
1167	75	9966	12145	9966	13234	0	3	15000+	4-8	Single	4	21	Medium	0	3e+05
1176	12198	2766	11295	2766	12976	0	3	7500-10000	4-8	Single	2	20	Low	0	1e+05
1196	4300	0	8923	0	16979	0	1	10000-15000	64-73	Married	2	86	Medium	0	3e+05
1214	5681	120	13049	120	13597	1	3	7500-10000	4-8	Single	1	21	Low	0	5e+04
1249	3203	120	11920	120	13275	0	2	15000+	24-33	Single	4	40	Medium	0	5e+04
1256	486	219	13907	219	14465	1	2	10000-15000	24-33	Single	2	45	Medium	0	3e+05
1277	2649	4915	15207	4915	17502	2	3	10000-15000	4-8	Single	2	20	Low	0	5e+04
1312	764	1375	10405	1375	12441	0	2	7500-10000	4-8	Single	2	23	Low	0	1e+05
1350	4734	5837	10405	5837	12441	0	2	7500-10000	4-8	Single	2	22	Medium	0	3e+05
1379	11919	16582	11601	16582	13905	0	2	15000+	4-8	Single	2	23	Low	0	3e+05
1442	196	0	11439	0	13937	0	2	15000+	4-8	Single	3	20	High	0	1e+05
1462	6432	0	9992	0	13228	2	1	10000-15000	34-43	Single	2	55	High	0	1e+05
1493	9315	1592	11860	1592	12481	0	2	0-7500	24-33	Single	4	46	Low	0	1e+05
1517	10042	26476	11381	26476	13103	0	2	0-7500	4-8	Single	3	21	High	0	1e+05
1543	13719	25510	11917	25510	13900	0	2	10000-15000	4-8	Single	3	23	Low	0	3e+05
1672	8125	25870	13335	25870	13699	1	2	0-7500	4-8	Single	1	22	Low	0	1e+05
1678	13775	0	11601	0	13905	0	2	15000+	4-8	Single	2	20	High	0	1e+05
1710	11822	56022	11080	56022	12430	1	2	7500-10000	4-8	Single	3	21	Low	0	1e+05
1721	11192	120	12086	120	13868	0	2	10000-15000	4-8	Single	2	20	Low	0	5e+04
1765	5484	3898	13963	3898	14532	1	2	10000-15000	4-8	Single	1	23	Low	0	3e+05
1807	11300	123	13472	123	15244	0	3	15000+	4-8	Single	1	21	Medium	0	5e+04
1829	13317	16991	13120	16991	14465	0	3	10000-15000	4-8	Single	2	20	Low	0	1e+05
1843	9209	5921	12145	5921	13234	0	3	15000+	4-8	Single	4	20	Low	0	3e+05
1867	8501	0	9844	0	16772	1	1	0-7500	64-73	Married	1	85	Low	0	5e+05
1895	12963	16068	8445	16068	17062	0	1	15000+	64-73	Married	3	86	High	0	5e+04
1975	13502	92530	11917	92530	13900	0	2	10000-15000	4-8	Single	3	21	Medium	0	1e+05
1993	2844	52	11439	52	13937	0	2	15000+	4-8	Single	3	21	Low	0	1e+05
2008	14190	3450	11601	3450	13905	0	2	15000+	4-8	Single	2	24	High	0	1e+05
2050	8006	10385	13600	10385	14458	1	3	15000+	4-8	Single	2	23	Low	0	3e+05
2069	7881	120	13049	120	13597	1	3	7500-10000	4-8	Single	1	21	Low	0	5e+04
2084	1109	4228	11188	4228	12688	0	2	15000+	4-8	Single	4	20	Medium	0	5e+05
2119	7205	720	11381	720	13103	0	2	0-7500	4-8	Single	3	23	High	0	3e+05
2209	1479	1087	13120	1087	14465	0	3	10000-15000	4-8	Single	2	21	Low	0	5e+04
2221	510	89074	13472	89074	15244	0	3	15000+	4-8	Single	1	24	Low	0	1e+05
2342	13622	11236	12145	11236	13234	0	3	15000+	4-8	Single	4	23	Low	0	3e+05
2352	4571	0	7408	0	13898	0	1	7500-10000	64-73	Married	4	86	Low	0	5e+04
2357	2824	53393	12086	53393	13868	0	2	10000-15000	4-8	Single	2	24	Medium	0	5e+05
2377	11124	14799	12870	14799	13857	1	2	10000-15000	4-8	Single	3	20	Low	0	5e+04
2385	1659	120	13404	120	14333	0	3	0-7500	4-8	Single	1	22	Low	0	5e+04
2419	1040	0	12086	0	13868	0	2	10000-15000	4-8	Single	2	21	Low	0	1e+05
2441	4993	4861	11946	4861	13053	0	2	15000+	34-43	Married	1	57	High	0	3e+05
2496	929	1682	12348	1682	13742	0	2	0-7500	4-8	Single	1	24	Low	0	1e+05
2534	597	122	12594	122	14503	0	3	15000+	4-8	Single	2	23	High	0	5e+04
2569	5574	0	12465	0	13033	1	2	0-7500	4-8	Single	2	20	Medium	0	1e+05
2580	8202	4801	12086	4801	13868	0	2	10000-15000	4-8	Single	2	23	Low	0	5e+04
2590	2820	8	11188	8	12688	0	2	15000+	4-8	Single	4	22	Medium	0	5e+04
2607	11909	20050	13120	20050	14465	0	3	10000-15000	4-8	Single	2	20	Medium	0	3e+05
2663	1983	9415	14036	9415	15204	0	3	10000-15000	4-8	Single	1	22	Medium	0	5e+04
2672	5138	179	12930	179	14577	0	2	10000-15000	4-8	Single	1	22	Medium	0	5e+04
2695	9013	26491	14036	26491	15204	0	3	10000-15000	4-8	Single	1	20	Medium	0	1e+05
2703	2156	231	13120	231	14465	0	3	10000-15000	4-8	Single	2	20	Low	0	5e+05
2722	8029	703	14008	703	16780	2	2	10000-15000	4-8	Single	2	24	High	0	5e+04
2750	11370	0	12411	0	14616	0	2	15000+	4-8	Single	1	20	Medium	0	1e+05
2781	12112	0	12188	0	14581	0	2	15000+	24-33	Single	3	49	Low	0	1e+05
2794	12111	16353	12594	16353	14503	0	3	15000+	4-8	Single	2	21	Medium	0	1e+05
2805	8348	27246	14169	27246	14420	1	3	10000-15000	4-8	Single	2	21	Low	0	5e+04
2813	14580	385	13120	385	14465	0	3	10000-15000	4-8	Single	2	21	High	0	1e+05
2835	500	231	12145	231	13234	0	3	15000+	4-8	Single	4	22	Low	0	1e+05
2837	7811	0	12930	0	14577	0	2	10000-15000	4-8	Single	1	24	Low	0	5e+05
2880	2538	0	12021	0	13036	1	2	7500-10000	4-8	Single	1	20	Low	0	3e+05
2883	8321	1377	11917	1377	13900	0	2	10000-15000	4-8	Single	3	22	Low	0	3e+05
2893	13736	100000	11656	119700	12655	0	2	10000-15000	4-8	Single	4	23	Low	0	1e+05
2934	4897	2380	13410	2380	14491	1	3	15000+	4-8	Single	3	23	Low	0	5e+05
2937	9728	8501	12930	8501	14577	0	2	10000-15000	4-8	Single	1	23	Low	0	1e+05
3034	6403	44	11188	44	12688	0	2	15000+	4-8	Single	4	24	Medium	0	1e+05
3051	1403	3583	11601	3583	13905	0	2	15000+	4-8	Single	2	23	Medium	0	5e+04
3067	117	4368	14244	4368	15794	0	3	0-7500	34-43	Single	3	51	Medium	0	5e+04
3220	11693	253	13049	253	13597	1	3	7500-10000	4-8	Single	1	22	Medium	0	5e+04
3259	2938	0	12291	0	13063	1	2	0-7500	4-8	Single	3	22	Medium	0	1e+05
3286	2782	19106	12291	19106	13063	1	2	0-7500	4-8	Single	3	21	Low	0	1e+05
3351	11006	6216	12930	6216	14577	0	2	10000-15000	4-8	Single	1	22	Low	0	1e+05
3361	13104	0	13052	0	13826	1	2	10000-15000	4-8	Single	2	24	Low	0	5e+05
3385	3461	462	12411	462	14616	0	2	15000+	4-8	Single	1	23	Medium	0	1e+05
3399	11887	120	11138	120	13005	0	3	7500-10000	4-8	Single	3	20	Medium	0	3e+05
3408	14848	2087	12021	2087	13036	1	2	7500-10000	4-8	Single	1	20	Low	0	5e+05
3449	13635	120	10405	120	12441	0	2	7500-10000	4-8	Single	2	24	High	0	3e+05
3459	439	635	13120	635	14465	0	3	10000-15000	4-8	Single	2	23	Low	0	5e+04
3493	10012	120	12937	120	14497	0	3	10000-15000	4-8	Single	3	24	Low	0	5e+04
3508	9009	409	14036	409	15204	0	3	10000-15000	4-8	Single	1	23	Low	0	3e+05
3519	2179	2440	11542	2440	13074	0	2	0-7500	4-8	Single	2	21	Medium	0	1e+05
3530	14261	0	11237	0	12402	1	2	7500-10000	4-8	Single	2	24	Low	0	1e+05
3552	4206	14421	11295	14421	12976	0	3	7500-10000	4-8	Single	2	22	Low	0	5e+04
3553	13983	3530	12594	3530	14503	0	3	15000+	4-8	Single	2	22	Low	0	3e+05
3556	8072	120	12937	120	14497	0	3	10000-15000	4-8	Single	3	21	Low	0	5e+04
3599	13195	0	8874	0	14560	1	1	0-7500	64-73	Married	4	83	Medium	0	5e+05
3640	2890	16987	9844	16987	16772	1	1	0-7500	64-73	Married	1	86	High	0	5e+05
3675	5708	175	14950	175	17742	2	2	15000+	34-43	Single	4	58	Low	0	5e+04
3748	6740	7095	12086	7095	13868	0	2	10000-15000	4-8	Single	2	20	Medium	0	5e+05
3753	6383	38374	11188	38374	12688	0	2	15000+	4-8	Single	4	21	Medium	0	1e+05
3780	1427	5088	12198	5088	12936	1	3	7500-10000	4-8	Single	2	22	Low	0	5e+04
3928	11576	0	10405	0	12441	0	2	7500-10000	4-8	Single	2	20	Low	0	3e+05
4025	9790	44359	12411	44359	14616	0	2	15000+	4-8	Single	1	23	Medium	0	1e+05
4030	2931	6727	10405	6727	12441	0	2	7500-10000	4-8	Single	2	23	Low	0	5e+04
4117	1272	120	12418	120	14536	0	3	15000+	4-8	Single	3	23	Low	0	5e+04
4125	10958	2844	8402	2844	16042	0	1	0-7500	64-73	Married	3	87	Medium	0	5e+04
4168	8803	11651	13600	11651	14458	1	3	15000+	4-8	Single	2	23	Low	0	3e+05
4174	6845	33709	11138	33709	13005	0	3	7500-10000	4-8	Single	3	24	High	0	5e+04
4183	11163	182	13335	182	13699	1	2	0-7500	4-8	Single	1	22	Medium	0	1e+05
4220	4119	59700	10260	59700	12469	0	2	7500-10000	4-8	Single	3	24	Low	0	5e+04
4229	898	32740	13472	32740	15244	0	3	15000+	4-8	Single	1	22	Low	0	1e+05
4297	4617	59880	13049	59880	13597	1	3	7500-10000	4-8	Single	1	21	Medium	0	5e+04
4336	5452	120	13404	120	14333	0	3	0-7500	4-8	Single	1	24	Low	0	5e+04
4348	9455	428	12348	428	13742	0	2	0-7500	4-8	Single	1	21	Medium	0	3e+05
4383	6201	79416	13472	79416	15244	0	3	15000+	4-8	Single	1	21	Low	0	5e+05
4401	5179	5450	13404	5450	14333	0	3	0-7500	4-8	Single	1	20	Low	0	5e+04
4483	9338	50468	11131	50468	13077	0	2	7500-10000	4-8	Single	1	22	Low	0	1e+05
4527	316	19757	10235	19757	12269	0	2	15000+	44-53	Married	3	66	Low	0	5e+05
4605	6611	0	12348	0	13742	0	2	0-7500	4-8	Single	1	23	High	0	5e+04
4639	1239	1637	12465	1637	13033	1	2	0-7500	4-8	Single	2	21	Low	0	5e+04
4689	10598	72	12355	72	13667	0	3	0-7500	4-8	Single	3	21	Medium	0	3e+05
4715	14591	2825	12653	2825	13199	0	3	10000-15000	4-8	Single	4	20	Low	0	1e+05
4754	7724	23597	12086	23597	13868	0	2	10000-15000	4-8	Single	2	20	High	0	5e+05
4803	34	3018	12411	3018	14616	0	2	15000+	4-8	Single	1	21	Low	0	1e+05
4805	13452	3664	13403	3664	14571	1	2	15000+	4-8	Single	1	21	Medium	0	3e+05
4841	14397	3500	12418	3500	14536	0	3	15000+	4-8	Single	3	22	Low	0	5e+04
4873	11193	55397	13971	55397	14453	1	3	10000-15000	4-8	Single	3	24	Low	0	5e+04
4888	3901	56974	11601	56974	13905	0	2	15000+	4-8	Single	2	22	Low	0	5e+05
4889	6305	13726	13120	13726	14465	0	3	10000-15000	4-8	Single	2	22	Low	0	5e+04
4936	10081	450	13282	450	23469	0	2	7500-10000	64-73	Married	1	86	Medium	0	3e+05
4960	419	994	13258	994	16863	2	2	15000+	4-8	Single	3	24	Low	0	3e+05
4964	12979	8982	11188	8982	12688	0	2	15000+	4-8	Single	4	24	Low	0	1e+05
4972	6998	165	11138	165	13005	0	3	7500-10000	4-8	Single	3	24	Low	0	5e+04
5055	9891	514	13472	514	15244	0	3	15000+	4-8	Single	1	21	Medium	0	5e+04
5100	5607	0	12348	0	13742	0	2	0-7500	4-8	Single	1	23	High	0	3e+05
5103	10672	0	11917	0	13900	0	2	10000-15000	4-8	Single	3	21	Medium	0	5e+04
5110	4923	13016	12418	13016	14536	0	3	15000+	4-8	Single	3	24	Medium	0	5e+04
5111	4085	143	11188	143	12688	0	2	15000+	4-8	Single	4	24	Low	0	1e+05
5148	8114	18872	14877	18872	15204	1	2	10000-15000	24-33	Single	1	41	High	0	1e+05
5174	11316	1735	13335	1735	13699	1	2	0-7500	4-8	Single	1	24	Medium	0	3e+05
5193	14919	0	11656	0	12655	0	2	10000-15000	4-8	Single	4	22	Low	0	5e+05
5248	12586	40700	12870	40700	13857	1	2	10000-15000	4-8	Single	3	20	High	0	1e+05
5269	4392	0	12901	0	13013	1	2	15000+	34-43	Married	1	59	High	0	3e+05
5277	6221	0	11131	0	13077	0	2	7500-10000	4-8	Single	1	23	Low	0	3e+05
5282	7766	2752	11633	2752	12386	0	2	10000-15000	34-43	Married	2	54	Low	0	3e+05
5310	892	158	13335	158	13699	1	2	0-7500	4-8	Single	1	20	High	0	3e+05
5312	14595	3272	11633	3272	12386	0	2	10000-15000	34-43	Married	2	59	High	0	5e+04
5410	10087	120	11946	120	13053	0	2	15000+	34-43	Married	1	58	Medium	0	5e+04
5459	14343	181	13713	181	14497	1	2	10000-15000	24-33	Single	3	44	Medium	0	5e+04
5462	9445	277	13472	277	15244	0	3	15000+	4-8	Single	1	20	Medium	0	5e+04
5476	3788	71194	12930	71194	14577	0	2	10000-15000	4-8	Single	1	20	High	0	1e+05
5497	5881	410	12411	410	14616	0	2	15000+	4-8	Single	1	23	Low	0	5e+04
5574	8878	0	11601	0	13905	0	2	15000+	4-8	Single	2	23	Low	0	1e+05
5646	10191	0	8564	0	17024	0	1	15000+	64-73	Married	2	87	High	0	3e+05
5675	3865	1454	12530	1454	13636	0	3	0-7500	4-8	Single	2	24	Medium	0	5e+04
5712	6203	156	15158	156	15157	1	3	10000-15000	4-8	Single	1	24	Low	0	3e+05
5717	11564	5120	12594	5120	14503	0	3	15000+	4-8	Single	2	21	Low	0	5e+04
5723	12765	1801	11601	1801	13905	0	2	15000+	4-8	Single	2	23	Low	0	1e+05
5760	10937	31079	10405	31079	12441	0	2	7500-10000	4-8	Single	2	23	Medium	0	5e+04
5790	13476	11915	13120	11915	14465	0	3	10000-15000	4-8	Single	2	24	Low	0	5e+04
5838	13063	13633	15615	13633	18445	2	3	15000+	4-8	Single	1	21	Low	0	5e+04
5843	3376	120	12418	120	14536	0	3	15000+	4-8	Single	3	23	Low	0	1e+05
5856	6237	1121	12937	1121	14497	0	3	10000-15000	4-8	Single	3	20	Low	0	1e+05
5864	727	13632	11295	13632	12976	0	3	7500-10000	4-8	Single	2	21	Medium	0	1e+05
5877	14762	0	11920	0	13275	0	2	15000+	24-33	Single	4	40	Low	0	3e+05
5908	12542	738	12084	738	13639	0	3	7500-10000	4-8	Single	1	20	Low	0	3e+05
5953	11819	608	12084	608	13639	0	3	7500-10000	4-8	Single	1	20	Low	0	3e+05
5962	4740	1488	13776	1488	15251	0	2	10000-15000	24-33	Single	1	40	High	0	1e+05
5973	4367	12948	12493	12948	12793	1	2	10000-15000	44-53	Married	1	62	Low	0	3e+05
6005	7451	11654	13472	11654	15244	0	3	15000+	4-8	Single	1	24	Low	0	1e+05
6011	10541	11843	11946	11843	13053	0	2	15000+	34-43	Married	1	56	Medium	0	5e+04
6015	13687	206	11188	206	12688	0	2	15000+	4-8	Single	4	24	Low	0	1e+05
6026	27	100000	11656	167332	12655	0	2	10000-15000	4-8	Single	4	23	Low	0	5e+05
6040	11038	11373	12086	11373	13868	0	2	10000-15000	4-8	Single	2	21	Low	0	5e+05
6041	1992	0	11131	0	13077	0	2	7500-10000	4-8	Single	1	24	Medium	0	5e+05
6055	13899	0	12411	0	14616	0	2	15000+	4-8	Single	1	22	Low	0	5e+05
6062	2351	63735	12084	63735	13639	0	3	7500-10000	4-8	Single	1	20	Low	0	3e+05
6087	13494	120	12411	120	14616	0	2	15000+	4-8	Single	1	22	Low	0	1e+05
6098	4698	14037	13403	14037	14571	1	2	15000+	4-8	Single	1	22	High	0	3e+05
6120	8243	123	13410	123	14491	1	3	15000+	4-8	Single	3	23	Low	0	5e+04
6141	7120	14879	12348	14879	13742	0	2	0-7500	4-8	Single	1	20	Low	0	5e+04
6169	12711	24974	14036	24974	15204	0	3	10000-15000	4-8	Single	1	21	Low	0	3e+05
6176	295	3854	13472	3854	15244	0	3	15000+	4-8	Single	1	22	Low	0	5e+04
6181	3781	5433	11656	5433	12655	0	2	10000-15000	4-8	Single	4	23	Low	0	5e+04
6196	12821	0	11917	0	13900	0	2	10000-15000	4-8	Single	3	20	Low	0	5e+04
6217	12059	3998	10260	3998	12469	0	2	7500-10000	4-8	Single	3	21	High	0	5e+04
6238	5600	0	10260	0	12469	0	2	7500-10000	4-8	Single	3	20	High	0	5e+04
6242	9168	0	12021	0	13036	1	2	7500-10000	4-8	Single	1	23	Low	0	3e+05
6272	13758	156	11439	156	13937	0	2	15000+	4-8	Single	3	20	High	0	5e+04
6280	3058	9325	12348	9325	13742	0	2	0-7500	4-8	Single	1	22	Low	0	5e+04
6280	14265	8732	12653	8732	13199	0	3	10000-15000	4-8	Single	4	24	Medium	0	5e+04
6297	9079	0	13739	0	16063	0	2	10000-15000	34-43	Single	3	52	High	0	3e+05
6304	12219	0	11542	0	13074	0	2	0-7500	4-8	Single	2	21	High	0	5e+04
6411	4113	0	22891	0	24089	3	1	7500-10000	24-33	Single	3	42	Medium	0	3e+05
6432	608	0	13156	0	14377	0	2	0-7500	24-33	Single	1	40	High	0	5e+04
6432	10368	51741	11131	51741	13077	0	2	7500-10000	4-8	Single	1	23	Low	0	5e+05
6434	585	100000	12411	119400	14616	0	2	15000+	4-8	Single	1	20	Medium	0	1e+05
6465	10441	137	12084	137	13639	0	3	7500-10000	4-8	Single	1	20	Medium	0	5e+04
6471	5023	6269	20972	6269	20517	3	1	7500-10000	34-43	Married	2	58	High	0	1e+05
6473	3842	30340	10814	30340	12209	0	2	10000-15000	44-53	Married	2	64	High	0	3e+05
6479	7618	0	8899	0	12063	2	1	15000+	4-8	Single	1	21	Low	0	1e+05
6592	11802	145	13404	145	14333	0	3	0-7500	4-8	Single	1	20	Low	0	5e+04
6613	10270	29560	13282	29560	21411	0	2	0-7500	64-73	Married	4	86	High	0	5e+04
6646	10277	36167	11656	36167	12655	0	2	10000-15000	4-8	Single	4	21	Low	0	3e+05
6657	7155	41774	11542	41774	13074	0	2	0-7500	4-8	Single	2	21	Low	0	5e+05
6673	6644	8949	12587	8949	12616	1	2	10000-15000	4-8	Single	4	24	Low	0	5e+04
6674	3671	120	11656	120	12655	0	2	10000-15000	4-8	Single	4	23	Medium	0	3e+05
6693	424	153	13120	153	14465	0	3	10000-15000	4-8	Single	2	20	Low	0	5e+04
6695	5673	47776	11569	47776	12833	0	2	10000-15000	44-53	Married	1	63	Medium	0	5e+04
6701	12334	3750	11601	3750	13905	0	2	15000+	4-8	Single	2	22	High	0	1e+05
6733	10312	0	11542	0	13074	0	2	0-7500	4-8	Single	2	22	Low	0	5e+05
6745	4117	7290	14597	7290	17548	2	3	15000+	4-8	Single	2	24	Low	0	5e+04
6780	11585	3583	9162	3583	17894	0	1	15000+	64-73	Married	1	85	High	0	5e+05
6803	831	145	10260	145	12469	0	2	7500-10000	4-8	Single	3	21	Low	0	1e+05
6806	11267	2412	10260	2412	12469	0	2	7500-10000	4-8	Single	3	24	Medium	0	5e+05
6811	1602	1670	12594	1670	14503	0	3	15000+	4-8	Single	2	20	Low	0	5e+04
6846	11697	120	13472	120	15244	0	3	15000+	4-8	Single	1	24	Low	0	5e+04
6873	2217	15324	12930	15324	14577	0	2	10000-15000	4-8	Single	1	22	Low	0	3e+05
6915	6676	854	11656	854	12655	0	2	10000-15000	4-8	Single	4	24	Low	0	1e+05
6933	1131	125	12624	125	14170	2	3	15000+	9-13	Single	1	25	Low	0	1e+05
6935	9680	120	12937	120	14497	0	3	10000-15000	4-8	Single	3	20	Low	0	5e+04
6946	619	0	12348	0	13742	0	2	0-7500	4-8	Single	1	24	Low	0	1e+05
6978	11740	0	8899	0	12063	2	1	15000+	4-8	Single	1	21	Low	0	5e+05
6997	14301	120	12145	120	13234	0	3	15000+	4-8	Single	4	24	Low	0	5e+04
7017	9996	12797	12418	12797	14536	0	3	15000+	4-8	Single	3	21	Medium	0	3e+05
7020	11449	0	12361	0	14548	0	2	15000+	24-33	Single	2	40	Low	0	5e+04
7046	1861	13142	15158	13142	15157	1	3	10000-15000	4-8	Single	1	21	Medium	0	1e+05
7064	2000	0	13403	0	14571	1	2	15000+	4-8	Single	1	20	Low	0	5e+05
7085	13053	23535	9894	23535	17839	1	1	15000+	64-73	Married	1	85	High	0	1e+05
7090	8087	41304	12411	41304	14616	0	2	15000+	4-8	Single	1	24	Low	0	3e+05
7102	10550	37772	12115	37772	13550	2	2	10000-15000	9-13	Single	1	29	Low	0	5e+04
7121	12430	15658	11131	15658	13077	0	2	7500-10000	4-8	Single	1	23	Low	0	5e+04
7130	12123	58454	13335	58454	13699	1	2	0-7500	4-8	Single	1	20	Low	0	5e+04
7140	10714	25497	13116	25497	13193	1	3	15000+	4-8	Single	4	21	Low	0	3e+05
7208	14150	0	11917	0	13900	0	2	10000-15000	4-8	Single	3	20	Low	0	5e+04
7218	14459	2028	10405	2028	12441	0	2	7500-10000	4-8	Single	2	21	Low	0	1e+05
7226	7972	40380	14877	40380	15204	1	2	10000-15000	24-33	Single	1	40	High	0	5e+05
7229	9803	120	11576	120	12704	2	3	0-7500	9-13	Single	3	27	Medium	0	5e+04
7250	315	300	15428	300	26162	0	2	10000-15000	64-73	Married	1	88	Low	0	5e+04
7251	7356	294	12021	294	13036	1	2	7500-10000	4-8	Single	1	20	Medium	0	1e+05
7312	9446	0	12354	0	13894	1	2	15000+	4-8	Single	3	24	Low	0	3e+05
7313	5776	19780	11601	19780	13905	0	2	15000+	4-8	Single	2	21	Low	0	3e+05
7316	5127	836	12021	836	13036	1	2	7500-10000	4-8	Single	1	22	Medium	0	1e+05
7376	14513	6010	12354	6010	13894	1	2	15000+	4-8	Single	3	24	Medium	0	1e+05
7377	11567	510	13120	510	14465	0	3	10000-15000	4-8	Single	2	21	Low	0	1e+05
7379	14373	120	13116	120	13193	1	3	15000+	4-8	Single	4	21	Low	0	5e+04
7391	4191	0	12529	0	13862	1	2	15000+	4-8	Single	2	23	Medium	0	5e+05
7392	13590	260	12104	260	13158	2	2	10000-15000	14-23	Single	1	30	Low	0	3e+05
7415	4511	4398	14549	4398	15197	1	3	15000+	4-8	Single	1	22	High	0	5e+04
7425	8870	385	13472	385	15244	0	3	15000+	4-8	Single	1	20	Low	0	5e+04
7431	9742	100000	14036	164434	15204	0	3	10000-15000	4-8	Single	1	21	Low	0	3e+05
7445	12519	44924	11295	44924	12976	0	3	7500-10000	4-8	Single	2	21	Low	0	5e+04
7493	3007	0	12870	0	13857	1	2	10000-15000	4-8	Single	3	23	Medium	0	1e+05
7503	10922	6677	12411	6677	14616	0	2	15000+	4-8	Single	1	24	Low	0	1e+05
7511	9964	40612	13116	40612	13193	1	3	15000+	4-8	Single	4	22	Low	0	1e+05
7532	7854	6277	11237	6277	12402	1	2	7500-10000	4-8	Single	2	21	Medium	0	5e+04
7587	10272	3311	12145	3311	13234	0	3	15000+	4-8	Single	4	22	Low	0	5e+04
7600	2381	0	11656	0	12655	0	2	10000-15000	4-8	Single	4	24	Medium	0	1e+05
7633	14750	10170	12908	10170	12942	1	3	15000+	34-43	Married	3	54	Low	0	5e+04
7729	4147	0	7574	0	15265	0	1	7500-10000	64-73	Married	3	81	High	0	5e+05
7749	5343	1013	11439	1013	13937	0	2	15000+	4-8	Single	3	21	Low	0	3e+05
7788	3302	20015	12084	20015	13639	0	3	7500-10000	4-8	Single	1	21	Low	0	1e+05
7893	12456	18150	12126	18150	13709	0	2	0-7500	24-33	Single	3	43	Low	0	1e+05
7988	13134	119	13410	119	14491	1	3	15000+	4-8	Single	3	23	Medium	0	1e+05
8007	5492	164	11295	164	12976	0	3	7500-10000	4-8	Single	2	20	Low	0	5e+04
8015	8116	0	12587	0	12616	1	2	10000-15000	4-8	Single	4	20	Low	0	3e+05
8048	14144	26539	11138	26539	13005	0	3	7500-10000	4-8	Single	3	22	Low	0	1e+05
8063	3226	11804	14320	11804	16536	2	3	0-7500	4-8	Single	3	22	Low	0	3e+05
8066	8446	1086	13404	1086	14333	0	3	0-7500	4-8	Single	1	21	Low	0	5e+04
8075	7377	47675	13120	47675	14465	0	3	10000-15000	4-8	Single	2	24	Low	0	5e+05
8105	4633	6111	14036	6111	15204	0	3	10000-15000	4-8	Single	1	24	Low	0	3e+05
8140	10640	3095	12937	3095	14497	0	3	10000-15000	4-8	Single	3	21	Medium	0	1e+05
8182	2954	293	12594	293	14503	0	3	15000+	4-8	Single	2	20	Low	0	1e+05
8226	3875	554	11381	554	13103	0	2	0-7500	4-8	Single	3	21	Medium	0	5e+05
8252	14926	5653	12291	5653	13063	1	2	0-7500	4-8	Single	3	21	Medium	0	5e+04
8255	13794	0	12086	0	13868	0	2	10000-15000	4-8	Single	2	20	Medium	0	3e+05
8281	3307	1551	13776	1551	15251	0	2	10000-15000	24-33	Single	1	40	High	0	5e+04
8299	9763	5756	11080	5756	12430	1	2	7500-10000	4-8	Single	3	22	Low	0	3e+05
8304	1298	11743	11439	11743	13937	0	2	15000+	4-8	Single	3	23	Low	0	5e+04
8323	10552	59880	12419	59880	13240	0	2	10000-15000	24-33	Single	4	44	High	0	5e+04
8341	7558	17663	12870	17663	13857	1	2	10000-15000	4-8	Single	3	24	Low	0	3e+05
8388	3406	7986	12587	7986	12616	1	2	10000-15000	4-8	Single	4	24	Low	0	1e+05
8415	10493	96853	11188	96853	12688	0	2	15000+	4-8	Single	4	20	Medium	0	3e+05
8431	13816	1031	11601	1031	13905	0	2	15000+	4-8	Single	2	21	Medium	0	3e+05
8502	156	16316	13600	16316	14458	1	3	15000+	4-8	Single	2	20	Low	0	1e+05
8507	7027	368	9272	368	12031	2	1	10000-15000	4-8	Single	1	21	High	0	5e+04
8523	13199	6223	11920	6223	13275	0	2	15000+	24-33	Single	4	49	Low	0	1e+05
8554	12913	11196	12354	11196	13894	1	2	15000+	4-8	Single	3	21	Medium	0	5e+04
8633	4980	27810	13410	27810	14491	1	3	15000+	4-8	Single	3	21	Low	0	1e+05
8641	12114	0	8798	0	17017	0	1	10000-15000	64-73	Married	3	86	High	0	5e+04
8667	14086	129	11086	129	13016	0	2	7500-10000	24-33	Single	2	41	High	0	5e+04
8680	13647	18398	10405	18398	12441	0	2	7500-10000	4-8	Single	2	23	Medium	0	5e+05
8690	12685	0	13440	0	12979	1	2	10000-15000	34-43	Married	1	55	Low	0	5e+04
8692	3259	0	11131	0	13077	0	2	7500-10000	4-8	Single	1	24	Medium	0	5e+05
8705	3188	26437	12594	26437	14503	0	3	15000+	4-8	Single	2	21	Low	0	1e+05
8709	3620	100000	11439	359400	13937	0	2	15000+	4-8	Single	3	20	Low	0	3e+05
8720	2533	2205	11601	2205	13905	0	2	15000+	4-8	Single	2	21	Medium	0	5e+04
8757	11135	10709	12594	10709	14503	0	3	15000+	4-8	Single	2	22	Low	0	5e+04
8766	14451	5900	12411	5900	14616	0	2	15000+	4-8	Single	1	22	Medium	0	1e+05
8781	5907	7957	12084	7957	13639	0	3	7500-10000	4-8	Single	1	23	Medium	0	1e+05
8791	14537	24544	12411	24544	14616	0	2	15000+	4-8	Single	1	22	High	0	1e+05
8837	3954	0	10405	0	12441	0	2	7500-10000	4-8	Single	2	21	Medium	0	1e+05
8845	2482	0	12291	0	13063	1	2	0-7500	4-8	Single	3	20	Medium	0	3e+05
8872	11047	0	11656	0	12655	0	2	10000-15000	4-8	Single	4	20	Medium	0	5e+04
8948	3371	123	15967	123	18453	2	2	10000-15000	24-33	Single	1	42	High	0	5e+04
8990	8504	2564	12354	2564	13894	1	2	15000+	4-8	Single	3	23	High	0	1e+05
9039	7910	2688	12937	2688	14497	0	3	10000-15000	4-8	Single	3	21	Low	0	5e+04
9043	855	1678	11946	1678	13053	0	2	15000+	34-43	Married	1	56	High	0	5e+05
9045	14057	451	12937	451	14497	0	3	10000-15000	4-8	Single	3	20	Low	0	1e+05
9071	6868	54168	12083	54168	12442	0	3	0-7500	4-8	Single	4	21	Low	0	5e+04
9111	11778	100000	14549	101391	15197	1	3	15000+	4-8	Single	1	21	Low	0	1e+05
9117	13004	8535	11601	8535	13905	0	2	15000+	4-8	Single	2	24	Low	0	5e+04
9133	11486	6779	13258	6779	16863	2	2	15000+	4-8	Single	3	20	Low	0	1e+05
9135	859	0	11439	0	13937	0	2	15000+	4-8	Single	3	21	Low	0	1e+05
9181	12917	0	11104	0	12867	0	2	15000+	44-53	Married	1	60	Medium	0	5e+05
9209	2525	5103	10405	5103	12441	0	2	7500-10000	4-8	Single	2	23	Medium	0	5e+04
9274	4293	159	13378	159	15819	2	2	0-7500	4-8	Single	2	22	Medium	0	5e+04
9279	11598	1355	12084	1355	13639	0	3	7500-10000	4-8	Single	1	20	Low	0	1e+05
9347	3168	249	11131	249	13077	0	2	7500-10000	4-8	Single	1	22	High	0	5e+04
9392	8751	0	11885	0	12273	0	2	0-7500	34-43	Married	1	53	Low	0	5e+04
9415	6070	0	12901	0	15822	2	2	7500-10000	4-8	Single	1	24	Medium	0	5e+05
9423	1987	89	13472	89	15244	0	3	15000+	4-8	Single	1	21	High	0	1e+05
9517	13016	100000	8217	281761	14605	0	1	0-7500	64-73	Married	4	87	High	0	3e+05
9551	5435	26666	10405	26666	12441	0	2	7500-10000	4-8	Single	2	20	Low	0	3e+05
9553	1865	54466	11086	54466	13016	0	2	7500-10000	24-33	Single	2	49	Medium	0	5e+04
9556	5209	15396	11080	15396	12430	1	2	7500-10000	4-8	Single	3	21	Low	0	5e+04
9568	13220	120	11629	120	13586	2	2	15000+	9-13	Single	1	27	Medium	0	5e+04
9590	4692	7233	12354	7233	13894	1	2	15000+	4-8	Single	3	20	Low	0	3e+05
9664	653	721	12411	721	14616	0	2	15000+	4-8	Single	1	22	Low	0	1e+05
9689	742	58510	11237	58510	12402	1	2	7500-10000	4-8	Single	2	21	Medium	0	3e+05
9695	2939	53	11439	53	13937	0	2	15000+	4-8	Single	3	23	Medium	0	1e+05
9715	12673	0	11656	0	12655	0	2	10000-15000	4-8	Single	4	21	Low	0	3e+05
9742	5064	473	14036	473	15204	0	3	10000-15000	4-8	Single	1	24	Low	0	5e+04
9760	1681	4311	13472	4311	15244	0	3	15000+	4-8	Single	1	21	Low	0	3e+05
9774	5269	0	12930	0	14577	0	2	10000-15000	4-8	Single	1	23	Low	0	1e+05
9801	12022	0	10260	0	13941	2	1	15000+	34-43	Single	1	56	Medium	0	5e+05
9812	10772	0	11381	0	13103	0	2	0-7500	4-8	Single	3	20	Medium	0	5e+05
9827	10045	0	12086	0	13868	0	2	10000-15000	4-8	Single	2	21	Medium	0	5e+04
9863	9165	546	12084	546	13639	0	3	7500-10000	4-8	Single	1	24	Low	0	5e+04
9921	11951	0	11917	0	13900	0	2	10000-15000	4-8	Single	3	22	Low	0	1e+05
9940	5132	132	13472	132	15244	0	3	15000+	4-8	Single	1	23	Low	0	5e+04
9991	8572	602	13052	602	13826	1	2	10000-15000	4-8	Single	2	21	High	0	5e+04
10	6386	144	11295	144	12976	0	3	7500-10000	4-8	Single	2	21	Low	0	5e+04
155	6927	0	12082	0	12649	1	2	15000+	4-8	Single	4	24	Medium	0	5e+05
160	5309	48816	13052	48816	13826	1	2	10000-15000	4-8	Single	2	22	Medium	0	1e+05
222	12590	35708	13404	35708	14333	0	3	0-7500	4-8	Single	1	22	Low	0	5e+04
228	9054	64189	12145	64189	13234	0	3	15000+	4-8	Single	4	23	Low	0	5e+05
255	12575	14118	10405	14118	12441	0	2	7500-10000	4-8	Single	2	21	Low	0	5e+04
281	14736	3395	10380	3395	12241	0	2	15000+	44-53	Married	2	69	Low	0	1e+05
295	7144	20287	13963	20287	14532	1	2	10000-15000	4-8	Single	1	23	Low	0	3e+05
311	2430	59647	11131	59647	13077	0	2	7500-10000	4-8	Single	1	22	Low	0	1e+05
351	6943	3288	12086	3288	13868	0	2	10000-15000	4-8	Single	2	23	Low	0	1e+05
404	5153	12974	11630	12974	13736	2	2	7500-10000	4-8	Single	4	22	High	0	5e+05
425	2623	9646	12084	9646	13639	0	3	7500-10000	4-8	Single	1	23	Low	0	1e+05
458	8477	14221	14549	14221	15197	1	3	15000+	4-8	Single	1	22	Low	0	5e+04
466	6452	54836	12594	54836	14503	0	3	15000+	4-8	Single	2	24	Low	0	5e+04
507	5816	232	11131	232	13077	0	2	7500-10000	4-8	Single	1	24	Low	0	5e+04
549	11096	14379	11601	14379	13905	0	2	15000+	4-8	Single	2	24	Medium	0	5e+04
567	5976	520	12594	520	14503	0	3	15000+	4-8	Single	2	23	High	0	1e+05
584	14769	6321	11917	6321	13900	0	2	10000-15000	4-8	Single	3	22	Low	0	1e+05
608	6741	39523	14549	39523	15197	1	3	15000+	4-8	Single	1	23	Low	0	1e+05
660	13300	26883	12411	26883	14616	0	2	15000+	4-8	Single	1	23	Low	0	3e+05
696	8004	3068	11188	3068	12688	0	2	15000+	4-8	Single	4	23	Low	0	5e+04
788	9747	14548	12084	14548	13639	0	3	7500-10000	4-8	Single	1	21	Medium	0	3e+05
806	3380	0	11439	0	13937	0	2	15000+	4-8	Single	3	21	Low	0	5e+04
808	14403	0	11188	0	12688	0	2	15000+	4-8	Single	4	21	Low	0	3e+05
883	11809	0	11188	0	12688	0	2	15000+	4-8	Single	4	23	Low	0	5e+04
959	5589	47104	14549	47104	15197	1	3	15000+	4-8	Single	1	23	Medium	0	1e+05
962	5826	24727	13963	24727	14532	1	2	10000-15000	4-8	Single	1	22	Low	0	5e+04
992	5507	7111	12418	7111	14536	0	3	15000+	4-8	Single	3	21	Medium	0	5e+04
1013	10079	0	12348	0	13742	0	2	0-7500	4-8	Single	1	23	Low	0	5e+04
1026	7959	1256	11542	1256	13074	0	2	0-7500	4-8	Single	2	22	Low	0	1e+05
1059	1423	24342	12411	24342	14616	0	2	15000+	4-8	Single	1	24	Medium	0	1e+05
1095	10470	14413	12355	14413	13667	0	3	0-7500	4-8	Single	3	21	Low	0	5e+04
1112	2718	7519	10260	7519	12469	0	2	7500-10000	4-8	Single	3	24	Low	0	3e+05
1121	12043	0	11086	0	13016	0	2	7500-10000	24-33	Single	2	43	High	0	1e+05
1123	13141	160	14036	160	15204	0	3	10000-15000	4-8	Single	1	23	Low	0	5e+04
1138	9841	9412	10405	9412	12441	0	2	7500-10000	4-8	Single	2	22	Low	0	5e+04
1162	12613	653	14036	653	15204	0	3	10000-15000	4-8	Single	1	21	Low	0	5e+04
1167	75	0	11188	0	12688	0	2	15000+	4-8	Single	4	22	Medium	0	3e+05
1176	12198	128	11295	128	12976	0	3	7500-10000	4-8	Single	2	21	Low	0	1e+05
1183	5892	0	12419	0	13240	0	2	10000-15000	24-33	Single	4	40	High	0	1e+05
1196	4300	0	8923	0	16979	0	1	10000-15000	64-73	Married	2	87	Medium	0	3e+05
1210	5908	120	13151	120	14133	2	3	10000-15000	9-13	Single	1	28	Low	0	5e+04
1214	5681	527	13049	527	13597	1	3	7500-10000	4-8	Single	1	22	Low	0	5e+04
1249	3203	0	11920	0	13275	0	2	15000+	24-33	Single	4	41	Medium	0	5e+04
1277	2649	9079	14169	9079	14420	1	3	10000-15000	4-8	Single	2	21	Low	0	5e+04
1312	764	12892	10405	12892	12441	0	2	7500-10000	4-8	Single	2	24	Low	0	1e+05
1332	2437	377	11080	377	12430	1	2	7500-10000	4-8	Single	3	23	Low	0	1e+05
1345	10136	13626	11946	13626	13053	0	2	15000+	34-43	Married	1	53	Medium	0	5e+05
1379	11919	21263	11601	21263	13905	0	2	15000+	4-8	Single	2	24	Low	0	3e+05
1382	4031	0	9879	0	12588	2	1	10000-15000	24-33	Single	1	48	Medium	0	1e+05
1397	13504	71395	11656	71395	12655	0	2	10000-15000	4-8	Single	4	23	Medium	0	5e+05
1408	321	26492	11656	26492	12655	0	2	10000-15000	4-8	Single	4	22	Low	0	5e+04
1517	10042	0	11381	0	13103	0	2	0-7500	4-8	Single	3	22	High	0	1e+05
1543	13719	184	12937	184	14497	0	3	10000-15000	4-8	Single	3	24	Low	0	3e+05
1574	422	5267	8899	5267	12063	2	1	15000+	4-8	Single	1	21	Medium	0	5e+05
1678	13775	212	11601	212	13905	0	2	15000+	4-8	Single	2	21	High	0	1e+05
1710	11822	32882	10260	32882	12469	0	2	7500-10000	4-8	Single	3	22	Low	0	1e+05
1721	11192	30064	13120	30064	14465	0	3	10000-15000	4-8	Single	2	21	Low	0	5e+04
1739	10845	33391	12348	33391	13742	0	2	0-7500	4-8	Single	1	21	Low	0	5e+05
1765	5484	0	13963	0	14532	1	2	10000-15000	4-8	Single	1	24	Low	0	3e+05
1807	11300	274	13472	274	15244	0	3	15000+	4-8	Single	1	22	Medium	0	5e+04
1829	13317	439	13120	439	14465	0	3	10000-15000	4-8	Single	2	21	Low	0	1e+05
1843	9209	0	11188	0	12688	0	2	15000+	4-8	Single	4	21	Low	0	3e+05
1867	8501	0	9116	0	16824	0	1	0-7500	64-73	Married	1	86	Low	0	5e+05
1895	12963	0	8445	0	17062	0	1	15000+	64-73	Married	3	87	High	0	5e+04
1960	4676	23152	11188	23152	12688	0	2	15000+	4-8	Single	4	22	Low	0	3e+05
1975	13502	0	11917	0	13900	0	2	10000-15000	4-8	Single	3	22	Medium	0	1e+05
1980	14693	1412	12021	1412	13036	1	2	7500-10000	4-8	Single	1	24	Low	0	5e+05
1993	2844	6564	11439	6564	13937	0	2	15000+	4-8	Single	3	22	Low	0	1e+05
2050	8006	176	12594	176	14503	0	3	15000+	4-8	Single	2	24	Low	0	3e+05
2069	7881	628	13049	628	13597	1	3	7500-10000	4-8	Single	1	22	Low	0	5e+04
2084	1109	863	12145	863	13234	0	3	15000+	4-8	Single	4	21	Medium	0	5e+05
2119	7205	3481	11381	3481	13103	0	2	0-7500	4-8	Single	3	24	High	0	3e+05
2209	1479	20599	14169	20599	14420	1	3	10000-15000	4-8	Single	2	22	Low	0	5e+04
2288	2024	0	10860	0	12551	2	2	15000+	14-23	Single	2	34	Medium	0	3e+05
2342	13622	0	11188	0	12688	0	2	15000+	4-8	Single	4	24	Low	0	3e+05
2377	11124	7050	12870	7050	13857	1	2	10000-15000	4-8	Single	3	21	Low	0	5e+04
2385	1659	301	13404	301	14333	0	3	0-7500	4-8	Single	1	23	Low	0	5e+04
2419	1040	6631	12086	6631	13868	0	2	10000-15000	4-8	Single	2	22	Low	0	1e+05
2489	8496	561	11542	561	13074	0	2	0-7500	4-8	Single	2	23	Low	0	1e+05
2534	597	0	11601	0	13905	0	2	15000+	4-8	Single	2	24	High	0	5e+04
2574	654	5809	12445	5809	13019	0	2	10000-15000	34-43	Married	1	50	Low	0	5e+04
2580	8202	59400	12086	59400	13868	0	2	10000-15000	4-8	Single	2	24	Low	0	5e+04
2607	11909	20493	13120	20493	14465	0	3	10000-15000	4-8	Single	2	21	Medium	0	3e+05
2631	7350	28504	12361	28504	14548	0	2	15000+	24-33	Single	2	45	Low	0	3e+05
2646	5436	850	12082	850	12649	1	2	15000+	4-8	Single	4	22	Low	0	1e+05
2663	1983	132	14036	132	15204	0	3	10000-15000	4-8	Single	1	23	Medium	0	5e+04
2672	5138	24187	14036	24187	15204	0	3	10000-15000	4-8	Single	1	23	Medium	0	5e+04
2695	9013	10944	14036	10944	15204	0	3	10000-15000	4-8	Single	1	21	Medium	0	1e+05
2703	2156	6189	13120	6189	14465	0	3	10000-15000	4-8	Single	2	21	Low	0	5e+05
2768	4832	991	13412	991	13199	1	2	10000-15000	24-33	Single	4	46	High	0	5e+04
2781	12112	680	13188	680	16106	0	2	15000+	34-43	Single	3	50	Low	0	1e+05
2794	12111	23202	12594	23202	14503	0	3	15000+	4-8	Single	2	22	Medium	0	1e+05
2799	10404	15489	11131	15489	13077	0	2	7500-10000	4-8	Single	1	24	Low	0	5e+04
2805	8348	20068	13120	20068	14465	0	3	10000-15000	4-8	Single	2	22	Low	0	5e+04
2813	14580	0	12086	0	13868	0	2	10000-15000	4-8	Single	2	22	High	0	1e+05
2835	500	2736	12145	2736	13234	0	3	15000+	4-8	Single	4	23	Low	0	1e+05
2883	8321	6657	11917	6657	13900	0	2	10000-15000	4-8	Single	3	23	Low	0	3e+05
2893	13736	4561	11656	4561	12655	0	2	10000-15000	4-8	Single	4	24	Low	0	1e+05
2901	1838	15707	11131	15707	13077	0	2	7500-10000	4-8	Single	1	24	High	0	5e+05
2934	4897	4318	13410	4318	14491	1	3	15000+	4-8	Single	3	24	Low	0	5e+05
2937	9728	57	12930	57	14577	0	2	10000-15000	4-8	Single	1	24	Low	0	1e+05
3000	5593	120	10932	120	13045	0	2	7500-10000	24-33	Single	3	42	High	0	5e+05
3051	1403	0	11601	0	13905	0	2	15000+	4-8	Single	2	24	Medium	0	5e+04
3067	117	0	13121	0	15143	0	2	0-7500	34-43	Single	3	52	Medium	0	5e+04
3071	12164	491	11542	491	13074	0	2	0-7500	4-8	Single	2	24	High	0	1e+05
3185	13724	78941	13776	78941	15251	0	2	10000-15000	24-33	Single	1	46	Low	0	1e+05
3220	11693	192	13049	192	13597	1	3	7500-10000	4-8	Single	1	23	Medium	0	5e+04
3224	14739	21707	12870	21707	13857	1	2	10000-15000	4-8	Single	3	24	Low	0	3e+05
3241	5821	1665	12122	1665	12953	0	3	15000+	34-43	Married	2	50	Low	0	5e+04
3330	11520	100000	10405	180341	12441	0	2	7500-10000	4-8	Single	2	24	Medium	0	5e+05
3331	14154	15702	12411	15702	14616	0	2	15000+	4-8	Single	1	22	High	0	5e+04
3351	11006	3459	14036	3459	15204	0	3	10000-15000	4-8	Single	1	23	Low	0	1e+05
3385	3461	1020	12411	1020	14616	0	2	15000+	4-8	Single	1	24	Medium	0	1e+05
3399	11887	972	11138	972	13005	0	3	7500-10000	4-8	Single	3	21	Medium	0	3e+05
3429	2036	0	9879	0	12588	2	1	10000-15000	24-33	Single	1	40	Low	0	1e+05
3451	5076	12724	11080	12724	12430	1	2	7500-10000	4-8	Single	3	22	Low	0	3e+05
3459	439	8315	14169	8315	14420	1	3	10000-15000	4-8	Single	2	24	Low	0	5e+04
3506	6342	608	12348	608	13742	0	2	0-7500	4-8	Single	1	23	Low	0	5e+04
3508	9009	404	14036	404	15204	0	3	10000-15000	4-8	Single	1	24	Low	0	3e+05
3519	2179	0	11542	0	13074	0	2	0-7500	4-8	Single	2	22	Medium	0	1e+05
3552	4206	30161	11295	30161	12976	0	3	7500-10000	4-8	Single	2	23	Low	0	5e+04
3553	13983	31115	12594	31115	14503	0	3	15000+	4-8	Single	2	23	Low	0	3e+05
3556	8072	121	12937	121	14497	0	3	10000-15000	4-8	Single	3	22	Low	0	5e+04
3611	4939	1415	11917	1415	13900	0	2	10000-15000	4-8	Single	3	22	High	0	5e+04
3640	2890	0	9844	0	16772	1	1	0-7500	64-73	Married	1	87	High	0	5e+05
3675	5708	0	9249	0	12102	2	1	15000+	34-43	Single	4	59	Low	0	5e+04
3685	8113	10914	13349	10914	14503	1	2	15000+	24-33	Single	2	40	High	0	5e+04
3730	8463	36	11601	36	13905	0	2	15000+	4-8	Single	2	23	Low	0	1e+05
3748	6740	30574	12086	30574	13868	0	2	10000-15000	4-8	Single	2	21	Medium	0	5e+05
3780	1427	1218	12198	1218	12936	1	3	7500-10000	4-8	Single	2	23	Low	0	5e+04
3891	11428	65846	11439	65846	13937	0	2	15000+	4-8	Single	3	22	Low	0	3e+05
3928	11576	4420	10405	4420	12441	0	2	7500-10000	4-8	Single	2	21	Low	0	3e+05
4014	8284	3455	15373	3455	15832	1	2	0-7500	34-43	Single	1	59	High	0	5e+04
4025	9790	3716	12411	3716	14616	0	2	15000+	4-8	Single	1	24	Medium	0	1e+05
4030	2931	122	11295	122	12976	0	3	7500-10000	4-8	Single	2	24	Low	0	5e+04
4117	1272	6272	12418	6272	14536	0	3	15000+	4-8	Single	3	24	Low	0	5e+04
4125	10958	0	8402	0	16042	0	1	0-7500	64-73	Married	3	88	Medium	0	5e+04
4126	3352	261	8798	261	17017	0	1	10000-15000	64-73	Married	3	88	Low	0	3e+05
4168	8803	16351	12594	16351	14503	0	3	15000+	4-8	Single	2	24	Low	0	3e+05
4183	11163	299	14476	299	14289	1	3	0-7500	4-8	Single	1	23	Medium	0	1e+05
4229	898	63435	13472	63435	15244	0	3	15000+	4-8	Single	1	23	Low	0	1e+05
4297	4617	2600	13049	2600	13597	1	3	7500-10000	4-8	Single	1	22	Medium	0	5e+04
4383	6201	20	13472	20	15244	0	3	15000+	4-8	Single	1	22	Low	0	5e+05
4401	5179	30796	13404	30796	14333	0	3	0-7500	4-8	Single	1	21	Low	0	5e+04
4483	9338	10871	12084	10871	13639	0	3	7500-10000	4-8	Single	1	23	Low	0	1e+05
4500	7182	120	11917	120	13900	0	2	10000-15000	4-8	Single	3	24	Low	0	5e+04
4605	6611	150	12348	150	13742	0	2	0-7500	4-8	Single	1	24	High	0	5e+04
4639	1239	53	13531	53	13594	1	3	0-7500	4-8	Single	2	22	Low	0	5e+04
4663	7489	44	11860	44	12481	0	2	0-7500	24-33	Single	4	46	High	0	5e+04
4689	10598	0	11381	0	13103	0	2	0-7500	4-8	Single	3	22	Medium	0	3e+05
4715	14591	120	12653	120	13199	0	3	10000-15000	4-8	Single	4	21	Low	0	1e+05
4718	2647	21810	11917	21810	13900	0	2	10000-15000	4-8	Single	3	23	Low	0	1e+05
4754	7724	0	12086	0	13868	0	2	10000-15000	4-8	Single	2	21	High	0	5e+05
4773	659	19	12348	19	13742	0	2	0-7500	4-8	Single	1	23	High	0	5e+05
4794	228	1623	12086	1623	13868	0	2	10000-15000	4-8	Single	2	23	Medium	0	1e+05
4803	34	0	12411	0	14616	0	2	15000+	4-8	Single	1	22	Low	0	1e+05
4805	13452	1250	12411	1250	14616	0	2	15000+	4-8	Single	1	22	Medium	0	3e+05
4841	14397	1132	12418	1132	14536	0	3	15000+	4-8	Single	3	23	Low	0	5e+04
4888	3901	890	12594	890	14503	0	3	15000+	4-8	Single	2	23	Low	0	5e+05
4889	6305	21585	13120	21585	14465	0	3	10000-15000	4-8	Single	2	23	Low	0	5e+04
4936	10081	5780	13282	5780	23469	0	2	7500-10000	64-73	Married	1	87	Medium	0	3e+05
5055	9891	1658	13472	1658	15244	0	3	15000+	4-8	Single	1	22	Medium	0	5e+04
5100	5607	100000	12348	122443	13742	0	2	0-7500	4-8	Single	1	24	High	0	3e+05
5103	10672	5144	11917	5144	13900	0	2	10000-15000	4-8	Single	3	22	Medium	0	5e+04
5148	8114	0	14877	0	15204	1	2	10000-15000	24-33	Single	1	42	High	0	1e+05
5248	12586	84521	12870	84521	13857	1	2	10000-15000	4-8	Single	3	21	High	0	1e+05
5269	4392	368	11104	368	12867	0	2	15000+	44-53	Married	1	60	High	0	3e+05
5310	892	3445	15536	3445	17342	2	3	0-7500	4-8	Single	1	21	High	0	3e+05
5312	14595	0	10814	0	12209	0	2	10000-15000	44-53	Married	2	60	High	0	5e+04
5410	10087	0	11946	0	13053	0	2	15000+	34-43	Married	1	59	Medium	0	5e+04
5459	14343	0	13713	0	14497	1	2	10000-15000	24-33	Single	3	45	Medium	0	5e+04
5462	9445	13266	13472	13266	15244	0	3	15000+	4-8	Single	1	21	Medium	0	5e+04
5476	3788	0	12930	0	14577	0	2	10000-15000	4-8	Single	1	21	High	0	1e+05
5497	5881	0	12411	0	14616	0	2	15000+	4-8	Single	1	24	Low	0	5e+04
5574	8878	1241	11601	1241	13905	0	2	15000+	4-8	Single	2	24	Low	0	1e+05
5646	10191	0	8564	0	17024	0	1	15000+	64-73	Married	2	88	High	0	3e+05
5683	11257	8464	12348	8464	13742	0	2	0-7500	4-8	Single	1	22	Low	0	3e+05
5717	11564	2299	12594	2299	14503	0	3	15000+	4-8	Single	2	22	Low	0	5e+04
5723	12765	5849	12594	5849	14503	0	3	15000+	4-8	Single	2	24	Low	0	1e+05
5760	10937	261	11295	261	12976	0	3	7500-10000	4-8	Single	2	24	Medium	0	5e+04
5815	10290	16131	11166	16131	12419	0	2	15000+	34-43	Married	2	54	Medium	0	3e+05
5834	2271	12317	13963	12317	14532	1	2	10000-15000	4-8	Single	1	21	Low	0	5e+05
5838	13063	196	14549	196	15197	1	3	15000+	4-8	Single	1	22	Low	0	5e+04
5843	3376	1632	12418	1632	14536	0	3	15000+	4-8	Single	3	24	Low	0	1e+05
5856	6237	0	11917	0	13900	0	2	10000-15000	4-8	Single	3	21	Low	0	1e+05
5864	727	0	10405	0	12441	0	2	7500-10000	4-8	Single	2	22	Medium	0	1e+05
5908	12542	1059	12084	1059	13639	0	3	7500-10000	4-8	Single	1	21	Low	0	3e+05
5953	11819	8099	12084	8099	13639	0	3	7500-10000	4-8	Single	1	21	Low	0	3e+05
5962	4740	0	13776	0	15251	0	2	10000-15000	24-33	Single	1	41	High	0	1e+05
5972	14241	2504	12878	2504	14509	0	2	10000-15000	24-33	Single	2	40	Low	0	5e+04
5973	4367	54405	12493	54405	12793	1	2	10000-15000	44-53	Married	1	63	Low	0	3e+05
6011	10541	0	11946	0	13053	0	2	15000+	34-43	Married	1	57	Medium	0	5e+04
6026	27	7227	11656	7227	12655	0	2	10000-15000	4-8	Single	4	24	Low	0	5e+05
6040	10838	127	12411	127	14616	0	2	15000+	4-8	Single	1	24	High	0	3e+05
6040	11038	19692	12086	19692	13868	0	2	10000-15000	4-8	Single	2	22	Low	0	5e+05
6055	13899	54894	12411	54894	14616	0	2	15000+	4-8	Single	1	23	Low	0	5e+05
6062	2351	0	11131	0	13077	0	2	7500-10000	4-8	Single	1	21	Low	0	3e+05
6087	13494	359	13472	359	15244	0	3	15000+	4-8	Single	1	23	Low	0	1e+05
6098	4698	0	13403	0	14571	1	2	15000+	4-8	Single	1	23	High	0	3e+05
6120	8243	288	13410	288	14491	1	3	15000+	4-8	Single	3	24	Low	0	5e+04
6146	3243	34271	12587	34271	12616	1	2	10000-15000	4-8	Single	4	22	Medium	0	3e+05
6169	12711	11899	14036	11899	15204	0	3	10000-15000	4-8	Single	1	22	Low	0	3e+05
6176	295	1678	13472	1678	15244	0	3	15000+	4-8	Single	1	23	Low	0	5e+04
6181	3781	4546	12653	4546	13199	0	3	10000-15000	4-8	Single	4	24	Low	0	5e+04
6196	12821	4531	11917	4531	13900	0	2	10000-15000	4-8	Single	3	21	Low	0	5e+04
6238	5600	10482	10260	10482	12469	0	2	7500-10000	4-8	Single	3	21	High	0	5e+04
6267	161	19862	12873	19862	13234	1	2	15000+	24-33	Single	4	41	High	0	1e+05
6272	13758	0	11439	0	13937	0	2	15000+	4-8	Single	3	21	High	0	5e+04
6280	3058	0	12348	0	13742	0	2	0-7500	4-8	Single	1	23	Low	0	5e+04
6432	10368	0	11131	0	13077	0	2	7500-10000	4-8	Single	1	24	Low	0	5e+05
6434	585	3595	12411	3595	14616	0	2	15000+	4-8	Single	1	21	Medium	0	1e+05
6465	10441	3984	12084	3984	13639	0	3	7500-10000	4-8	Single	1	21	Medium	0	5e+04
6473	3842	0	10814	0	12209	0	2	10000-15000	44-53	Married	2	65	High	0	3e+05
6590	8663	1466	13713	1466	14497	1	2	10000-15000	24-33	Single	3	42	High	0	1e+05
6592	11802	597	13404	597	14333	0	3	0-7500	4-8	Single	1	21	Low	0	5e+04
6613	10270	0	13282	0	21411	0	2	0-7500	64-73	Married	4	87	High	0	5e+04
6657	7155	0	11542	0	13074	0	2	0-7500	4-8	Single	2	22	Low	0	5e+05
6674	3671	0	11656	0	12655	0	2	10000-15000	4-8	Single	4	24	Medium	0	3e+05
6693	424	8035	13120	8035	14465	0	3	10000-15000	4-8	Single	2	21	Low	0	5e+04
6695	5673	0	11569	0	12833	0	2	10000-15000	44-53	Married	1	64	Medium	0	5e+04
6701	12334	4516	12594	4516	14503	0	3	15000+	4-8	Single	2	23	High	0	1e+05
6745	4117	16770	11800	16770	13481	2	3	15000+	9-13	Single	2	25	Low	0	5e+04
6780	11585	0	9162	0	17894	0	1	15000+	64-73	Married	1	86	High	0	5e+05
6811	1602	3061	12594	3061	14503	0	3	15000+	4-8	Single	2	21	Low	0	5e+04
6819	10415	41	10260	41	12469	0	2	7500-10000	4-8	Single	3	23	Low	0	1e+05
6873	2217	0	12930	0	14577	0	2	10000-15000	4-8	Single	1	23	Low	0	3e+05
6892	7452	6609	11131	6609	13077	0	2	7500-10000	4-8	Single	1	24	Low	0	3e+05
6900	14871	3223	11542	3223	13074	0	2	0-7500	4-8	Single	2	21	Low	0	5e+05
6911	9979	4240	12878	4240	14509	0	2	10000-15000	24-33	Single	2	48	Medium	0	5e+04
6935	9680	186	12937	186	14497	0	3	10000-15000	4-8	Single	3	21	Low	0	5e+04
7010	7116	6574	11188	6574	12688	0	2	15000+	4-8	Single	4	21	Low	0	1e+05
7013	6490	728	8920	728	15486	1	1	15000+	64-73	Married	4	88	High	0	5e+04
7017	9996	0	11439	0	13937	0	2	15000+	4-8	Single	3	22	Medium	0	3e+05
7046	1861	1043	15158	1043	15157	1	3	10000-15000	4-8	Single	1	22	Medium	0	1e+05
7085	13053	0	9894	0	17839	1	1	15000+	64-73	Married	1	86	High	0	1e+05
7121	12430	963	11131	963	13077	0	2	7500-10000	4-8	Single	1	24	Low	0	5e+04
7130	12123	0	13335	0	13699	1	2	0-7500	4-8	Single	1	21	Low	0	5e+04
7140	10714	19523	13116	19523	13193	1	3	15000+	4-8	Single	4	22	Low	0	3e+05
7208	14150	1270	11917	1270	13900	0	2	10000-15000	4-8	Single	3	21	Low	0	5e+04
7218	14459	11882	10405	11882	12441	0	2	7500-10000	4-8	Single	2	22	Low	0	1e+05
7226	7972	0	13776	0	15251	0	2	10000-15000	24-33	Single	1	41	High	0	5e+05
7250	315	147	16748	147	27287	0	3	10000-15000	64-73	Married	1	89	Low	0	5e+04
7251	7356	0	12021	0	13036	1	2	7500-10000	4-8	Single	1	21	Medium	0	1e+05
7316	5127	2212	12084	2212	13639	0	3	7500-10000	4-8	Single	1	23	Medium	0	1e+05
7377	11567	120	13120	120	14465	0	3	10000-15000	4-8	Single	2	22	Low	0	1e+05
7379	14373	139	13116	139	13193	1	3	15000+	4-8	Single	4	22	Low	0	5e+04
7392	13590	0	12104	0	13158	2	2	10000-15000	14-23	Single	1	31	Low	0	3e+05
7415	4511	120	13472	120	15244	0	3	15000+	4-8	Single	1	23	High	0	5e+04
7425	8870	449	13472	449	15244	0	3	15000+	4-8	Single	1	21	Low	0	5e+04
7431	9742	303	14036	303	15204	0	3	10000-15000	4-8	Single	1	22	Low	0	3e+05
7445	12519	155	11295	155	12976	0	3	7500-10000	4-8	Single	2	22	Low	0	5e+04
7493	3007	16698	12870	16698	13857	1	2	10000-15000	4-8	Single	3	24	Medium	0	1e+05
7511	9964	158	13116	158	13193	1	3	15000+	4-8	Single	4	23	Low	0	1e+05
7532	7854	15437	12198	15437	12936	1	3	7500-10000	4-8	Single	2	22	Medium	0	5e+04
7587	10272	178	12145	178	13234	0	3	15000+	4-8	Single	4	23	Low	0	5e+04
7633	14750	0	11891	0	12408	1	2	15000+	34-43	Married	3	55	Low	0	5e+04
7749	5343	18254	11439	18254	13937	0	2	15000+	4-8	Single	3	22	Low	0	3e+05
7765	2392	6992	12348	6992	13742	0	2	0-7500	4-8	Single	1	24	Low	0	1e+05
7788	3302	273	12084	273	13639	0	3	7500-10000	4-8	Single	1	22	Low	0	1e+05
7789	8099	563	13963	563	14532	1	2	10000-15000	4-8	Single	1	23	High	0	1e+05
7893	12456	0	12126	0	13709	0	2	0-7500	24-33	Single	3	44	Low	0	1e+05
7903	8529	100000	11946	139641	13053	0	2	15000+	34-43	Married	1	54	Medium	0	5e+05
7953	1523	147	10380	147	12241	0	2	15000+	44-53	Married	2	67	High	0	1e+05
7983	13700	177	11601	177	13905	0	2	15000+	4-8	Single	2	24	Low	0	3e+05
7988	13134	8093	12418	8093	14536	0	3	15000+	4-8	Single	3	24	Medium	0	1e+05
7994	12617	100000	11381	157621	13103	0	2	0-7500	4-8	Single	3	24	Low	0	3e+05
8007	5492	7148	11295	7148	12976	0	3	7500-10000	4-8	Single	2	21	Low	0	5e+04
8015	8116	131	12587	131	12616	1	2	10000-15000	4-8	Single	4	21	Low	0	3e+05
8048	14144	50012	11138	50012	13005	0	3	7500-10000	4-8	Single	3	23	Low	0	1e+05
8063	3226	820	14320	820	16536	2	3	0-7500	4-8	Single	3	23	Low	0	3e+05
8066	8446	1903	13404	1903	14333	0	3	0-7500	4-8	Single	1	22	Low	0	5e+04
8140	10640	2998	12937	2998	14497	0	3	10000-15000	4-8	Single	3	22	Medium	0	1e+05
8182	2954	1871	12594	1871	14503	0	3	15000+	4-8	Single	2	21	Low	0	1e+05
8226	3875	0	11381	0	13103	0	2	0-7500	4-8	Single	3	22	Medium	0	5e+05
8252	14926	0	11381	0	13103	0	2	0-7500	4-8	Single	3	22	Medium	0	5e+04
8255	13794	22811	12086	22811	13868	0	2	10000-15000	4-8	Single	2	21	Medium	0	3e+05
8281	3307	0	13776	0	15251	0	2	10000-15000	24-33	Single	1	41	High	0	5e+04
8299	9763	0	10260	0	12469	0	2	7500-10000	4-8	Single	3	23	Low	0	3e+05
8304	1298	0	11439	0	13937	0	2	15000+	4-8	Single	3	24	Low	0	5e+04
8413	13192	15415	10260	15415	12469	0	2	7500-10000	4-8	Single	3	23	Low	0	1e+05
8415	10493	39364	11188	39364	12688	0	2	15000+	4-8	Single	4	21	Medium	0	3e+05
8431	13816	4001	11601	4001	13905	0	2	15000+	4-8	Single	2	22	Medium	0	3e+05
8476	4203	499	11917	499	13900	0	2	10000-15000	4-8	Single	3	23	Low	0	5e+04
8502	156	69095	13600	69095	14458	1	3	15000+	4-8	Single	2	21	Low	0	1e+05
8507	7027	0	9272	0	12031	2	1	10000-15000	4-8	Single	1	22	High	0	5e+04
8523	13199	0	12898	0	14663	0	2	15000+	34-43	Single	4	50	Low	0	1e+05
8545	8659	120	11601	120	13905	0	2	15000+	4-8	Single	2	23	Medium	0	1e+05
8554	12913	120	11439	120	13937	0	2	15000+	4-8	Single	3	22	Medium	0	5e+04
8633	4980	0	11439	0	13937	0	2	15000+	4-8	Single	3	22	Low	0	1e+05
8641	12114	0	8798	0	17017	0	1	10000-15000	64-73	Married	3	87	High	0	5e+04
8655	14469	52013	10260	52013	12469	0	2	7500-10000	4-8	Single	3	23	Low	0	3e+05
8680	13647	0	10405	0	12441	0	2	7500-10000	4-8	Single	2	24	Medium	0	5e+05
8705	3188	0	11601	0	13905	0	2	15000+	4-8	Single	2	22	Low	0	1e+05
8709	3620	632	12418	632	14536	0	3	15000+	4-8	Single	3	21	Low	0	3e+05
8710	4917	2991	13335	2991	13699	1	2	0-7500	4-8	Single	1	23	Low	0	5e+05
8720	2533	4352	11601	4352	13905	0	2	15000+	4-8	Single	2	22	Medium	0	5e+04
8757	11135	22341	12594	22341	14503	0	3	15000+	4-8	Single	2	23	Low	0	5e+04
8766	14451	10969	13472	10969	15244	0	3	15000+	4-8	Single	1	23	Medium	0	1e+05
8781	5907	464	12084	464	13639	0	3	7500-10000	4-8	Single	1	24	Medium	0	1e+05
8784	9822	1788	13403	1788	14571	1	2	15000+	4-8	Single	1	23	Medium	0	3e+05
8837	3954	120	10405	120	12441	0	2	7500-10000	4-8	Single	2	22	Medium	0	1e+05
8872	11047	124	11656	124	12655	0	2	10000-15000	4-8	Single	4	21	Medium	0	5e+04
8948	3371	0	14877	0	15204	1	2	10000-15000	24-33	Single	1	43	High	0	5e+04
8949	7890	746	12411	746	14616	0	2	15000+	4-8	Single	1	23	Low	0	1e+05
9039	7910	4443	12937	4443	14497	0	3	10000-15000	4-8	Single	3	22	Low	0	5e+04
9043	10199	6948	12930	6948	14577	0	2	10000-15000	4-8	Single	1	24	Medium	0	5e+04
9045	14057	17615	12937	17615	14497	0	3	10000-15000	4-8	Single	3	21	Low	0	1e+05
9057	13656	35	13776	35	15251	0	2	10000-15000	24-33	Single	1	40	Medium	0	1e+05
9071	6868	125	12083	125	12442	0	3	0-7500	4-8	Single	4	22	Low	0	5e+04
9090	1308	49448	12411	49448	14616	0	2	15000+	4-8	Single	1	21	Medium	0	3e+05
9111	11778	19111	14549	19111	15197	1	3	15000+	4-8	Single	1	22	Low	0	1e+05
9123	7099	2581	11917	2581	13900	0	2	10000-15000	4-8	Single	3	22	Low	0	5e+05
9133	11486	15558	13258	15558	16863	2	2	15000+	4-8	Single	3	21	Low	0	1e+05
9135	859	10947	11439	10947	13937	0	2	15000+	4-8	Single	3	22	Low	0	1e+05
9209	2525	638	11295	638	12976	0	3	7500-10000	4-8	Single	2	24	Medium	0	5e+04
9274	4293	0	12465	0	13033	1	2	0-7500	4-8	Single	2	23	Medium	0	5e+04
9279	11598	20	12084	20	13639	0	3	7500-10000	4-8	Single	1	21	Low	0	1e+05
9292	12383	1908	12411	1908	14616	0	2	15000+	4-8	Single	1	23	Low	0	5e+05
9347	3168	0	11131	0	13077	0	2	7500-10000	4-8	Single	1	23	High	0	5e+04
9359	10523	120	11086	120	13016	0	2	7500-10000	24-33	Single	2	40	Low	0	5e+04
9380	5074	55069	11104	55069	12867	0	2	15000+	44-53	Married	1	66	Low	0	5e+04
9423	1987	0	12411	0	14616	0	2	15000+	4-8	Single	1	22	High	0	1e+05
9517	13016	0	8217	0	14605	0	1	0-7500	64-73	Married	4	88	High	0	3e+05
9551	5435	0	10405	0	12441	0	2	7500-10000	4-8	Single	2	21	Low	0	3e+05
9553	1865	0	11996	0	14377	0	2	7500-10000	34-43	Single	2	50	Medium	0	5e+04
9556	5209	20791	12028	20791	12965	1	3	7500-10000	4-8	Single	3	22	Low	0	5e+04
9590	4692	0	12354	0	13894	1	2	15000+	4-8	Single	3	21	Low	0	3e+05
9669	8981	6800	12059	6800	12380	1	2	15000+	34-43	Married	2	50	Medium	0	3e+05
9689	742	23092	11295	23092	12976	0	3	7500-10000	4-8	Single	2	22	Medium	0	3e+05
9695	2939	10488	11439	10488	13937	0	2	15000+	4-8	Single	3	24	Medium	0	1e+05
9716	4729	411	12086	411	13868	0	2	10000-15000	4-8	Single	2	23	Medium	0	5e+04
9760	1681	0	12411	0	14616	0	2	15000+	4-8	Single	1	22	Low	0	3e+05
9801	12022	1163	10260	1163	13941	2	1	15000+	34-43	Single	1	57	Medium	0	5e+05
9827	10045	37061	12086	37061	13868	0	2	10000-15000	4-8	Single	2	22	Medium	0	5e+04
9838	11554	49220	10260	49220	12469	0	2	7500-10000	4-8	Single	3	24	Medium	0	3e+05
9940	5132	8836	13472	8836	15244	0	3	15000+	4-8	Single	1	24	Low	0	5e+04

Let’s visualize our rejection regions in order to fine-tune exactly who we need to reject.

Drivers Under Age 25

compare.pp.capped %>% filter(`Driver Age` < 25) %>% ggplot(aes(x = `Annual Mileage`, y = `Predicted Pure Premium`)) + geom_bar(aes(fill = `Annual Mileage`), stat = "summary", fun.y = "mean", show.legend = TRUE) + facet_grid(. ~ `Marital Status`) + theme(legend.position = "bottom", axis.text.x = element_blank(), axis.ticks.x = element_blank()) + ggtitle("Total Rejection: Average Projected Loss by Annual Mileage")

rej %>% filter(`Driver Age` < 25) %>% ggplot(aes(x = `Annual Mileage`, y = `Predicted Pure Premium`)) + geom_bar(aes(fill = `Annual Mileage`), stat = "summary", fun.y = "mean", show.legend = TRUE) + facet_grid(. ~ `Marital Status`) + theme(legend.position = "bottom", axis.text.x = element_blank(), axis.ticks.x = element_blank()) + ggtitle("Desired Rejection: Average Projected Loss by Annual Mileage")

Comparing the two exhibits, we conclude that we’ll reject drivers with <10 years of driving experience who are married with 0-7500 annual mileage. This may be a group of high-risk (early marriage), low-experience drivers (low mileage) who we cannot charge adequate premiums to cover losses, at least in this aggregation of data.

Territory 4

compare.pp.capped %>% filter(`Driver Age` < 30) %>% ggplot(aes(x = `Territory`, y = `Predicted Pure Premium`)) + geom_bar(aes(fill = `Territory`), stat = "summary", fun.y = "mean", show.legend = TRUE) + facet_grid(. ~ `Marital Status`) + theme(legend.position = "bottom", axis.text.x = element_blank(), axis.ticks.x = element_blank()) + ggtitle("Total Rejection: Average Projected Loss by Territory")

rej %>% filter(`Driver Age` < 30) %>% ggplot(aes(x = `Territory`, y = `Predicted Pure Premium`)) + geom_bar(aes(fill = `Territory`), stat = "summary", fun.y = "mean", show.legend = TRUE) + facet_grid(. ~ `Marital Status`) + theme(legend.position = "bottom", axis.text.x = element_blank(), axis.ticks.x = element_blank()) + ggtitle("Desired Rejection: Average Projected Loss by Territory")

Territory 4 has the lowest charged premiums of all territories, yet the expected losses in this territory among married policyholders is very high. In general, Territory 4 has the lowest average loss, so we’ll reject young (<15 years driver experience) married drivers from territory 4.

Territory 2

compare.pp.capped %>% filter(`Driver Age` > 60) %>% ggplot(aes(x = `Territory`, y = `Predicted Pure Premium`)) + geom_bar(aes(fill = `Territory`), stat = "summary", fun.y = "mean", show.legend = TRUE) + facet_grid(. ~ `Marital Status`) + theme(legend.position = "bottom", axis.text.x = element_blank(), axis.ticks.x = element_blank()) + ggtitle("Total Rejection: Average Projected Loss by Territory")

rej %>% filter(`Driver Age` > 60) %>% ggplot(aes(x = `Territory`, y = `Predicted Pure Premium`)) + geom_bar(aes(fill = `Territory`), stat = "summary", fun.y = "mean", show.legend = TRUE) + facet_grid(. ~ `Marital Status`) + theme(legend.position = "bottom", axis.text.x = element_blank(), axis.ticks.x = element_blank()) + ggtitle("Desired Rejection: Average Projected Loss by Territory")

We’ll reject older (45+ years driver experience) from Territory 2.

Driving History (Accident Points, Conviction Points)

Accident Points:

compare.pp.capped %>% filter(`Driver Age` > 10) %>% ggplot(aes(x = `Accident Points (AP) last 3 years`, y = `Predicted Pure Premium`)) + geom_bar(aes(fill = `Accident Points (AP) last 3 years`), stat = "summary", fun.y = "mean", show.legend = TRUE) + facet_grid(. ~ `Liability Limit`) + theme(legend.position = "bottom", axis.text.x = element_blank(), axis.ticks.x = element_blank()) + ggtitle("Total Rejection: Average Projected Loss by Accident Points (AP) last 3 years")

rej %>% filter(`Driver Age` > 10) %>% ggplot(aes(x = `Accident Points (AP) last 3 years`, y = `Predicted Pure Premium`)) + geom_bar(aes(fill = `Accident Points (AP) last 3 years`), stat = "summary", fun.y = "mean", show.legend = TRUE) + facet_grid(. ~ `Liability Limit`) + theme(legend.position = "bottom", axis.text.x = element_blank(), axis.ticks.x = element_blank()) + ggtitle("Desired Rejection: Average Projected Loss by Accident Points (AP) last 3 years")

Unfortunately it seems as though we cannot safely perform rejections via this aggregation without inadvertently rejecting desired drivers. To be conservative here, we’ll reject all drivers with 2+ accident points in the last 3 years for all coverage of $100,000 liability and above. However, we can offer coverage at the $50,000 limit with a much higher AP relativity. We’ll try conviction points instead of accident points.

Conviction Points:

compare.pp.capped %>% filter(`Driver Age` > 10) %>% ggplot(aes(x = `Conviction Points (CP) last 3 years`, y = `Predicted Pure Premium`)) + geom_bar(aes(fill = `Conviction Points (CP) last 3 years`), stat = "summary", fun.y = "mean", show.legend = TRUE) + facet_grid(. ~ `Liability Limit`) + theme(legend.position = "bottom", axis.text.x = element_blank(), axis.ticks.x = element_blank()) + ggtitle("Total Rejection: Average Projected Loss by Conviction Points (CP) last 3 years")

rej %>% filter(`Driver Age` > 10) %>% ggplot(aes(x = `Conviction Points (CP) last 3 years`, y = `Predicted Pure Premium`)) + geom_bar(aes(fill = `Conviction Points (CP) last 3 years`), stat = "summary", fun.y = "mean", show.legend = TRUE) + facet_grid(. ~ `Liability Limit`) + theme(legend.position = "bottom", axis.text.x = element_blank(), axis.ticks.x = element_blank()) + ggtitle("Desired Rejection: Average Projected Loss by Conviction Points (CP) last 3 years")

From this exhibit, we choose to reject drivers with 3+ conviction points in the last 3 years. However, we want to allow them the least coverage at $50,000 liability, albeit with a high premium relativity.

However, in the present case, we cannot change the rating structure and must take judgement regarding this. We choose to not place restrictions on policyholders with 3+ conviction points in the past 3 years, because we will be making the assumption that no drivers have conviction points in any of policy years (PY) 2016, 2017, 2018.

Recall that we cannot use Credit Score in our underwriting guideline or rating mechanism. Interestingly, our observed and projected pure premiums both show the monotonic trend that lower credit scores incur higher losses.

# compare.pp.capped %>% filter(`Driver Age` > 85) %>% ggplot(aes(x = `Annual Mileage`, y = `Pure Premium`)) + geom_bar(fill = `Annual Mileage`, stat = "summary", fun.y = "mean") + facet_grid(. ~ `Marital Status`)


compare.pp.capped %>% filter(`Driver Age` > 10) %>% ggplot(aes(x = `Credit Score`, y = `Pure Premium`)) + geom_bar(aes(fill = `Credit Score`), stat = "summary", fun.y = "mean", show.legend = TRUE) + facet_grid(. ~ `Marital Status`) + theme(legend.position = "bottom", axis.text.x = element_blank(), axis.ticks.x = element_blank()) + ggtitle("Observed Pure Premium by Credit Score")

compare.pp.capped %>% filter(`Driver Age` > 10) %>% ggplot(aes(x = `Credit Score`, y = `Predicted Pure Premium`)) + geom_bar(aes(fill = `Credit Score`), stat = "summary", fun.y = "mean", show.legend = TRUE) + facet_grid(. ~ `Marital Status`) + theme(legend.position = "bottom", axis.text.x = element_blank(), axis.ticks.x = element_blank()) + ggtitle("Predicted Pure Premium by Credit Score")

Comparing the above two figures, we filtered down to drivers only ages 60+ and find that single drivers of age 60+ with low credit scores on average incur high losses. This is not caught in our model, so we need to reject this category somehow.

7. Automating and Applying UW Guidelines to 2019 Applicants

First we note that there is no overlap in vehicle numbers or policy numbers. In particular, no existing policy is attempting to add another vehicle.

apps <- read_excel("Dropbox/Actuary/proj/case-comp/GA/ga-csv/GA_Data - Applications.xlsx")

max(tbl$`Policy Number`)

## [1] 10000

# [1] 10000
min(apps$`Policy Number`)

## [1] 10001

# [1] 10001

max(tbl$`Vehicle Number`)

## [1] 15000

# [1] 15000
min(apps$`Policy Number`)

## [1] 10001

# [1] 15001

In summary, our underwriting guidelines are to reject any applicant who satisfies one of the following rows:

45+ Years Driver Experience & Single
35+ Years Driver Experience & Single & 0-7500 or 10000-15000 Annual Mileage
<10 Years Driver Experience & Married & 0-7500 Annual Mileage
<15 Years Driver Experience & Married & Territory 4

Ideally, we’ll allow the following but only at the lowest liability (with higher relativities to compensate). But for now, we’ll wholly still accept the following, but with increased rates (as the premiums will be naturally adjusted via relativities: 1/1.2/1.4/1.6)

2+ Accident Points (last 3 years)
3+ Conviction Points (last 3 years) <-> these recent data are incredible, so DEFINITELY do not use for underwriting guideline.

Now for #6, we would like to reject all. However, in a realistic setting, rejecting longterm loyal customers due to a sudden restriction in risk appetite reflects poorly on Cal Insurance. In terms of public relations and trust, it is much preferrable to retain customers to not have to provide introductory discounts for new customers with Cal Insurance (further analysis required to support this).

Programming the UW Guidelines

# implement UW guidelines as logic check to assign 0: reject, 1: accept

apps <- apps %>% mutate(`Driver Experience` = `Driver Age` - 15) # adjust age into driver experience
apps <- apps %>% mutate(`Decision` = 1) # default decisions to accept and reject in specific scenarios


for (i in 1:15000) {
  # 1: reject 45+ years driver experience + single
  if (apps$`Driver Experience`[i] >= 45 & apps$`Marital Status`[i] == "Single") {
    apps$Decision[i] <- 0
  }
  
  # 2: reject 35+ yrs driver exp + single + either low or mid-high annual mileage
  if (apps$`Driver Experience`[i] >= 35 & apps$`Marital Status`[i] == "Single" & (apps$`Annual Mileage`[i] == "0-7500" || apps$`Annual Mileage`[i] == "10000-15000") ) {
    apps$Decision[i] <- 0
  }
  
  # 3: reject <10 yrs driver exp + married + low mileage
  if (apps$`Driver Experience`[i] <= 10 & apps$`Marital Status`[i] == "Married" & apps$`Annual Mileage`[i] == "0-7500") {
    apps$Decision[i] <- 0
  }
  
  # 4: reject <15 yrs driver exp + married + territory 4
  if (apps$`Driver Experience`[i] <= 15 & apps$`Marital Status`[i] == "Married" & apps$Territory[i] == 4) {
    apps$Decision[i] <- 0
  }
  
  

}

print(paste0("The acceptance rate is: ", sum(apps$Decision)/length(apps$Decision) * 100, "%" ) ) # only reject 171 people

## [1] "The acceptance rate is: 98.86%"

# write into .csv
apps %>% select(`Vehicle Number`, `Decision`) %>% write.csv(file = "decisions.csv", )


# apps %>% select(`Vehicle Number`, `Decision`)  %>% qkable()

We only reject a very few applications here because we opt to not use incredible data (conviction points) or reject

Here’s a quick look at the applications we reject:

app.rej <- apps %>% filter(`Decision` == 0)
app.acc <- apps %>% filter(`Decision` == 1) # accepted applications

app.rej %>% slice(1:100) %>% qkable(height = "500px") # excerpt of people we reject

Vehicle Number	Policy Year	Policy Number	Marital Status	Driver Age	Driver Age Band	Annual Mileage	Territory	Credit Score	Car Value	Car Value Band	Accident Points	Liability Limit	Physical Damage Deductible	Conviction Points	Base_PP	Rel_Age	Rel_Mileage	Rel_Territory	Rel_Car	Rel_Accident	Rel_Conviction	Rel_Limit	Rel_Deductible	Charged Premium	Driver Experience
15011	2019	11950	Single	55	50-59	10000-15000	3	High	39110	30000-40000	0	3e+05	500	0	1500	0.8	1.0	0.9	1.045	1.0	1.0	1.00	1.000	1128.6000	40
15143	2019	14769	Single	77	70-79	15000+	3	High	20000	20000-30000	0	5e+04	100	0	1500	0.8	1.2	0.9	1.000	1.0	1.0	0.60	1.080	839.8080	62
15381	2019	19695	Married	24	20-24	0-7500	2	Medium	10550	10000-20000	0	3e+05	500	1	1500	2.0	0.7	1.1	0.880	1.0	1.2	1.00	1.000	2439.3600	9
15386	2019	11282	Single	51	50-59	0-7500	4	Medium	12590	10000-20000	0	5e+04	250	0	1500	0.8	0.7	0.8	0.880	1.0	1.0	0.60	1.045	370.7827	36
15401	2019	14122	Married	30	30-39	15000+	4	Low	29340	20000-30000	1	1e+05	250	0	1500	1.0	1.2	0.8	1.000	1.2	1.0	0.88	1.045	1589.0688	15
15408	2019	15895	Single	51	50-59	10000-15000	4	Medium	56350	40000+	1	5e+05	250	0	1500	0.8	1.0	0.8	1.080	1.2	1.0	1.12	1.045	1456.1649	36
15508	2019	18825	Married	29	25-29	0-7500	4	Low	20090	20000-30000	0	3e+05	500	0	1500	1.5	0.7	0.8	1.000	1.0	1.0	1.00	1.000	1260.0000	14
15532	2019	10767	Single	96	90+	0-7500	1	Medium	29440	20000-30000	0	1e+05	100	0	1500	0.8	0.7	1.2	1.000	1.0	1.0	0.88	1.080	958.0032	81
15570	2019	10491	Married	28	25-29	15000+	4	Medium	10940	10000-20000	1	5e+05	1000	0	1500	1.5	1.2	0.8	0.880	1.2	1.0	1.12	0.935	2388.6213	13
15784	2019	17651	Single	50	50-59	0-7500	2	High	39330	30000-40000	0	1e+05	250	0	1500	0.8	0.7	1.1	1.045	1.0	1.0	0.88	1.045	887.9474	35
15831	2019	15278	Married	26	25-29	15000+	4	High	22570	20000-30000	0	5e+04	100	1	1500	1.5	1.2	0.8	1.000	1.0	1.2	0.60	1.080	1679.6160	11
15836	2019	13190	Single	51	50-59	0-7500	3	High	27880	20000-30000	0	1e+05	1000	0	1500	0.8	0.7	0.9	1.000	1.0	1.0	0.88	0.935	622.0368	36
15971	2019	17901	Single	52	50-59	0-7500	3	High	95950	40000+	0	5e+04	100	0	1500	0.8	0.7	0.9	1.080	1.0	1.0	0.60	1.080	529.0790	37
16076	2019	18996	Single	50	50-59	0-7500	3	High	28240	20000-30000	0	5e+05	500	0	1500	0.8	0.7	0.9	1.000	1.0	1.0	1.12	1.000	846.7200	35
16097	2019	13917	Single	56	50-59	10000-15000	1	Low	22500	20000-30000	0	3e+05	500	0	1500	0.8	1.0	1.2	1.000	1.0	1.0	1.00	1.000	1440.0000	41
16285	2019	16536	Single	51	50-59	10000-15000	1	Low	35950	30000-40000	1	1e+05	250	0	1500	0.8	1.0	1.2	1.045	1.2	1.0	0.88	1.045	1660.5769	36
16383	2019	13714	Single	55	50-59	0-7500	4	High	31360	30000-40000	0	1e+05	100	1	1500	0.8	0.7	0.8	1.045	1.0	1.2	0.88	1.080	800.8907	40
16448	2019	18604	Single	74	70-79	0-7500	4	High	17420	10000-20000	0	5e+04	100	0	1500	0.8	0.7	0.8	0.880	1.0	1.0	0.60	1.080	383.2013	59
16502	2019	12951	Single	50	50-59	10000-15000	4	High	75490	40000+	0	5e+05	1000	0	1500	0.8	1.0	0.8	1.080	1.0	1.0	1.12	0.935	1085.7370	35
16563	2019	14487	Single	52	50-59	0-7500	2	High	20980	20000-30000	0	5e+05	500	1	1500	0.8	0.7	1.1	1.000	1.0	1.2	1.12	1.000	1241.8560	37
16566	2019	12270	Married	28	25-29	0-7500	4	High	38470	30000-40000	0	5e+04	100	0	1500	1.5	0.7	0.8	1.045	1.0	1.0	0.60	1.080	853.2216	13
16593	2019	12976	Single	54	50-59	0-7500	2	High	78260	40000+	0	5e+05	100	0	1500	0.8	0.7	1.1	1.080	1.0	1.0	1.12	1.080	1207.0840	39
16597	2019	11754	Single	63	60-69	0-7500	4	High	94850	40000+	0	5e+05	100	0	1500	0.8	0.7	0.8	1.080	1.0	1.0	1.12	1.080	877.8793	48
16730	2019	17163	Single	59	50-59	0-7500	2	Medium	47950	40000+	0	5e+05	500	0	1500	0.8	0.7	1.1	1.080	1.0	1.0	1.12	1.000	1117.6704	44
16745	2019	12495	Single	51	50-59	10000-15000	2	Low	25740	20000-30000	0	5e+04	100	0	1500	0.8	1.0	1.1	1.000	1.0	1.0	0.60	1.080	855.3600	36
17033	2019	16611	Single	50	50-59	0-7500	4	High	23440	20000-30000	0	5e+05	1000	0	1500	0.8	0.7	0.8	1.000	1.0	1.0	1.12	0.935	703.7184	35
17095	2019	14138	Single	53	50-59	10000-15000	4	Medium	86160	40000+	0	1e+05	500	0	1500	0.8	1.0	0.8	1.080	1.0	1.0	0.88	1.000	912.3840	38
17188	2019	14888	Single	51	50-59	0-7500	2	Low	36320	30000-40000	1	5e+04	100	0	1500	0.8	0.7	1.1	1.045	1.2	1.0	0.60	1.080	750.8350	36
17330	2019	14570	Married	30	30-39	10000-15000	4	High	29170	20000-30000	0	1e+05	250	0	1500	1.0	1.0	0.8	1.000	1.0	1.0	0.88	1.045	1103.5200	15
17381	2019	18039	Single	50	50-59	0-7500	1	High	13290	10000-20000	0	5e+04	1000	0	1500	0.8	0.7	1.2	0.880	1.0	1.0	0.60	0.935	497.6294	35
17391	2019	13963	Single	51	50-59	10000-15000	3	High	15490	10000-20000	1	3e+05	500	0	1500	0.8	1.0	0.9	0.880	1.2	1.0	1.00	1.000	1140.4800	36
17408	2019	18332	Single	55	50-59	0-7500	3	High	16590	10000-20000	0	3e+05	500	0	1500	0.8	0.7	0.9	0.880	1.0	1.0	1.00	1.000	665.2800	40
17475	2019	16397	Single	58	50-59	10000-15000	1	High	32580	30000-40000	1	3e+05	250	0	1500	0.8	1.0	1.2	1.045	1.2	1.0	1.00	1.045	1887.0192	43
17726	2019	10859	Single	50	50-59	10000-15000	2	Low	28360	20000-30000	0	3e+05	500	0	1500	0.8	1.0	1.1	1.000	1.0	1.0	1.00	1.000	1320.0000	35
17740	2019	19902	Single	50	50-59	10000-15000	4	High	14590	10000-20000	0	3e+05	250	0	1500	0.8	1.0	0.8	0.880	1.0	1.0	1.00	1.045	882.8160	35
17748	2019	11324	Single	51	50-59	0-7500	4	High	48720	40000+	0	5e+05	500	0	1500	0.8	0.7	0.8	1.080	1.0	1.0	1.12	1.000	812.8512	36
17811	2019	12670	Single	54	50-59	0-7500	4	High	22730	20000-30000	0	1e+05	250	0	1500	0.8	0.7	0.8	1.000	1.0	1.0	0.88	1.045	617.9712	39
17896	2019	16212	Married	29	25-29	10000-15000	4	Medium	14360	10000-20000	0	3e+05	500	1	1500	1.5	1.0	0.8	0.880	1.0	1.2	1.00	1.000	1900.8000	14
17921	2019	15497	Single	52	50-59	10000-15000	3	High	95150	40000+	0	3e+05	100	0	1500	0.8	1.0	0.9	1.080	1.0	1.0	1.00	1.080	1259.7120	37
17933	2019	12202	Single	51	50-59	0-7500	4	Low	27230	20000-30000	0	1e+05	250	0	1500	0.8	0.7	0.8	1.000	1.0	1.0	0.88	1.045	617.9712	36
18033	2019	13837	Single	50	50-59	0-7500	1	High	21280	20000-30000	0	1e+05	500	0	1500	0.8	0.7	1.2	1.000	1.0	1.0	0.88	1.000	887.0400	35
18084	2019	17627	Single	53	50-59	10000-15000	3	High	28990	20000-30000	0	1e+05	500	0	1500	0.8	1.0	0.9	1.000	1.0	1.0	0.88	1.000	950.4000	38
18164	2019	11406	Single	52	50-59	0-7500	2	High	83140	40000+	0	5e+05	1000	1	1500	0.8	0.7	1.1	1.080	1.0	1.2	1.12	0.935	1254.0262	37
18179	2019	16759	Married	24	20-24	0-7500	4	Low	32350	30000-40000	1	5e+05	100	0	1500	2.0	0.7	0.8	1.045	1.2	1.0	1.12	1.080	2548.2885	9
18189	2019	13544	Single	52	50-59	10000-15000	3	High	73850	40000+	1	1e+05	1000	0	1500	0.8	1.0	0.9	1.080	1.2	1.0	0.88	0.935	1151.6567	37
18237	2019	18602	Married	27	25-29	0-7500	4	Medium	34620	30000-40000	0	1e+05	500	0	1500	1.5	0.7	0.8	1.045	1.0	1.0	0.88	1.000	1158.6960	12
18573	2019	10850	Married	28	25-29	7500-10000	4	High	7770	0-10000	0	5e+04	100	0	1500	1.5	0.9	0.8	0.720	1.0	1.0	0.60	1.080	755.8272	13
18600	2019	16671	Married	30	30-39	10000-15000	4	High	21190	20000-30000	0	1e+05	1000	0	1500	1.0	1.0	0.8	1.000	1.0	1.0	0.88	0.935	987.3600	15
18681	2019	10736	Single	51	50-59	0-7500	4	High	35290	30000-40000	0	5e+05	1000	0	1500	0.8	0.7	0.8	1.045	1.0	1.0	1.12	0.935	735.3857	36
18816	2019	16241	Single	55	50-59	0-7500	1	Low	87800	40000+	0	3e+05	500	0	1500	0.8	0.7	1.2	1.080	1.0	1.0	1.00	1.000	1088.6400	40
18900	2019	15798	Single	62	60-69	15000+	1	High	12250	10000-20000	0	3e+05	500	0	1500	0.8	1.2	1.2	0.880	1.0	1.0	1.00	1.000	1520.6400	47
19075	2019	16890	Single	51	50-59	0-7500	2	High	33690	30000-40000	0	5e+04	100	0	1500	0.8	0.7	1.1	1.045	1.0	1.0	0.60	1.080	625.6958	36
19173	2019	13588	Single	50	50-59	0-7500	2	High	18410	10000-20000	0	5e+04	250	1	1500	0.8	0.7	1.1	0.880	1.0	1.2	0.60	1.045	611.7915	35
19271	2019	16704	Married	25	25-29	0-7500	3	High	15780	10000-20000	0	5e+05	1000	0	1500	1.5	0.7	0.9	0.880	1.0	1.0	1.12	0.935	1306.2773	10
19361	2019	18789	Single	50	50-59	10000-15000	3	Medium	61480	40000+	0	5e+05	1000	0	1500	0.8	1.0	0.9	1.080	1.0	1.0	1.12	0.935	1221.4541	35
19428	2019	19903	Single	53	50-59	10000-15000	2	High	24910	20000-30000	0	5e+04	100	0	1500	0.8	1.0	1.1	1.000	1.0	1.0	0.60	1.080	855.3600	38
19490	2019	15786	Single	57	50-59	0-7500	3	Medium	11750	10000-20000	0	5e+04	250	0	1500	0.8	0.7	0.9	0.880	1.0	1.0	0.60	1.045	417.1306	42
19504	2019	17946	Single	63	60-69	10000-15000	2	Medium	33110	30000-40000	0	3e+05	500	0	1500	0.8	1.0	1.1	1.045	1.0	1.0	1.00	1.000	1379.4000	48
19531	2019	10611	Single	51	50-59	10000-15000	4	High	21450	20000-30000	0	5e+05	1000	0	1500	0.8	1.0	0.8	1.000	1.0	1.0	1.12	0.935	1005.3120	36
19615	2019	19559	Married	29	25-29	15000+	4	Medium	18170	10000-20000	0	3e+05	100	1	1500	1.5	1.2	0.8	0.880	1.0	1.2	1.00	1.080	2463.4368	14
19637	2019	14221	Single	75	70-79	15000+	4	High	19250	10000-20000	0	5e+05	250	1	1500	0.8	1.2	0.8	0.880	1.0	1.2	1.12	1.045	1423.8056	60
19656	2019	12538	Single	67	60-69	10000-15000	1	Medium	2650	0-10000	1	5e+05	500	0	1500	0.8	1.0	1.2	0.720	1.2	1.0	1.12	1.000	1393.4592	52
19708	2019	18824	Single	62	60-69	10000-15000	3	High	8970	0-10000	0	5e+05	250	0	1500	0.8	1.0	0.9	0.720	1.0	1.0	1.12	1.045	910.1030	47
19832	2019	12178	Single	51	50-59	0-7500	3	Medium	19100	10000-20000	0	5e+05	250	1	1500	0.8	0.7	0.9	0.880	1.0	1.2	1.12	1.045	934.3725	36
19931	2019	11860	Single	56	50-59	0-7500	4	Medium	71450	40000+	0	5e+05	1000	0	1500	0.8	0.7	0.8	1.080	1.0	1.0	1.12	0.935	760.0159	41
19963	2019	19380	Single	50	50-59	0-7500	2	Low	23930	20000-30000	0	5e+05	1000	0	1500	0.8	0.7	1.1	1.000	1.0	1.0	1.12	0.935	967.6128	35
20070	2019	12634	Single	65	60-69	15000+	1	Medium	36560	30000-40000	0	5e+05	1000	1	1500	0.8	1.2	1.2	1.045	1.0	1.2	1.12	0.935	2269.1902	50
20103	2019	14470	Married	28	25-29	15000+	4	Low	36360	30000-40000	0	5e+05	500	0	1500	1.5	1.2	0.8	1.045	1.0	1.0	1.12	1.000	2528.0640	13
20132	2019	17793	Single	57	50-59	10000-15000	1	High	67350	40000+	1	1e+05	100	1	1500	0.8	1.0	1.2	1.080	1.2	1.2	0.88	1.080	2128.4094	42
20454	2019	13536	Single	51	50-59	10000-15000	3	High	39340	30000-40000	0	3e+05	500	0	1500	0.8	1.0	0.9	1.045	1.0	1.0	1.00	1.000	1128.6000	36
20677	2019	18112	Single	55	50-59	10000-15000	1	High	18580	10000-20000	0	3e+05	1000	0	1500	0.8	1.0	1.2	0.880	1.0	1.0	1.00	0.935	1184.8320	40
20813	2019	18737	Single	57	50-59	10000-15000	3	High	12040	10000-20000	0	1e+05	100	0	1500	0.8	1.0	0.9	0.880	1.0	1.0	0.88	1.080	903.2602	42
20923	2019	12578	Single	51	50-59	10000-15000	2	Medium	24350	20000-30000	0	1e+05	500	0	1500	0.8	1.0	1.1	1.000	1.0	1.0	0.88	1.000	1161.6000	36
21213	2019	19589	Married	27	25-29	10000-15000	4	Medium	13020	10000-20000	0	5e+04	100	0	1500	1.5	1.0	0.8	0.880	1.0	1.0	0.60	1.080	1026.4320	12
21253	2019	18425	Single	52	50-59	0-7500	3	Low	22190	20000-30000	0	5e+04	100	0	1500	0.8	0.7	0.9	1.000	1.0	1.0	0.60	1.080	489.8880	37
21258	2019	11584	Single	54	50-59	0-7500	3	High	26000	20000-30000	0	5e+05	500	0	1500	0.8	0.7	0.9	1.000	1.0	1.0	1.12	1.000	846.7200	39
21354	2019	18700	Single	54	50-59	10000-15000	4	High	13700	10000-20000	0	5e+04	250	0	1500	0.8	1.0	0.8	0.880	1.0	1.0	0.60	1.045	529.6896	39
21425	2019	18333	Single	53	50-59	10000-15000	4	Low	59790	40000+	0	3e+05	500	0	1500	0.8	1.0	0.8	1.080	1.0	1.0	1.00	1.000	1036.8000	38
21446	2019	19821	Single	66	60-69	0-7500	3	High	96860	40000+	1	5e+05	1000	0	1500	0.8	0.7	0.9	1.080	1.2	1.0	1.12	0.935	1026.0214	51
21454	2019	10966	Single	50	50-59	10000-15000	3	High	25120	20000-30000	0	5e+05	1000	0	1500	0.8	1.0	0.9	1.000	1.0	1.0	1.12	0.935	1130.9760	35
21642	2019	14574	Single	51	50-59	10000-15000	3	High	19030	10000-20000	0	5e+05	500	0	1500	0.8	1.0	0.9	0.880	1.0	1.0	1.12	1.000	1064.4480	36
21724	2019	18296	Single	52	50-59	0-7500	3	High	39550	30000-40000	0	5e+05	500	0	1500	0.8	0.7	0.9	1.045	1.0	1.0	1.12	1.000	884.8224	37
21844	2019	19932	Single	53	50-59	10000-15000	3	Low	48240	40000+	0	5e+04	100	0	1500	0.8	1.0	0.9	1.080	1.0	1.0	0.60	1.080	755.8272	38
22023	2019	10929	Single	50	50-59	10000-15000	1	High	32350	30000-40000	0	5e+05	1000	0	1500	0.8	1.0	1.2	1.045	1.0	1.0	1.12	0.935	1575.8266	35
22080	2019	11807	Single	50	50-59	10000-15000	1	Low	4470	0-10000	0	3e+05	500	0	1500	0.8	1.0	1.2	0.720	1.0	1.0	1.00	1.000	1036.8000	35
22259	2019	19451	Married	30	30-39	7500-10000	4	High	39660	30000-40000	0	5e+05	500	0	1500	1.0	0.9	0.8	1.045	1.0	1.0	1.12	1.000	1264.0320	15
22402	2019	18196	Single	54	50-59	0-7500	2	High	15600	10000-20000	0	1e+05	500	1	1500	0.8	0.7	1.1	0.880	1.0	1.2	0.88	1.000	858.6547	39
22436	2019	13613	Single	50	50-59	0-7500	1	Low	2440	0-10000	0	3e+05	500	0	1500	0.8	0.7	1.2	0.720	1.0	1.0	1.00	1.000	725.7600	35
22529	2019	18387	Single	55	50-59	0-7500	4	Low	20240	20000-30000	0	3e+05	250	1	1500	0.8	0.7	0.8	1.000	1.0	1.2	1.00	1.045	842.6880	40
22645	2019	19620	Single	88	80-89	15000+	2	High	28750	20000-30000	0	5e+04	100	0	1500	0.8	1.2	1.1	1.000	1.0	1.0	0.60	1.080	1026.4320	73
22951	2019	15405	Married	29	25-29	10000-15000	4	Low	20390	20000-30000	0	1e+05	1000	0	1500	1.5	1.0	0.8	1.000	1.0	1.0	0.88	0.935	1481.0400	14
23083	2019	14385	Single	52	50-59	0-7500	2	Low	35600	30000-40000	0	5e+04	250	0	1500	0.8	0.7	1.1	1.045	1.0	1.0	0.60	1.045	605.4187	37
23229	2019	12391	Single	50	50-59	10000-15000	2	High	28630	20000-30000	1	5e+05	1000	0	1500	0.8	1.0	1.1	1.000	1.2	1.0	1.12	0.935	1658.7648	35
23287	2019	10301	Single	52	50-59	10000-15000	1	High	23660	20000-30000	0	3e+05	1000	0	1500	0.8	1.0	1.2	1.000	1.0	1.0	1.00	0.935	1346.4000	37
23335	2019	12440	Married	23	20-24	0-7500	3	Low	17050	10000-20000	0	1e+05	250	1	1500	2.0	0.7	0.9	0.880	1.0	1.2	0.88	1.045	1835.3745	8
23340	2019	15861	Single	54	50-59	10000-15000	3	Medium	22440	20000-30000	1	1e+05	250	0	1500	0.8	1.0	0.9	1.000	1.2	1.0	0.88	1.045	1191.8016	39
23366	2019	16578	Single	52	50-59	10000-15000	2	High	62070	40000+	1	5e+04	100	0	1500	0.8	1.0	1.1	1.080	1.2	1.0	0.60	1.080	1108.5466	37
23473	2019	18110	Single	50	50-59	0-7500	1	Low	22940	20000-30000	0	5e+04	100	0	1500	0.8	0.7	1.2	1.000	1.0	1.0	0.60	1.080	653.1840	35
23485	2019	11138	Single	52	50-59	10000-15000	3	High	8970	0-10000	1	5e+04	100	0	1500	0.8	1.0	0.9	0.720	1.2	1.0	0.60	1.080	604.6618	37
23499	2019	10589	Single	53	50-59	10000-15000	2	Medium	11930	10000-20000	0	1e+05	500	0	1500	0.8	1.0	1.1	0.880	1.0	1.0	0.88	1.000	1022.2080	38

Visualizing the Rejection Region

Here are a few exhibits of their structures.

app.rej %>% ggplot(aes(x = `Annual Mileage`)) + geom_bar( aes(fill = `Annual Mileage`), stat = "count") + facet_grid(. ~ `Driver Age Band`) + theme(legend.position = "bottom", axis.text.x = element_blank(), axis.ticks.x = element_blank()) + ggtitle("Distribution of Annual Mileage of Rejected Applicants by Driver Age Band")

app.rej %>% ggplot(aes(x = `Driver Age Band`)) + geom_bar( aes(fill = `Driver Age Band`), stat = "count") + facet_grid(. ~ `Car Value Band`) + theme(legend.position = "bottom", axis.text.x = element_blank(), axis.ticks.x = element_blank()) + ggtitle("Distribution of Driver Age of Rejected Applicants by Car Value")

8. Projecting Premiums

We would like to estimate the projected charged premiums in 2020, but this is guaranteed to yield a bad result. Conviction points as a statistic is surely broken in the current database, and the new applicants’ data are incomplete (only 2018 conviction points). We’ll populate the data with zeros with the understanding that our results will be skewed.

If we extrapolate these (purely for projection reasons and not in practice as this is illegal) to assign premiums as if all policyholders have zero Conviction Points for both 2016 and 2017, where we have the data for 2018. We do the same for Accident Points. Recall our multiplicative rating formula was:

We’ll perform this calculation in Excel again, simply for ease and speed of index/match in Excel as this is a one-time calculation.

Here are some exhibits of the projected premium structure.

app.acc %>% ggplot(aes(x = `Driver Age Band`, y = `Charged Premium`)) + geom_bar( aes(fill = `Driver Age Band`), stat = "summary", fun.y = "mean") + facet_grid(. ~ `Marital Status`) + theme(legend.position = "bottom", axis.text.x = element_blank(), axis.ticks.x = element_blank()) + ggtitle("Projected Average Charged Premium")

app.acc %>% ggplot(aes(x = `Driver Age Band`, y = `Charged Premium`)) + geom_bar( aes(fill = `Driver Age Band`), stat = "identity") + facet_grid(. ~ `Marital Status`) + theme(legend.position = "bottom", axis.text.x = element_blank(), axis.ticks.x = element_blank()) + ggtitle("Projected Total Charged Premium")

We can use these models as a (conservative) under-estimate of the expected premiums. These figures use the 3-year accident and conviction point relativities based only on 1 year, and zeros for the other two years. Because we are requiring that applicants self-report past conviction and accident history, we can expect a proportion of policies to accurately reflect a number of accidents and convictions that result in higher rates.

Thank you for reviewing this document. It’s a pleasure to be a part of the intern team with you all. Please don’t hesitate to pull me aside for a conversation if you have any questions or feedback.

General Analytics: Cal Insurance

Daniel Suryakusuma

10/23/2019

Completing the Data (Calculating Charged Premiums)

Setting (Ordered) Factor Levels

Primary Auto Rating Factors

Optional Factors

1. Data Cleaning: Validation and Investigation

Deleting Repeated Columns

Constant 2010-2018

Constant 2014-2018

Constant 2016-2018

2. Understanding the Premium Structure

The Age Structure

The Independence Assumption: Reasons for Tweedie Modelling

Investigating Credit Score vs Charged Premiums

3. Understanding the Reported Loss

Adjusting the Losses to Liability Limit Caps and Deductible Minimums

4. Building the Predictive Model

Selecting \(p\)-value for Tweedie via Gamma Fitting

Compute negative log-likelihood

Re-constructing the Model with Capped Severity

5. Interpreting the Model

GLM factors as a proxy for `Credit Score`

6. Creating Underwriting Guidelines

Drivers Under Age 25

Territory 4

Territory 2

Driving History (Accident Points, Conviction Points)

7. Automating and Applying UW Guidelines to 2019 Applicants

Programming the UW Guidelines

Visualizing the Rejection Region

8. Projecting Premiums

General Analytics: Cal Insurance

Daniel Suryakusuma

10/23/2019

Completing the Data (Calculating Charged Premiums)

Setting (Ordered) Factor Levels

Primary Auto Rating Factors

Optional Factors

1. Data Cleaning: Validation and Investigation

Deleting Repeated Columns

Constant 2010-2018

Constant 2014-2018

Constant 2016-2018

2. Understanding the Premium Structure

The Age Structure

The Independence Assumption: Reasons for Tweedie Modelling

Investigating Credit Score vs Charged Premiums

3. Understanding the Reported Loss

Adjusting the Losses to Liability Limit Caps and Deductible Minimums

4. Building the Predictive Model

Selecting \(p\)-value for Tweedie via Gamma Fitting

Compute negative log-likelihood

Re-constructing the Model with Capped Severity

5. Interpreting the Model

GLM factors as a proxy for Credit Score

6. Creating Underwriting Guidelines

Drivers Under Age 25

Territory 4

Territory 2

Driving History (Accident Points, Conviction Points)

7. Automating and Applying UW Guidelines to 2019 Applicants

Programming the UW Guidelines

Visualizing the Rejection Region

8. Projecting Premiums

GLM factors as a proxy for `Credit Score`