Data 621 - HW4
Devin Teran, Atina Karim, Tom Hill, Amit Kapoor
5/2/2021
Overview
In this homework assignment, you will explore, analyze and model a data set containing approximately 8000 records representing a customer at an auto insurance company. Each record has two response variables. The first response variable, TARGET_FLAG, is a 1 or a 0. A “1” means that the person was in a car crash. A zero means that the person was not in a car crash. The second response variable is TARGET_AMT. This value is zero if the person did not crash their car. But if they did crash their car, this number will be a value greater than zero.
Your objective is to build multiple linear regression and binary logistic regression models on the training data to predict the probability that a person will crash their car and also the amount of money it will cost if the person does crash their car. You can only use the variables given to you (or variables that you derive from the variables provided). Below is a short description of the variables of interest in the data set:
Response Variables:
| VARIABLE NAME | DEFINITION | THEORETICAL EFFECT |
|---|---|---|
| TARGET_FLAG | Was Car in a crash? 1=YES 0=NO | None |
| TARGET_AMT | If car was in a crash, what was the cost | None |
Explanatory Variables:
| VARIABLE NAME | DEFINITION | THEORETICAL EFFECT |
|---|---|---|
| AGE | Age of Driver | Very young people tend to be risky. Maybe very old people also. |
| BLUEBOOK | Value of Vehicle | Unknown effect on probability of collision, but probably effect the payout if there is a crash |
| CAR_AGE | Vehicle Age | Unknown effect on probability of collision, but probably effect the payout if there is a crash |
| CAR_TYPE | Type of Car | Unknown effect on probability of collision, but probably effect the payout if there is a crash |
| CAR_USE | Vehicle Use | Commercial vehicles are driven more, so might increase probability of collision |
| CLM_FREQ | # Claims (Past 5 Years) | The more claims you filed in the past, the more you are likely to file in the future |
| EDUCATION | Max Education Level | Unknown effect, but in theory more educated people tend to drive more safely |
| HOMEKIDS | # Children at Home | Unknown effect |
| HOME_VAL | Home Value | In theory, home owners tend to drive more responsibly |
| INCOME | Income | In theory, rich people tend to get into fewer crashes |
| JOB | Job Category | In theory, white collar jobs tend to be safer |
| KIDSDRIV | # Driving Children | When teenagers drive your car, you are more likely to get into crashes |
| MSTATUS | Marital Status | In theory, married people drive more safely |
| MVR_PTS | Motor Vehicle Record Points | If you get lots of traffic tickets, you tend to get into more crashes |
| OLDCLAIM | Total Claims (Past 5 Years) | If your total payout over the past five years was high, this suggests future payouts will be high |
| PARENT1 | Single Parent | Unknown effect |
| RED_CAR | A Red Car | Urban legend says that red cars (especially red sports cars) are more risky. Is that true? |
| REVOKED | License Revoked (Past 7 Years) | If your license was revoked in the past 7 years, you probably are a more risky driver. |
| SEX | Gender | Urban legend says that women have less crashes then men. Is that true? |
| TIF | Time in Force | People who have been customers for a long time are usually more safe. |
| TRAVTIME | Distance to Work | Long drives to work usually suggest greater risk |
| URBANICITY | Home/Work Area | Unknown |
| YOJ | Years on Job | People who stay at a job for a long time are usually more safe |
Data Exploration
## Rows: 8,161
## Columns: 26
## $ INDEX <int> 1, 2, 4, 5, 6, 7, 8, 11, 12, 13, 14, 15, 16, 17, 19, 20, 2…
## $ TARGET_FLAG <int> 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1…
## $ TARGET_AMT <dbl> 0.000, 0.000, 0.000, 0.000, 0.000, 2946.000, 0.000, 4021.0…
## $ KIDSDRIV <int> 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
## $ AGE <int> 60, 43, 35, 51, 50, 34, 54, 37, 34, 50, 53, 43, 55, 53, 45…
## $ HOMEKIDS <int> 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 3, 2, 1…
## $ YOJ <int> 11, 11, 10, 14, NA, 12, NA, NA, 10, 7, 14, 5, 11, 11, 0, 1…
## $ INCOME <chr> "$67,349", "$91,449", "$16,039", "", "$114,986", "$125,301…
## $ PARENT1 <chr> "No", "No", "No", "No", "No", "Yes", "No", "No", "No", "No…
## $ HOME_VAL <chr> "$0", "$257,252", "$124,191", "$306,251", "$243,925", "$0"…
## $ MSTATUS <chr> "z_No", "z_No", "Yes", "Yes", "Yes", "z_No", "Yes", "Yes",…
## $ SEX <chr> "M", "M", "z_F", "M", "z_F", "z_F", "z_F", "M", "z_F", "M"…
## $ EDUCATION <chr> "PhD", "z_High School", "z_High School", "<High School", "…
## $ JOB <chr> "Professional", "z_Blue Collar", "Clerical", "z_Blue Colla…
## $ TRAVTIME <int> 14, 22, 5, 32, 36, 46, 33, 44, 34, 48, 15, 36, 25, 64, 48,…
## $ CAR_USE <chr> "Private", "Commercial", "Private", "Private", "Private", …
## $ BLUEBOOK <chr> "$14,230", "$14,940", "$4,010", "$15,440", "$18,000", "$17…
## $ TIF <int> 11, 1, 4, 7, 1, 1, 1, 1, 1, 7, 1, 7, 7, 6, 1, 6, 6, 7, 4, …
## $ CAR_TYPE <chr> "Minivan", "Minivan", "z_SUV", "Minivan", "z_SUV", "Sports…
## $ RED_CAR <chr> "yes", "yes", "no", "yes", "no", "no", "no", "yes", "no", …
## $ OLDCLAIM <chr> "$4,461", "$0", "$38,690", "$0", "$19,217", "$0", "$0", "$…
## $ CLM_FREQ <int> 2, 0, 2, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2…
## $ REVOKED <chr> "No", "No", "No", "No", "Yes", "No", "No", "Yes", "No", "N…
## $ MVR_PTS <int> 3, 0, 3, 0, 3, 0, 0, 10, 0, 1, 0, 0, 3, 3, 3, 0, 0, 0, 0, …
## $ CAR_AGE <int> 18, 1, 10, 6, 17, 7, 1, 7, 1, 17, 11, 1, 9, 10, 5, 13, 16,…
## $ URBANICITY <chr> "Highly Urban/ Urban", "Highly Urban/ Urban", "Highly Urba…There are 8161 observation in the training dataset having 21 feature variables and 2 target variables.
## INDEX TARGET_FLAG TARGET_AMT KIDSDRIV AGE HOMEKIDS YOJ INCOME PARENT1
## 1 1 0 0 0 60 0 11 $67,349 No
## 2 2 0 0 0 43 0 11 $91,449 No
## 3 4 0 0 0 35 1 10 $16,039 No
## 4 5 0 0 0 51 0 14 No
## 5 6 0 0 0 50 0 NA $114,986 No
## 6 7 1 2946 0 34 1 12 $125,301 Yes
## HOME_VAL MSTATUS SEX EDUCATION JOB TRAVTIME CAR_USE BLUEBOOK
## 1 $0 z_No M PhD Professional 14 Private $14,230
## 2 $257,252 z_No M z_High School z_Blue Collar 22 Commercial $14,940
## 3 $124,191 Yes z_F z_High School Clerical 5 Private $4,010
## 4 $306,251 Yes M <High School z_Blue Collar 32 Private $15,440
## 5 $243,925 Yes z_F PhD Doctor 36 Private $18,000
## 6 $0 z_No z_F Bachelors z_Blue Collar 46 Commercial $17,430
## TIF CAR_TYPE RED_CAR OLDCLAIM CLM_FREQ REVOKED MVR_PTS CAR_AGE
## 1 11 Minivan yes $4,461 2 No 3 18
## 2 1 Minivan yes $0 0 No 0 1
## 3 4 z_SUV no $38,690 2 No 3 10
## 4 7 Minivan yes $0 0 No 0 6
## 5 1 z_SUV no $19,217 2 Yes 3 17
## 6 1 Sports Car no $0 0 No 0 7
## URBANICITY
## 1 Highly Urban/ Urban
## 2 Highly Urban/ Urban
## 3 Highly Urban/ Urban
## 4 Highly Urban/ Urban
## 5 Highly Urban/ Urban
## 6 Highly Urban/ Urban## INDEX TARGET_FLAG TARGET_AMT KIDSDRIV
## Min. : 1 Min. :0.0000 Min. : 0 Min. :0.0000
## 1st Qu.: 2559 1st Qu.:0.0000 1st Qu.: 0 1st Qu.:0.0000
## Median : 5133 Median :0.0000 Median : 0 Median :0.0000
## Mean : 5152 Mean :0.2638 Mean : 1504 Mean :0.1711
## 3rd Qu.: 7745 3rd Qu.:1.0000 3rd Qu.: 1036 3rd Qu.:0.0000
## Max. :10302 Max. :1.0000 Max. :107586 Max. :4.0000
##
## AGE HOMEKIDS YOJ INCOME
## Min. :16.00 Min. :0.0000 Min. : 0.0 Length:8161
## 1st Qu.:39.00 1st Qu.:0.0000 1st Qu.: 9.0 Class :character
## Median :45.00 Median :0.0000 Median :11.0 Mode :character
## Mean :44.79 Mean :0.7212 Mean :10.5
## 3rd Qu.:51.00 3rd Qu.:1.0000 3rd Qu.:13.0
## Max. :81.00 Max. :5.0000 Max. :23.0
## NA's :6 NA's :454
## PARENT1 HOME_VAL MSTATUS SEX
## Length:8161 Length:8161 Length:8161 Length:8161
## Class :character Class :character Class :character Class :character
## Mode :character Mode :character Mode :character Mode :character
##
##
##
##
## EDUCATION JOB TRAVTIME CAR_USE
## Length:8161 Length:8161 Min. : 5.00 Length:8161
## Class :character Class :character 1st Qu.: 22.00 Class :character
## Mode :character Mode :character Median : 33.00 Mode :character
## Mean : 33.49
## 3rd Qu.: 44.00
## Max. :142.00
##
## BLUEBOOK TIF CAR_TYPE RED_CAR
## Length:8161 Min. : 1.000 Length:8161 Length:8161
## Class :character 1st Qu.: 1.000 Class :character Class :character
## Mode :character Median : 4.000 Mode :character Mode :character
## Mean : 5.351
## 3rd Qu.: 7.000
## Max. :25.000
##
## OLDCLAIM CLM_FREQ REVOKED MVR_PTS
## Length:8161 Min. :0.0000 Length:8161 Min. : 0.000
## Class :character 1st Qu.:0.0000 Class :character 1st Qu.: 0.000
## Mode :character Median :0.0000 Mode :character Median : 1.000
## Mean :0.7986 Mean : 1.696
## 3rd Qu.:2.0000 3rd Qu.: 3.000
## Max. :5.0000 Max. :13.000
##
## CAR_AGE URBANICITY
## Min. :-3.000 Length:8161
## 1st Qu.: 1.000 Class :character
## Median : 8.000 Mode :character
## Mean : 8.328
## 3rd Qu.:12.000
## Max. :28.000
## NA's :510There are several recurring issues with some columns: all columns containing money amounts have incomptaible punctuation and characters. Also, categorical variables neeed to be changed to factors and their factor names edited for intelligibility.
## TARGET_FLAG TARGET_AMT KIDSDRIV AGE
## Min. :0.0000 Min. : 0 Min. :0.0000 Min. :16.00
## 1st Qu.:0.0000 1st Qu.: 0 1st Qu.:0.0000 1st Qu.:39.00
## Median :0.0000 Median : 0 Median :0.0000 Median :45.00
## Mean :0.2638 Mean : 1504 Mean :0.1711 Mean :44.79
## 3rd Qu.:1.0000 3rd Qu.: 1036 3rd Qu.:0.0000 3rd Qu.:51.00
## Max. :1.0000 Max. :107586 Max. :4.0000 Max. :81.00
## NA's :6
## HOMEKIDS YOJ INCOME PARENT1 HOME_VAL
## Min. :0.0000 Min. : 0.0 Min. : 0 No :7084 Min. : 0
## 1st Qu.:0.0000 1st Qu.: 9.0 1st Qu.: 28097 Yes:1077 1st Qu.: 0
## Median :0.0000 Median :11.0 Median : 54028 Median :161160
## Mean :0.7212 Mean :10.5 Mean : 61898 Mean :154867
## 3rd Qu.:1.0000 3rd Qu.:13.0 3rd Qu.: 85986 3rd Qu.:238724
## Max. :5.0000 Max. :23.0 Max. :367030 Max. :885282
## NA's :454 NA's :445 NA's :464
## MSTATUS SEX EDUCATION JOB
## No :3267 F:4375 Bachelors :2242 Blue Collar :1825
## Yes:4894 M:3786 High School :2330 Clerical :1271
## Less than High School:1203 Professional:1117
## Masters :1658 Manager : 988
## PhD : 728 Lawyer : 835
## Student : 712
## (Other) :1413
## TRAVTIME CAR_USE BLUEBOOK TIF
## Min. : 5.00 Commercial:3029 Min. : 1500 Min. : 1.000
## 1st Qu.: 22.00 Private :5132 1st Qu.: 9280 1st Qu.: 1.000
## Median : 33.00 Median :14440 Median : 4.000
## Mean : 33.49 Mean :15710 Mean : 5.351
## 3rd Qu.: 44.00 3rd Qu.:20850 3rd Qu.: 7.000
## Max. :142.00 Max. :69740 Max. :25.000
##
## CAR_TYPE RED_CAR OLDCLAIM CLM_FREQ REVOKED
## Minivan :2145 no :5783 Min. : 0 Min. :0.0000 No :7161
## Panel Truck: 676 yes:2378 1st Qu.: 0 1st Qu.:0.0000 Yes:1000
## Pickup :1389 Median : 0 Median :0.0000
## Sports Car : 907 Mean : 4037 Mean :0.7986
## SUV :2294 3rd Qu.: 4636 3rd Qu.:2.0000
## Van : 750 Max. :57037 Max. :5.0000
##
## MVR_PTS CAR_AGE URBANICITY
## Min. : 0.000 Min. :-3.000 Highly Rural/ Rural:1669
## 1st Qu.: 0.000 1st Qu.: 1.000 Highly Urban/ Urban:6492
## Median : 1.000 Median : 8.000
## Mean : 1.696 Mean : 8.328
## 3rd Qu.: 3.000 3rd Qu.:12.000
## Max. :13.000 Max. :28.000
## NA's :510The fixed dataframe now only includes columns that are numeric or factors. Car age appears to have some values less than 1, including a negative values. These will be changed to the mode of 1.
Categorical variables
## [1] "PARENT1"
## [1] "No" "Yes"
## [1] "MSTATUS"
## [1] "No" "Yes"
## [1] "SEX"
## [1] "F" "M"
## [1] "EDUCATION"
## [1] "Bachelors" "High School" "Less than High School"
## [4] "Masters" "PhD"
## [1] "JOB"
## [1] "Blue Collar" "Clerical" "Doctor" "Home Maker" "Lawyer"
## [6] "Manager" "Other Job" "Professional" "Student"
## [1] "CAR_USE"
## [1] "Commercial" "Private"
## [1] "CAR_TYPE"
## [1] "Minivan" "Panel Truck" "Pickup" "Sports Car" "SUV"
## [6] "Van"
## [1] "RED_CAR"
## [1] "no" "yes"
## [1] "REVOKED"
## [1] "No" "Yes"
## [1] "URBANICITY"
## [1] "Highly Rural/ Rural" "Highly Urban/ Urban"Looking at categorical variables, most of the columns are binary.
Below graphs shows the distribution of all categorical predictors.
Numeric Variables
Below 2 graphs shows the distribution of numeric variables. The red graphs are on normal scale and the green ones are on log10 scale. Many numeric variables feature the value of zero as a mode.
Missing Values
Here are columns having missing values coded as NA:
## AGE YOJ INCOME HOME_VAL CAR_AGE
## 1 6 454 445 464 510
## TARGET_FLAG TARGET_AMT KIDSDRIV AGE HOMEKIDS YOJ
## 0.000 0.000 0.000 0.001 0.000 0.056
## INCOME PARENT1 HOME_VAL MSTATUS SEX EDUCATION
## 0.055 0.000 0.057 0.000 0.000 0.000
## JOB TRAVTIME CAR_USE BLUEBOOK TIF CAR_TYPE
## 0.000 0.000 0.000 0.000 0.000 0.000
## RED_CAR OLDCLAIM CLM_FREQ REVOKED MVR_PTS CAR_AGE
## 0.000 0.000 0.000 0.000 0.000 0.062
## URBANICITY
## 0.000
Four variables have missing values, however there doesn’t appear to be a pattern and it’s safe to assume they’re missing at random.
Correlation
For the purposes of seeing correlation between variables, we’re going to replace NA values with the median. 
It’s clear there are some positive correlations between the following variables:
* Income & Home value: 0.54
* Income & Bluebook: 0.42
* Income & Car age: 0.39
* Claim Frequency & Old claims: 0.50
* Claim Frequence & MVR_PTS:0.39
Data Preparation
Removing TARGET_FLAG
Our multiple linear regression model will be predicting the amount of money someone receives if they crash, so we will be removing the variable TARGET_FLAG
Handling Missing Data - Multiple Linear Regression
For the multiple linear regression, we’re going to assume that the NULL values will take the median value for the variable.
Transforming Variables - Multiple Linear Regression
There some variables that are not normally distributed so we’re going to try using a log transformation later to see if that creates a better model. For a few variables with values, 0, we added 1 to avoid negative infinity when taking the log of those variables. This will not alter our modeling results significantly.
Zeroes in Home Value
It seems from the histogram above, that the mode of the variable HOME_VAL is 0. Given that, the distribution seems normal if we remove 0s and that the difference between 0 and the number that appears next on the axis is significant, we are assuming that 0 indicates missing values for HOME_VAL. Therefore, we will convert 0s to NAs in HOME_VAL prior to imputing missing values for Binary Logistic Regression Model 3 below.
Addressing Zeroes using Binning
The histograms for several variables indicate that there many with an overrepresentation of ‘zero’ values. Some of the worst offenders include CAR_AGE, HOME_VAL, HOMEKIDS, KIDSDRIV, OLDCLAIM, TIF, and YOJ. INCOME also has many ‘zero’ or very low values, and also similar to CAR_AGE and HOME_VAL because, omitting zero, the rest of the distributions appear to be skewed, approximately normal distributions. To avoid problems with interpretation, the 4th model will consider these continuous variables as categorical variables defined as a number range.
## TARGET_FLAG TARGET_AMT AGE INCOME PARENT1
## Min. :0.0000 Min. : 0 Min. :16.00 Min. : 0 No :7084
## 1st Qu.:0.0000 1st Qu.: 0 1st Qu.:39.00 1st Qu.: 28097 Yes:1077
## Median :0.0000 Median : 0 Median :45.00 Median : 54028
## Mean :0.2638 Mean : 1504 Mean :44.79 Mean : 61898
## 3rd Qu.:1.0000 3rd Qu.: 1036 3rd Qu.:51.00 3rd Qu.: 85986
## Max. :1.0000 Max. :107586 Max. :81.00 Max. :367030
## NA's :6 NA's :445
## MSTATUS SEX EDUCATION JOB
## No :3267 F:4375 Bachelors :2242 Blue Collar :1825
## Yes:4894 M:3786 High School :2330 Clerical :1271
## Less than High School:1203 Professional:1117
## Masters :1658 Manager : 988
## PhD : 728 Lawyer : 835
## Student : 712
## (Other) :1413
## TRAVTIME CAR_USE BLUEBOOK CAR_TYPE
## Min. : 5.00 Commercial:3029 Min. : 1500 Minivan :2145
## 1st Qu.: 22.00 Private :5132 1st Qu.: 9280 Panel Truck: 676
## Median : 33.00 Median :14440 Pickup :1389
## Mean : 33.49 Mean :15710 Sports Car : 907
## 3rd Qu.: 44.00 3rd Qu.:20850 SUV :2294
## Max. :142.00 Max. :69740 Van : 750
##
## RED_CAR CLM_FREQ REVOKED MVR_PTS
## no :5783 Min. :0.0000 No :7161 Min. : 0.000
## yes:2378 1st Qu.:0.0000 Yes:1000 1st Qu.: 0.000
## Median :0.0000 Median : 1.000
## Mean :0.7986 Mean : 1.696
## 3rd Qu.:2.0000 3rd Qu.: 3.000
## Max. :5.0000 Max. :13.000
##
## URBANICITY CAR_AGE_BIN HOME_VAL_BIN HAS_HOME_KIDS
## Highly Rural/ Rural:1669 New :1938 Zero :2294 Has kids:2872
## Highly Urban/ Urban:6492 Like New: 66 $0-$50k : 0 No kids :5289
## Average :3775 $50k-$150k :1274
## Old :1872 $150k-$250k:2445
## NA's : 510 Over $250k :1684
## NA's : 464
##
## HAS_KIDSDRIV OLDCLAIM_BIN TIF_BIN
## Has kids driving: 981 Zero :5009 Zero : 0
## No kids driving :7180 $0-$3k : 584 Less than 1 year:2533
## $3k-$6k : 970 1-4 years :1672
## $6k-$9k : 720 4-7 years :2013
## Over $9k: 878 Over 7 years :1943
##
##
## YOJ_BIN
## Zero : 625
## Less than 10 years :2313
## Between 10-15 years:4425
## Over 15 years : 344
## NA's : 454
##
## ## TARGET_FLAG TARGET_AMT AGE INCOME PARENT1 MSTATUS SEX EDUCATION
## 1 0 0 60 67349 No No M PhD
## 2 0 0 43 91449 No No M High School
## 3 0 0 35 16039 No Yes F High School
## 4 0 0 51 NA No Yes M Less than High School
## 5 0 0 50 114986 No Yes F PhD
## 6 1 2946 34 125301 Yes No F Bachelors
## JOB TRAVTIME CAR_USE BLUEBOOK CAR_TYPE RED_CAR CLM_FREQ REVOKED
## 1 Professional 14 Private 14230 Minivan yes 2 No
## 2 Blue Collar 22 Commercial 14940 Minivan yes 0 No
## 3 Clerical 5 Private 4010 SUV no 2 No
## 4 Blue Collar 32 Private 15440 Minivan yes 0 No
## 5 Doctor 36 Private 18000 SUV no 2 Yes
## 6 Blue Collar 46 Commercial 17430 Sports Car no 0 No
## MVR_PTS URBANICITY CAR_AGE_BIN HOME_VAL_BIN HAS_HOME_KIDS
## 1 3 Highly Urban/ Urban Old Zero No kids
## 2 0 Highly Urban/ Urban New Over $250k No kids
## 3 3 Highly Urban/ Urban Average $50k-$150k Has kids
## 4 0 Highly Urban/ Urban Average Over $250k No kids
## 5 3 Highly Urban/ Urban Old $150k-$250k No kids
## 6 0 Highly Urban/ Urban Average Zero Has kids
## HAS_KIDSDRIV OLDCLAIM_BIN TIF_BIN YOJ_BIN
## 1 No kids driving $3k-$6k Over 7 years Between 10-15 years
## 2 No kids driving Zero Less than 1 year Between 10-15 years
## 3 No kids driving Over $9k 1-4 years Less than 10 years
## 4 No kids driving Zero 4-7 years Between 10-15 years
## 5 No kids driving Over $9k Less than 1 year <NA>
## 6 No kids driving Zero Less than 1 year Between 10-15 yearsBuild Models
Model1
The first model to consider includes all given variables and does not impute any values.
##
## Call:
## glm(formula = TARGET_FLAG ~ . - TARGET_AMT, family = "binomial",
## data = insurance_fix)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.5843 -0.7124 -0.3998 0.6195 3.1633
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.881e+00 3.199e-01 -9.005 < 2e-16 ***
## KIDSDRIV 3.385e-01 6.908e-02 4.900 9.57e-07 ***
## AGE -3.665e-03 4.531e-03 -0.809 0.418503
## HOMEKIDS 3.349e-02 4.176e-02 0.802 0.422588
## YOJ -1.071e-02 9.589e-03 -1.117 0.263837
## INCOME -2.988e-06 1.260e-06 -2.371 0.017738 *
## PARENT1Yes 4.337e-01 1.225e-01 3.541 0.000398 ***
## HOME_VAL -1.301e-06 3.899e-07 -3.337 0.000848 ***
## MSTATUSYes -4.389e-01 9.666e-02 -4.541 5.61e-06 ***
## SEXM 1.914e-01 1.241e-01 1.543 0.122880
## EDUCATIONHigh School 3.716e-01 1.020e-01 3.645 0.000268 ***
## EDUCATIONLess than High School 3.724e-01 1.306e-01 2.852 0.004342 **
## EDUCATIONMasters 2.887e-02 1.607e-01 0.180 0.857462
## EDUCATIONPhD 2.617e-01 2.054e-01 1.274 0.202597
## JOBClerical 2.052e-01 1.193e-01 1.720 0.085428 .
## JOBDoctor -5.011e-01 3.136e-01 -1.598 0.110084
## JOBHome Maker -8.529e-02 1.750e-01 -0.487 0.625972
## JOBLawyer -1.923e-02 2.126e-01 -0.090 0.927939
## JOBManager -8.826e-01 1.595e-01 -5.534 3.13e-08 ***
## JOBOther Job -3.071e-01 2.117e-01 -1.450 0.146938
## JOBProfessional -1.066e-01 1.360e-01 -0.784 0.433062
## JOBStudent -1.370e-01 1.497e-01 -0.915 0.359966
## TRAVTIME 1.562e-02 2.118e-03 7.374 1.66e-13 ***
## CAR_USEPrivate -8.256e-01 1.040e-01 -7.935 2.10e-15 ***
## BLUEBOOK -2.101e-05 5.885e-06 -3.570 0.000357 ***
## TIF -5.318e-02 8.241e-03 -6.453 1.10e-10 ***
## CAR_TYPEPanel Truck 6.097e-01 1.807e-01 3.374 0.000740 ***
## CAR_TYPEPickup 5.246e-01 1.136e-01 4.619 3.85e-06 ***
## CAR_TYPESports Car 1.128e+00 1.450e-01 7.784 7.05e-15 ***
## CAR_TYPESUV 8.518e-01 1.241e-01 6.866 6.59e-12 ***
## CAR_TYPEVan 6.335e-01 1.421e-01 4.460 8.21e-06 ***
## RED_CARyes -1.227e-01 9.685e-02 -1.267 0.205139
## OLDCLAIM -1.180e-05 4.375e-06 -2.698 0.006977 **
## CLM_FREQ 1.953e-01 3.183e-02 6.136 8.46e-10 ***
## REVOKEDYes 8.644e-01 1.035e-01 8.354 < 2e-16 ***
## MVR_PTS 1.143e-01 1.528e-02 7.485 7.16e-14 ***
## CAR_AGE -7.075e-03 8.448e-03 -0.837 0.402334
## URBANICITYHighly Urban/ Urban 2.313e+00 1.241e-01 18.640 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 7445.1 on 6447 degrees of freedom
## Residual deviance: 5764.7 on 6410 degrees of freedom
## (1713 observations deleted due to missingness)
## AIC: 5840.7
##
## Number of Fisher Scoring iterations: 5## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 862 188
## 1 77 149
##
## Accuracy : 0.7923
## 95% CI : (0.769, 0.8143)
## No Information Rate : 0.7359
## P-Value [Acc > NIR] : 1.650e-06
##
## Kappa : 0.4026
##
## Mcnemar's Test P-Value : 1.406e-11
##
## Sensitivity : 0.9180
## Specificity : 0.4421
## Pos Pred Value : 0.8210
## Neg Pred Value : 0.6593
## Prevalence : 0.7359
## Detection Rate : 0.6755
## Detection Prevalence : 0.8229
## Balanced Accuracy : 0.6801
##
## 'Positive' Class : 0
## 
Model2
The second model imputes values using the ‘mice’ library using classification and regression trees. We will use glm.mids() that applies glm() to a multiply imputed data set.
##
## iter imp variable
## 1 1 AGE YOJ INCOME HOME_VAL CAR_AGE
## 2 1 AGE YOJ INCOME HOME_VAL CAR_AGE
## 3 1 AGE YOJ INCOME HOME_VAL CAR_AGE
## 4 1 AGE YOJ INCOME HOME_VAL CAR_AGE
## 5 1 AGE YOJ INCOME HOME_VAL CAR_AGE## call :
## glm.mids(formula = TARGET_FLAG ~ . - TARGET_AMT, family = "binomial",
## data = insurance_impute)
##
## call1 :
## mice(data = insurance_fix, m = 1, method = "cart")
##
## nmis :
## TARGET_FLAG TARGET_AMT KIDSDRIV AGE HOMEKIDS YOJ
## 0 0 0 6 0 454
## INCOME PARENT1 HOME_VAL MSTATUS SEX EDUCATION
## 445 0 464 0 0 0
## JOB TRAVTIME CAR_USE BLUEBOOK TIF CAR_TYPE
## 0 0 0 0 0 0
## RED_CAR OLDCLAIM CLM_FREQ REVOKED MVR_PTS CAR_AGE
## 0 0 0 0 0 510
## URBANICITY
## 0
##
## analyses :
## [[1]]
##
## Call: glm(formula = formula, family = family, data = complete(data,
## i))
##
## Coefficients:
## (Intercept) KIDSDRIV
## -2.896e+00 3.840e-01
## AGE HOMEKIDS
## -6.800e-04 5.566e-02
## YOJ INCOME
## -1.784e-02 -3.413e-06
## PARENT1Yes HOME_VAL
## 3.802e-01 -1.293e-06
## MSTATUSYes SEXM
## -4.818e-01 8.755e-02
## EDUCATIONHigh School EDUCATIONLess than High School
## 3.765e-01 3.506e-01
## EDUCATIONMasters EDUCATIONPhD
## 1.187e-01 2.530e-01
## JOBClerical JOBDoctor
## 9.534e-02 -7.712e-01
## JOBHome Maker JOBLawyer
## -1.305e-01 -2.040e-01
## JOBManager JOBOther Job
## -8.666e-01 -3.031e-01
## JOBProfessional JOBStudent
## -1.459e-01 -1.525e-01
## TRAVTIME CAR_USEPrivate
## 1.462e-02 -7.552e-01
## BLUEBOOK TIF
## -2.042e-05 -5.558e-02
## CAR_TYPEPanel Truck CAR_TYPEPickup
## 5.559e-01 5.547e-01
## CAR_TYPESports Car CAR_TYPESUV
## 1.023e+00 7.681e-01
## CAR_TYPEVan RED_CARyes
## 6.174e-01 -1.227e-02
## OLDCLAIM CLM_FREQ
## -1.378e-05 1.965e-01
## REVOKEDYes MVR_PTS
## 8.870e-01 1.133e-01
## CAR_AGE URBANICITYHighly Urban/ Urban
## -5.686e-03 2.391e+00
##
## Degrees of Freedom: 8160 Total (i.e. Null); 8123 Residual
## Null Deviance: 9418
## Residual Deviance: 7292 AIC: 7368## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 878 190
## 1 70 136
##
## Accuracy : 0.7959
## 95% CI : (0.7727, 0.8177)
## No Information Rate : 0.7441
## P-Value [Acc > NIR] : 8.412e-06
##
## Kappa : 0.3905
##
## Mcnemar's Test P-Value : 1.582e-13
##
## Sensitivity : 0.9262
## Specificity : 0.4172
## Pos Pred Value : 0.8221
## Neg Pred Value : 0.6602
## Prevalence : 0.7441
## Detection Rate : 0.6892
## Detection Prevalence : 0.8383
## Balanced Accuracy : 0.6717
##
## 'Positive' Class : 0
## 
Model 3
Now we will replicate the model above to see if our assumption about treating 0s in HOME_VAL as missing data, yields a better model fit.
##
## iter imp variable
## 1 1 AGE YOJ INCOME HOME_VAL CAR_AGE
## 2 1 AGE YOJ INCOME HOME_VAL CAR_AGE
## 3 1 AGE YOJ INCOME HOME_VAL CAR_AGE
## 4 1 AGE YOJ INCOME HOME_VAL CAR_AGE
## 5 1 AGE YOJ INCOME HOME_VAL CAR_AGE## call :
## glm.mids(formula = TARGET_FLAG ~ . - TARGET_AMT, family = "binomial",
## data = insurance_impute2)
##
## call1 :
## mice(data = insurance_fix2, m = 1, method = "cart")
##
## nmis :
## TARGET_FLAG TARGET_AMT KIDSDRIV AGE HOMEKIDS YOJ
## 0 0 0 6 0 454
## INCOME PARENT1 HOME_VAL MSTATUS SEX EDUCATION
## 445 0 2758 0 0 0
## JOB TRAVTIME CAR_USE BLUEBOOK TIF CAR_TYPE
## 0 0 0 0 0 0
## RED_CAR OLDCLAIM CLM_FREQ REVOKED MVR_PTS CAR_AGE
## 0 0 0 0 0 510
## URBANICITY
## 0
##
## analyses :
## [[1]]
##
## Call: glm(formula = formula, family = family, data = complete(data,
## i))
##
## Coefficients:
## (Intercept) KIDSDRIV
## -2.920e+00 3.863e-01
## AGE HOMEKIDS
## -2.083e-03 5.737e-02
## YOJ INCOME
## -1.598e-02 -5.084e-06
## PARENT1Yes HOME_VAL
## 3.585e-01 -4.278e-08
## MSTATUSYes SEXM
## -6.449e-01 7.930e-02
## EDUCATIONHigh School EDUCATIONLess than High School
## 4.095e-01 3.924e-01
## EDUCATIONMasters EDUCATIONPhD
## 9.530e-02 2.425e-01
## JOBClerical JOBDoctor
## 9.797e-02 -7.434e-01
## JOBHome Maker JOBLawyer
## -1.180e-01 -2.033e-01
## JOBManager JOBOther Job
## -8.532e-01 -2.962e-01
## JOBProfessional JOBStudent
## -1.489e-01 -5.974e-02
## TRAVTIME CAR_USEPrivate
## 1.462e-02 -7.546e-01
## BLUEBOOK TIF
## -1.992e-05 -5.572e-02
## CAR_TYPEPanel Truck CAR_TYPEPickup
## 5.418e-01 5.527e-01
## CAR_TYPESports Car CAR_TYPESUV
## 1.028e+00 7.653e-01
## CAR_TYPEVan RED_CARyes
## 6.128e-01 -4.897e-03
## OLDCLAIM CLM_FREQ
## -1.395e-05 1.989e-01
## REVOKEDYes MVR_PTS
## 8.933e-01 1.138e-01
## CAR_AGE URBANICITYHighly Urban/ Urban
## 3.030e-04 2.396e+00
##
## Degrees of Freedom: 8160 Total (i.e. Null); 8123 Residual
## Null Deviance: 9418
## Residual Deviance: 7307 AIC: 7383## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 666 116
## 1 53 58
##
## Accuracy : 0.8108
## 95% CI : (0.7835, 0.8359)
## No Information Rate : 0.8052
## P-Value [Acc > NIR] : 0.3547
##
## Kappa : 0.3009
##
## Mcnemar's Test P-Value : 1.849e-06
##
## Sensitivity : 0.9263
## Specificity : 0.3333
## Pos Pred Value : 0.8517
## Neg Pred Value : 0.5225
## Prevalence : 0.8052
## Detection Rate : 0.7458
## Detection Prevalence : 0.8757
## Balanced Accuracy : 0.6298
##
## 'Positive' Class : 0
## 
Model 4
##
## Call:
## glm(formula = TARGET_FLAG ~ . - TARGET_AMT, family = "binomial",
## data = insurance_bins)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.4626 -0.7053 -0.3955 0.6199 3.1398
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.797e+00 3.584e-01 -5.013 5.36e-07 ***
## AGE -2.185e-03 4.754e-03 -0.459 0.645876
## INCOME -2.814e-06 1.344e-06 -2.094 0.036240 *
## PARENT1Yes 2.826e-01 1.374e-01 2.057 0.039716 *
## MSTATUSYes -4.613e-01 1.046e-01 -4.408 1.04e-05 ***
## SEXM 1.923e-01 1.249e-01 1.540 0.123660
## EDUCATIONHigh School 3.623e-01 1.022e-01 3.545 0.000393 ***
## EDUCATIONLess than High School 3.819e-01 1.300e-01 2.937 0.003312 **
## EDUCATIONMasters -5.378e-04 1.664e-01 -0.003 0.997421
## EDUCATIONPhD 2.007e-01 2.092e-01 0.959 0.337374
## JOBClerical 1.937e-01 1.213e-01 1.597 0.110252
## JOBDoctor -4.930e-01 3.153e-01 -1.564 0.117906
## JOBHome Maker -2.461e-01 1.915e-01 -1.285 0.198816
## JOBLawyer -6.033e-03 2.145e-01 -0.028 0.977560
## JOBManager -8.712e-01 1.609e-01 -5.413 6.18e-08 ***
## JOBOther Job -3.073e-01 2.131e-01 -1.442 0.149177
## JOBProfessional -9.770e-02 1.369e-01 -0.714 0.475349
## JOBStudent -4.025e-01 1.690e-01 -2.381 0.017254 *
## TRAVTIME 1.617e-02 2.135e-03 7.572 3.66e-14 ***
## CAR_USEPrivate -8.233e-01 1.048e-01 -7.855 4.00e-15 ***
## BLUEBOOK -2.099e-05 5.904e-06 -3.555 0.000378 ***
## CAR_TYPEPanel Truck 6.416e-01 1.818e-01 3.530 0.000415 ***
## CAR_TYPEPickup 5.401e-01 1.141e-01 4.734 2.21e-06 ***
## CAR_TYPESports Car 1.113e+00 1.460e-01 7.625 2.43e-14 ***
## CAR_TYPESUV 8.572e-01 1.249e-01 6.864 6.72e-12 ***
## CAR_TYPEVan 6.329e-01 1.429e-01 4.428 9.51e-06 ***
## RED_CARyes -1.138e-01 9.730e-02 -1.170 0.242142
## CLM_FREQ 5.041e-02 5.036e-02 1.001 0.316827
## REVOKEDYes 8.822e-01 1.024e-01 8.619 < 2e-16 ***
## MVR_PTS 9.784e-02 1.588e-02 6.163 7.15e-10 ***
## URBANICITYHighly Urban/ Urban 2.289e+00 1.249e-01 18.321 < 2e-16 ***
## CAR_AGE_BINLike New -1.338e-01 3.469e-01 -0.386 0.699741
## CAR_AGE_BINAverage -1.262e-01 8.393e-02 -1.503 0.132808
## CAR_AGE_BINOld -1.346e-01 1.290e-01 -1.044 0.296614
## HOME_VAL_BIN$50k-$150k -3.229e-01 1.266e-01 -2.551 0.010744 *
## HOME_VAL_BIN$150k-$250k -3.035e-01 1.089e-01 -2.787 0.005324 **
## HOME_VAL_BINOver $250k -5.742e-01 1.330e-01 -4.316 1.59e-05 ***
## HAS_HOME_KIDSNo kids -2.294e-01 1.149e-01 -1.996 0.045923 *
## HAS_KIDSDRIVNo kids driving -4.551e-01 1.114e-01 -4.085 4.41e-05 ***
## OLDCLAIM_BIN$0-$3k 4.055e-01 1.614e-01 2.513 0.011983 *
## OLDCLAIM_BIN$3k-$6k 3.729e-01 1.479e-01 2.522 0.011683 *
## OLDCLAIM_BIN$6k-$9k 5.461e-01 1.555e-01 3.512 0.000445 ***
## OLDCLAIM_BINOver $9k 3.841e-02 1.549e-01 0.248 0.804231
## TIF_BIN1-4 years -2.044e-01 9.180e-02 -2.226 0.025982 *
## TIF_BIN4-7 years -4.302e-01 8.854e-02 -4.859 1.18e-06 ***
## TIF_BINOver 7 years -5.787e-01 9.156e-02 -6.320 2.62e-10 ***
## YOJ_BINLess than 10 years -5.332e-01 1.659e-01 -3.214 0.001307 **
## YOJ_BINBetween 10-15 years -5.828e-01 1.605e-01 -3.631 0.000282 ***
## YOJ_BINOver 15 years -3.052e-01 2.154e-01 -1.417 0.156469
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 7445.1 on 6447 degrees of freedom
## Residual deviance: 5718.0 on 6399 degrees of freedom
## (1713 observations deleted due to missingness)
## AIC: 5816
##
## Number of Fisher Scoring iterations: 5This and the consequent model considers all binned variables plus old variables.
## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 862 196
## 1 65 167
##
## Accuracy : 0.7977
## 95% CI : (0.7747, 0.8193)
## No Information Rate : 0.7186
## P-Value [Acc > NIR] : 4.259e-11
##
## Kappa : 0.438
##
## Mcnemar's Test P-Value : 8.499e-16
##
## Sensitivity : 0.9299
## Specificity : 0.4601
## Pos Pred Value : 0.8147
## Neg Pred Value : 0.7198
## Prevalence : 0.7186
## Detection Rate : 0.6682
## Detection Prevalence : 0.8202
## Balanced Accuracy : 0.6950
##
## 'Positive' Class : 0
## 
Model 5
The next model provides a combination of imputation and binning.
##
## iter imp variable
## 1 1 AGE INCOME CAR_AGE_BIN HOME_VAL_BIN YOJ_BIN
## 2 1 AGE INCOME CAR_AGE_BIN HOME_VAL_BIN YOJ_BIN
## 3 1 AGE INCOME CAR_AGE_BIN HOME_VAL_BIN YOJ_BIN
## 4 1 AGE INCOME CAR_AGE_BIN HOME_VAL_BIN YOJ_BIN
## 5 1 AGE INCOME CAR_AGE_BIN HOME_VAL_BIN YOJ_BIN## call :
## glm.mids(formula = TARGET_FLAG ~ . - TARGET_AMT, family = "binomial",
## data = insurance_binned_impute)
##
## call1 :
## mice(data = insurance_bins, m = 1, method = "cart")
##
## nmis :
## TARGET_FLAG TARGET_AMT AGE INCOME PARENT1
## 0 0 6 445 0
## MSTATUS SEX EDUCATION JOB TRAVTIME
## 0 0 0 0 0
## CAR_USE BLUEBOOK CAR_TYPE RED_CAR CLM_FREQ
## 0 0 0 0 0
## REVOKED MVR_PTS URBANICITY CAR_AGE_BIN HOME_VAL_BIN
## 0 0 0 510 464
## HAS_HOME_KIDS HAS_KIDSDRIV OLDCLAIM_BIN TIF_BIN YOJ_BIN
## 0 0 0 0 454
##
## analyses :
## [[1]]
##
## Call: glm(formula = formula, family = family, data = complete(data,
## i))
##
## Coefficients:
## (Intercept) AGE
## -1.734e+00 -7.178e-04
## INCOME PARENT1Yes
## -3.449e-06 2.461e-01
## MSTATUSYes SEXM
## -5.170e-01 9.158e-02
## EDUCATIONHigh School EDUCATIONLess than High School
## 3.891e-01 3.798e-01
## EDUCATIONMasters EDUCATIONPhD
## 1.073e-01 2.039e-01
## JOBClerical JOBDoctor
## 8.246e-02 -7.537e-01
## JOBHome Maker JOBLawyer
## -2.709e-01 -2.062e-01
## JOBManager JOBOther Job
## -8.592e-01 -3.156e-01
## JOBProfessional JOBStudent
## -1.531e-01 -3.632e-01
## TRAVTIME CAR_USEPrivate
## 1.488e-02 -7.493e-01
## BLUEBOOK CAR_TYPEPanel Truck
## -2.023e-05 5.765e-01
## CAR_TYPEPickup CAR_TYPESports Car
## 5.616e-01 1.011e+00
## CAR_TYPESUV CAR_TYPEVan
## 7.750e-01 6.148e-01
## RED_CARyes CLM_FREQ
## -3.817e-03 5.084e-02
## REVOKEDYes MVR_PTS
## 8.913e-01 9.843e-02
## URBANICITYHighly Urban/ Urban CAR_AGE_BINLike New
## 2.369e+00 1.287e-01
## CAR_AGE_BINAverage CAR_AGE_BINOld
## -6.374e-02 -7.366e-02
## HOME_VAL_BIN$50k-$150k HOME_VAL_BIN$150k-$250k
## -3.077e-01 -2.663e-01
## HOME_VAL_BINOver $250k HAS_HOME_KIDSNo kids
## -5.013e-01 -2.195e-01
## HAS_KIDSDRIVNo kids driving OLDCLAIM_BIN$0-$3k
## -5.669e-01 3.926e-01
## OLDCLAIM_BIN$3k-$6k OLDCLAIM_BIN$6k-$9k
## 3.579e-01 4.999e-01
## OLDCLAIM_BINOver $9k TIF_BIN1-4 years
## 2.028e-02 -1.924e-01
## TIF_BIN4-7 years TIF_BINOver 7 years
## -4.310e-01 -5.888e-01
## YOJ_BINLess than 10 years YOJ_BINBetween 10-15 years
## -5.673e-01 -6.194e-01
## YOJ_BINOver 15 years
## -4.101e-01
##
## Degrees of Freedom: 8160 Total (i.e. Null); 8112 Residual
## Null Deviance: 9418
## Residual Deviance: 7250 AIC: 7348## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 889 186
## 1 74 150
##
## Accuracy : 0.7998
## 95% CI : (0.777, 0.8213)
## No Information Rate : 0.7413
## P-Value [Acc > NIR] : 4.533e-07
##
## Kappa : 0.4146
##
## Mcnemar's Test P-Value : 5.822e-12
##
## Sensitivity : 0.9232
## Specificity : 0.4464
## Pos Pred Value : 0.8270
## Neg Pred Value : 0.6696
## Prevalence : 0.7413
## Detection Rate : 0.6844
## Detection Prevalence : 0.8276
## Balanced Accuracy : 0.6848
##
## 'Positive' Class : 0
## 
Multiple Linear Regression
Model 1
Below code shows output for preliminary regression modelling insurance payout given that a claim has been predicted. R-squared values are very low, but this assumes that a correct prediction from the binary logistic model has been made.
##
## Call:
## lm(formula = TARGET_AMT ~ ., data = mlr_crash)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9657 -3165 -1474 574 76279
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.075e+03 1.809e+03 2.253 0.0244 *
## KIDSDRIV -1.771e+02 3.556e+02 -0.498 0.6185
## AGE 5.833e-01 2.351e+01 0.025 0.9802
## HOMEKIDS 2.752e+02 2.295e+02 1.199 0.2306
## YOJ 1.917e+01 5.463e+01 0.351 0.7256
## INCOME -1.510e-02 7.821e-03 -1.930 0.0537 .
## PARENT1Yes -9.951e+01 6.469e+02 -0.154 0.8778
## HOME_VAL 2.230e-03 2.268e-03 0.984 0.3255
## MSTATUSYes -1.387e+03 5.662e+02 -2.450 0.0144 *
## SEXM 1.816e+03 7.167e+02 2.534 0.0114 *
## EDUCATIONHigh School -8.578e+02 5.772e+02 -1.486 0.1374
## EDUCATIONLess than High School -1.712e+02 7.149e+02 -0.239 0.8108
## EDUCATIONMasters 6.457e+02 1.048e+03 0.616 0.5380
## EDUCATIONPhD 2.938e+03 1.282e+03 2.293 0.0220 *
## JOBClerical -1.143e+03 6.452e+02 -1.772 0.0766 .
## JOBDoctor -3.784e+03 1.998e+03 -1.894 0.0584 .
## JOBHome Maker -1.046e+03 9.995e+02 -1.047 0.2954
## JOBLawyer -6.243e+02 1.323e+03 -0.472 0.6370
## JOBManager -1.788e+03 1.042e+03 -1.716 0.0864 .
## JOBOther Job -4.589e+02 1.304e+03 -0.352 0.7250
## JOBProfessional 7.702e+02 7.712e+02 0.999 0.3181
## JOBStudent -1.059e+03 8.089e+02 -1.309 0.1905
## TRAVTIME 4.108e+00 1.234e+01 0.333 0.7393
## CAR_USEPrivate -2.737e+02 5.849e+02 -0.468 0.6399
## BLUEBOOK 1.486e-01 3.376e-02 4.402 1.14e-05 ***
## TIF -5.847e+00 4.695e+01 -0.125 0.9009
## CAR_TYPEPanel Truck -2.619e+02 1.053e+03 -0.249 0.8036
## CAR_TYPEPickup 3.003e+02 6.627e+02 0.453 0.6505
## CAR_TYPESports Car 1.951e+03 8.262e+02 2.361 0.0183 *
## CAR_TYPESUV 1.657e+03 7.363e+02 2.251 0.0245 *
## CAR_TYPEVan -2.228e+02 8.588e+02 -0.259 0.7953
## RED_CARyes -3.138e+02 5.511e+02 -0.569 0.5692
## OLDCLAIM 5.024e-02 2.528e-02 1.987 0.0471 *
## CLM_FREQ -2.048e+02 1.749e+02 -1.171 0.2416
## REVOKEDYes -1.259e+03 5.850e+02 -2.152 0.0315 *
## MVR_PTS 8.937e+01 7.564e+01 1.182 0.2375
## CAR_AGE -9.797e+01 4.878e+01 -2.009 0.0447 *
## URBANICITYHighly Urban/ Urban 5.991e+01 8.182e+02 0.073 0.9416
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7586 on 1665 degrees of freedom
## (450 observations deleted due to missingness)
## Multiple R-squared: 0.04273, Adjusted R-squared: 0.02145
## F-statistic: 2.009 on 37 and 1665 DF, p-value: 0.000334The R^2 value is very low, around 4%, and many of the variables are not significant.
Model 2
Using our log transformation on certain variables, the results are slightly worse.
##
## Call:
## lm(formula = TARGET_AMT ~ ., data = mlr_crash_transf)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8045 -3199 -1526 438 99546
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -9715.099 4630.184 -2.098 0.0360 *
## KIDSDRIV -186.329 320.282 -0.582 0.5608
## AGE 544.526 882.174 0.617 0.5371
## HOMEKIDS 187.340 209.948 0.892 0.3723
## YOJ 8.150 61.050 0.133 0.8938
## INCOME 22.840 96.307 0.237 0.8126
## PARENT1Yes 331.308 588.943 0.563 0.5738
## HOME_VAL 58.650 38.287 1.532 0.1257
## MSTATUSYes -868.702 509.343 -1.706 0.0882 .
## SEXM 1212.639 630.947 1.922 0.0547 .
## EDUCATIONHigh School -457.376 505.973 -0.904 0.3661
## EDUCATIONLess than High School 51.500 635.038 0.081 0.9354
## EDUCATIONMasters 548.316 883.446 0.621 0.5349
## EDUCATIONPhD 1658.219 1088.609 1.523 0.1278
## JOBClerical -85.075 581.159 -0.146 0.8836
## JOBDoctor -2759.504 1870.439 -1.475 0.1403
## JOBHome Maker -73.493 941.671 -0.078 0.9378
## JOBLawyer -249.977 1173.707 -0.213 0.8314
## JOBManager -1310.356 904.347 -1.449 0.1475
## JOBOther Job -529.041 1140.250 -0.464 0.6427
## JOBProfessional 509.067 684.161 0.744 0.4569
## JOBStudent 317.311 799.632 0.397 0.6915
## TRAVTIME -51.921 299.067 -0.174 0.8622
## CAR_USEPrivate -345.492 522.462 -0.661 0.5085
## BLUEBOOK 1398.356 328.055 4.263 2.11e-05 ***
## TIF -14.903 42.536 -0.350 0.7261
## CAR_TYPEPanel Truck -29.775 881.064 -0.034 0.9730
## CAR_TYPEPickup -136.236 596.552 -0.228 0.8194
## CAR_TYPESports Car 1011.268 735.029 1.376 0.1690
## CAR_TYPESUV 677.040 643.223 1.053 0.2927
## CAR_TYPEVan 135.500 762.155 0.178 0.8589
## RED_CARyes -192.707 497.240 -0.388 0.6984
## OLDCLAIM 7.773 67.902 0.114 0.9089
## CLM_FREQ -67.375 232.751 -0.289 0.7722
## REVOKEDYes -765.210 422.770 -1.810 0.0704 .
## MVR_PTS 126.448 70.048 1.805 0.0712 .
## CAR_AGE -380.023 263.152 -1.444 0.1489
## URBANICITYHighly Urban/ Urban 31.111 755.064 0.041 0.9671
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7695 on 2115 degrees of freedom
## Multiple R-squared: 0.02941, Adjusted R-squared: 0.01244
## F-statistic: 1.732 on 37 and 2115 DF, p-value: 0.004147Model 3: Backwards Elimination
Now let’s use backwards elimination to remove some of variables that are not significant.
##
## Call:
## lm(formula = TARGET_AMT ~ ., data = mlr_crash_transf)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8045 -3199 -1526 438 99546
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -9715.099 4630.184 -2.098 0.0360 *
## KIDSDRIV -186.329 320.282 -0.582 0.5608
## AGE 544.526 882.174 0.617 0.5371
## HOMEKIDS 187.340 209.948 0.892 0.3723
## YOJ 8.150 61.050 0.133 0.8938
## INCOME 22.840 96.307 0.237 0.8126
## PARENT1Yes 331.308 588.943 0.563 0.5738
## HOME_VAL 58.650 38.287 1.532 0.1257
## MSTATUSYes -868.702 509.343 -1.706 0.0882 .
## SEXM 1212.639 630.947 1.922 0.0547 .
## EDUCATIONHigh School -457.376 505.973 -0.904 0.3661
## EDUCATIONLess than High School 51.500 635.038 0.081 0.9354
## EDUCATIONMasters 548.316 883.446 0.621 0.5349
## EDUCATIONPhD 1658.219 1088.609 1.523 0.1278
## JOBClerical -85.075 581.159 -0.146 0.8836
## JOBDoctor -2759.504 1870.439 -1.475 0.1403
## JOBHome Maker -73.493 941.671 -0.078 0.9378
## JOBLawyer -249.977 1173.707 -0.213 0.8314
## JOBManager -1310.356 904.347 -1.449 0.1475
## JOBOther Job -529.041 1140.250 -0.464 0.6427
## JOBProfessional 509.067 684.161 0.744 0.4569
## JOBStudent 317.311 799.632 0.397 0.6915
## TRAVTIME -51.921 299.067 -0.174 0.8622
## CAR_USEPrivate -345.492 522.462 -0.661 0.5085
## BLUEBOOK 1398.356 328.055 4.263 2.11e-05 ***
## TIF -14.903 42.536 -0.350 0.7261
## CAR_TYPEPanel Truck -29.775 881.064 -0.034 0.9730
## CAR_TYPEPickup -136.236 596.552 -0.228 0.8194
## CAR_TYPESports Car 1011.268 735.029 1.376 0.1690
## CAR_TYPESUV 677.040 643.223 1.053 0.2927
## CAR_TYPEVan 135.500 762.155 0.178 0.8589
## RED_CARyes -192.707 497.240 -0.388 0.6984
## OLDCLAIM 7.773 67.902 0.114 0.9089
## CLM_FREQ -67.375 232.751 -0.289 0.7722
## REVOKEDYes -765.210 422.770 -1.810 0.0704 .
## MVR_PTS 126.448 70.048 1.805 0.0712 .
## CAR_AGE -380.023 263.152 -1.444 0.1489
## URBANICITYHighly Urban/ Urban 31.111 755.064 0.041 0.9671
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7695 on 2115 degrees of freedom
## Multiple R-squared: 0.02941, Adjusted R-squared: 0.01244
## F-statistic: 1.732 on 37 and 2115 DF, p-value: 0.004147##
## Call:
## lm(formula = TARGET_AMT ~ KIDSDRIV + AGE + HOMEKIDS + YOJ + INCOME +
## PARENT1 + HOME_VAL + MSTATUS + SEX + EDUCATION + JOB + TRAVTIME +
## CAR_USE + BLUEBOOK + TIF + CAR_TYPE + RED_CAR + CLM_FREQ +
## REVOKED + MVR_PTS + CAR_AGE + URBANICITY, data = mlr_crash_transf)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8055 -3195 -1534 449 99520
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -9703.231 4627.944 -2.097 0.0361 *
## KIDSDRIV -186.712 320.190 -0.583 0.5599
## AGE 543.441 881.917 0.616 0.5378
## HOMEKIDS 187.371 209.899 0.893 0.3721
## YOJ 8.449 60.979 0.139 0.8898
## INCOME 22.822 96.285 0.237 0.8127
## PARENT1Yes 328.742 588.379 0.559 0.5764
## HOME_VAL 58.642 38.278 1.532 0.1257
## MSTATUSYes -869.123 509.211 -1.707 0.0880 .
## SEXM 1213.494 630.756 1.924 0.0545 .
## EDUCATIONHigh School -457.887 505.835 -0.905 0.3655
## EDUCATIONLess than High School 51.393 634.890 0.081 0.9355
## EDUCATIONMasters 543.613 882.285 0.616 0.5379
## EDUCATIONPhD 1652.076 1087.033 1.520 0.1287
## JOBClerical -82.867 580.703 -0.143 0.8865
## JOBDoctor -2765.994 1869.144 -1.480 0.1391
## JOBHome Maker -69.836 940.909 -0.074 0.9408
## JOBLawyer -242.197 1171.465 -0.207 0.8362
## JOBManager -1307.098 903.688 -1.446 0.1482
## JOBOther Job -522.305 1138.465 -0.459 0.6464
## JOBProfessional 511.708 683.613 0.749 0.4542
## JOBStudent 319.696 799.174 0.400 0.6892
## TRAVTIME -52.423 298.965 -0.175 0.8608
## CAR_USEPrivate -347.085 522.155 -0.665 0.5063
## BLUEBOOK 1398.320 327.978 4.263 2.1e-05 ***
## TIF -14.956 42.524 -0.352 0.7251
## CAR_TYPEPanel Truck -33.151 880.365 -0.038 0.9700
## CAR_TYPEPickup -137.900 596.236 -0.231 0.8171
## CAR_TYPESports Car 1012.421 734.788 1.378 0.1684
## CAR_TYPESUV 676.299 643.040 1.052 0.2930
## CAR_TYPEVan 135.417 761.977 0.178 0.8590
## RED_CARyes -194.931 496.745 -0.392 0.6948
## CLM_FREQ -46.161 140.797 -0.328 0.7431
## REVOKEDYes -756.269 415.397 -1.821 0.0688 .
## MVR_PTS 128.158 68.418 1.873 0.0612 .
## CAR_AGE -379.748 263.080 -1.443 0.1490
## URBANICITYHighly Urban/ Urban 31.696 754.871 0.042 0.9665
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7693 on 2116 degrees of freedom
## Multiple R-squared: 0.02941, Adjusted R-squared: 0.0129
## F-statistic: 1.781 on 36 and 2116 DF, p-value: 0.003007##
## Call:
## lm(formula = TARGET_AMT ~ KIDSDRIV + AGE + HOMEKIDS + INCOME +
## PARENT1 + HOME_VAL + MSTATUS + SEX + EDUCATION + JOB + TRAVTIME +
## CAR_USE + BLUEBOOK + TIF + CAR_TYPE + RED_CAR + CLM_FREQ +
## REVOKED + MVR_PTS + CAR_AGE + URBANICITY, data = mlr_crash_transf)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8028 -3203 -1530 439 99526
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -9802.39 4571.21 -2.144 0.0321 *
## KIDSDRIV -190.69 318.83 -0.598 0.5498
## AGE 565.15 867.68 0.651 0.5149
## HOMEKIDS 193.93 204.45 0.949 0.3430
## INCOME 30.91 76.57 0.404 0.6865
## PARENT1Yes 329.39 588.22 0.560 0.5756
## HOME_VAL 58.81 38.25 1.538 0.1243
## MSTATUSYes -860.73 505.48 -1.703 0.0888 .
## SEXM 1215.25 630.48 1.927 0.0541 .
## EDUCATIONHigh School -456.40 505.60 -0.903 0.3668
## EDUCATIONLess than High School 57.35 633.28 0.091 0.9278
## EDUCATIONMasters 544.42 882.06 0.617 0.5372
## EDUCATIONPhD 1651.22 1086.76 1.519 0.1288
## JOBClerical -81.44 580.48 -0.140 0.8884
## JOBDoctor -2766.26 1868.71 -1.480 0.1389
## JOBHome Maker -71.81 940.58 -0.076 0.9392
## JOBLawyer -244.04 1171.12 -0.208 0.8350
## JOBManager -1307.12 903.48 -1.447 0.1481
## JOBOther Job -524.53 1138.09 -0.461 0.6449
## JOBProfessional 508.91 683.16 0.745 0.4564
## JOBStudent 321.71 798.86 0.403 0.6872
## TRAVTIME -53.43 298.81 -0.179 0.8581
## CAR_USEPrivate -344.52 521.71 -0.660 0.5091
## BLUEBOOK 1400.31 327.59 4.275 2e-05 ***
## TIF -15.01 42.51 -0.353 0.7241
## CAR_TYPEPanel Truck -39.29 879.05 -0.045 0.9644
## CAR_TYPEPickup -138.62 596.07 -0.233 0.8161
## CAR_TYPESports Car 1008.47 734.06 1.374 0.1696
## CAR_TYPESUV 676.28 642.89 1.052 0.2929
## CAR_TYPEVan 129.97 760.79 0.171 0.8644
## RED_CARyes -195.58 496.61 -0.394 0.6938
## CLM_FREQ -46.05 140.76 -0.327 0.7436
## REVOKEDYes -753.35 414.77 -1.816 0.0695 .
## MVR_PTS 128.13 68.40 1.873 0.0612 .
## CAR_AGE -380.42 262.97 -1.447 0.1482
## URBANICITYHighly Urban/ Urban 32.33 754.68 0.043 0.9658
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7691 on 2117 degrees of freedom
## Multiple R-squared: 0.0294, Adjusted R-squared: 0.01335
## F-statistic: 1.832 on 35 and 2117 DF, p-value: 0.002154##
## Call:
## lm(formula = TARGET_AMT ~ KIDSDRIV + AGE + HOMEKIDS + INCOME +
## PARENT1 + HOME_VAL + MSTATUS + SEX + EDUCATION + JOB + TRAVTIME +
## CAR_USE + BLUEBOOK + TIF + CAR_TYPE + RED_CAR + CLM_FREQ +
## REVOKED + MVR_PTS + CAR_AGE, data = mlr_crash_transf)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8029 -3200 -1530 442 99526
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -9767.63 4497.57 -2.172 0.0300 *
## KIDSDRIV -191.06 318.64 -0.600 0.5488
## AGE 563.91 866.99 0.650 0.5155
## HOMEKIDS 193.78 204.37 0.948 0.3432
## INCOME 30.97 76.54 0.405 0.6858
## PARENT1Yes 329.24 588.07 0.560 0.5756
## HOME_VAL 58.77 38.23 1.537 0.1244
## MSTATUSYes -859.38 504.37 -1.704 0.0886 .
## SEXM 1214.56 630.13 1.927 0.0541 .
## EDUCATIONHigh School -456.51 505.48 -0.903 0.3666
## EDUCATIONLess than High School 57.49 633.13 0.091 0.9277
## EDUCATIONMasters 544.35 881.85 0.617 0.5371
## EDUCATIONPhD 1651.00 1086.49 1.520 0.1288
## JOBClerical -83.04 579.13 -0.143 0.8860
## JOBDoctor -2764.75 1867.94 -1.480 0.1390
## JOBHome Maker -71.56 940.34 -0.076 0.9393
## JOBLawyer -244.07 1170.84 -0.208 0.8349
## JOBManager -1305.71 902.66 -1.447 0.1482
## JOBOther Job -523.68 1137.64 -0.460 0.6453
## JOBProfessional 508.32 682.86 0.744 0.4567
## JOBStudent 318.99 796.14 0.401 0.6887
## TRAVTIME -54.22 298.16 -0.182 0.8557
## CAR_USEPrivate -344.51 521.58 -0.661 0.5090
## BLUEBOOK 1400.54 327.47 4.277 1.98e-05 ***
## TIF -14.97 42.49 -0.352 0.7246
## CAR_TYPEPanel Truck -38.22 878.48 -0.044 0.9653
## CAR_TYPEPickup -138.32 595.89 -0.232 0.8165
## CAR_TYPESports Car 1008.24 733.87 1.374 0.1696
## CAR_TYPESUV 676.31 642.74 1.052 0.2928
## CAR_TYPEVan 130.50 760.51 0.172 0.8638
## RED_CARyes -195.48 496.49 -0.394 0.6938
## CLM_FREQ -45.73 140.53 -0.325 0.7449
## REVOKEDYes -752.87 414.51 -1.816 0.0695 .
## MVR_PTS 128.21 68.36 1.875 0.0609 .
## CAR_AGE -380.35 262.91 -1.447 0.1481
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7689 on 2118 degrees of freedom
## Multiple R-squared: 0.0294, Adjusted R-squared: 0.01382
## F-statistic: 1.887 on 34 and 2118 DF, p-value: 0.001515##
## Call:
## lm(formula = TARGET_AMT ~ KIDSDRIV + AGE + HOMEKIDS + INCOME +
## PARENT1 + HOME_VAL + MSTATUS + SEX + EDUCATION + JOB + CAR_USE +
## BLUEBOOK + TIF + CAR_TYPE + RED_CAR + CLM_FREQ + REVOKED +
## MVR_PTS + CAR_AGE, data = mlr_crash_transf)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7928 -3193 -1536 437 99511
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -9919.35 4418.51 -2.245 0.0249 *
## KIDSDRIV -190.38 318.54 -0.598 0.5501
## AGE 561.46 866.69 0.648 0.5172
## HOMEKIDS 193.67 204.33 0.948 0.3433
## INCOME 30.55 76.49 0.399 0.6896
## PARENT1Yes 332.46 587.67 0.566 0.5716
## HOME_VAL 58.96 38.20 1.543 0.1229
## MSTATUSYes -860.93 504.18 -1.708 0.0879 .
## SEXM 1212.02 629.83 1.924 0.0544 .
## EDUCATIONHigh School -453.99 505.17 -0.899 0.3689
## EDUCATIONLess than High School 59.11 632.92 0.093 0.9256
## EDUCATIONMasters 542.00 881.56 0.615 0.5387
## EDUCATIONPhD 1647.94 1086.12 1.517 0.1293
## JOBClerical -81.79 578.96 -0.141 0.8877
## JOBDoctor -2761.12 1867.40 -1.479 0.1394
## JOBHome Maker -74.69 939.97 -0.079 0.9367
## JOBLawyer -239.16 1170.26 -0.204 0.8381
## JOBManager -1301.37 902.14 -1.443 0.1493
## JOBOther Job -517.79 1136.92 -0.455 0.6488
## JOBProfessional 508.69 682.70 0.745 0.4563
## JOBStudent 322.09 795.78 0.405 0.6857
## CAR_USEPrivate -348.16 521.08 -0.668 0.5041
## BLUEBOOK 1398.46 327.19 4.274 2e-05 ***
## TIF -14.75 42.47 -0.347 0.7284
## CAR_TYPEPanel Truck -39.82 878.24 -0.045 0.9638
## CAR_TYPEPickup -136.54 595.68 -0.229 0.8187
## CAR_TYPESports Car 1009.62 733.66 1.376 0.1689
## CAR_TYPESUV 673.92 642.46 1.049 0.2943
## CAR_TYPEVan 133.45 760.16 0.176 0.8607
## RED_CARyes -197.06 496.30 -0.397 0.6914
## CLM_FREQ -46.24 140.47 -0.329 0.7421
## REVOKEDYes -751.98 414.39 -1.815 0.0697 .
## MVR_PTS 128.03 68.34 1.873 0.0611 .
## CAR_AGE -381.09 262.82 -1.450 0.1472
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7688 on 2119 degrees of freedom
## Multiple R-squared: 0.02938, Adjusted R-squared: 0.01427
## F-statistic: 1.944 on 33 and 2119 DF, p-value: 0.001059##
## Call:
## lm(formula = TARGET_AMT ~ KIDSDRIV + AGE + HOMEKIDS + PARENT1 +
## HOME_VAL + MSTATUS + SEX + EDUCATION + JOB + CAR_USE + BLUEBOOK +
## TIF + CAR_TYPE + RED_CAR + CLM_FREQ + REVOKED + MVR_PTS +
## CAR_AGE, data = mlr_crash_transf)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7925 -3197 -1545 443 99526
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -9694.85 4381.75 -2.213 0.0270 *
## KIDSDRIV -185.98 318.29 -0.584 0.5591
## AGE 564.77 866.48 0.652 0.5146
## HOMEKIDS 192.47 204.26 0.942 0.3462
## PARENT1Yes 326.40 587.36 0.556 0.5785
## HOME_VAL 59.53 38.17 1.560 0.1190
## MSTATUSYes -866.79 503.87 -1.720 0.0855 .
## SEXM 1214.06 629.69 1.928 0.0540 .
## EDUCATIONHigh School -457.37 505.00 -0.906 0.3652
## EDUCATIONLess than High School 39.79 630.95 0.063 0.9497
## EDUCATIONMasters 551.82 881.04 0.626 0.5312
## EDUCATIONPhD 1658.08 1085.60 1.527 0.1268
## JOBClerical -97.88 577.44 -0.170 0.8654
## JOBDoctor -2783.28 1866.21 -1.491 0.1360
## JOBHome Maker -292.97 764.65 -0.383 0.7017
## JOBLawyer -254.76 1169.38 -0.218 0.8276
## JOBManager -1308.39 901.79 -1.451 0.1470
## JOBOther Job -521.56 1136.66 -0.459 0.6464
## JOBProfessional 502.63 682.39 0.737 0.4615
## JOBStudent 129.67 633.27 0.205 0.8378
## CAR_USEPrivate -337.81 520.33 -0.649 0.5163
## BLUEBOOK 1408.77 326.11 4.320 1.63e-05 ***
## TIF -15.27 42.44 -0.360 0.7191
## CAR_TYPEPanel Truck -30.76 877.77 -0.035 0.9721
## CAR_TYPEPickup -125.32 594.89 -0.211 0.8332
## CAR_TYPESports Car 1007.17 733.49 1.373 0.1699
## CAR_TYPESUV 682.65 641.96 1.063 0.2877
## CAR_TYPEVan 139.30 759.87 0.183 0.8546
## RED_CARyes -199.44 496.16 -0.402 0.6878
## CLM_FREQ -46.11 140.44 -0.328 0.7427
## REVOKEDYes -752.76 414.30 -1.817 0.0694 .
## MVR_PTS 126.28 68.18 1.852 0.0642 .
## CAR_AGE -380.99 262.76 -1.450 0.1472
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7686 on 2120 degrees of freedom
## Multiple R-squared: 0.02931, Adjusted R-squared: 0.01466
## F-statistic: 2 on 32 and 2120 DF, p-value: 0.0007551##
## Call:
## lm(formula = TARGET_AMT ~ KIDSDRIV + AGE + HOMEKIDS + PARENT1 +
## HOME_VAL + MSTATUS + SEX + EDUCATION + JOB + CAR_USE + BLUEBOOK +
## TIF + CAR_TYPE + RED_CAR + REVOKED + MVR_PTS + CAR_AGE, data = mlr_crash_transf)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7934 -3210 -1541 443 99469
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -9717.22 4380.30 -2.218 0.0266 *
## KIDSDRIV -187.09 318.20 -0.588 0.5566
## AGE 560.79 866.21 0.647 0.5174
## HOMEKIDS 192.96 204.21 0.945 0.3448
## PARENT1Yes 327.70 587.22 0.558 0.5769
## HOME_VAL 59.68 38.16 1.564 0.1180
## MSTATUSYes -868.05 503.75 -1.723 0.0850 .
## SEXM 1215.55 629.54 1.931 0.0536 .
## EDUCATIONHigh School -455.67 504.87 -0.903 0.3669
## EDUCATIONLess than High School 42.80 630.75 0.068 0.9459
## EDUCATIONMasters 546.87 880.72 0.621 0.5347
## EDUCATIONPhD 1655.60 1085.35 1.525 0.1273
## JOBClerical -98.34 577.31 -0.170 0.8648
## JOBDoctor -2814.40 1863.41 -1.510 0.1311
## JOBHome Maker -294.97 764.46 -0.386 0.6996
## JOBLawyer -238.46 1168.08 -0.204 0.8383
## JOBManager -1296.96 900.93 -1.440 0.1501
## JOBOther Job -517.27 1136.35 -0.455 0.6490
## JOBProfessional 503.33 682.25 0.738 0.4607
## JOBStudent 131.22 633.12 0.207 0.8358
## CAR_USEPrivate -335.11 520.16 -0.644 0.5195
## BLUEBOOK 1409.19 326.04 4.322 1.62e-05 ***
## TIF -15.71 42.41 -0.370 0.7111
## CAR_TYPEPanel Truck -29.39 877.58 -0.033 0.9733
## CAR_TYPEPickup -127.40 594.74 -0.214 0.8304
## CAR_TYPESports Car 1000.79 733.08 1.365 0.1723
## CAR_TYPESUV 683.27 641.82 1.065 0.2872
## CAR_TYPEVan 143.65 759.59 0.189 0.8500
## RED_CARyes -202.05 495.99 -0.407 0.6838
## REVOKEDYes -754.20 414.19 -1.821 0.0688 .
## MVR_PTS 119.70 65.16 1.837 0.0663 .
## CAR_AGE -385.16 262.40 -1.468 0.1423
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7685 on 2121 degrees of freedom
## Multiple R-squared: 0.02926, Adjusted R-squared: 0.01507
## F-statistic: 2.062 on 31 and 2121 DF, p-value: 0.0005236##
## Call:
## lm(formula = TARGET_AMT ~ KIDSDRIV + AGE + HOMEKIDS + PARENT1 +
## HOME_VAL + MSTATUS + SEX + EDUCATION + JOB + CAR_USE + BLUEBOOK +
## CAR_TYPE + RED_CAR + REVOKED + MVR_PTS + CAR_AGE, data = mlr_crash_transf)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7929 -3210 -1538 442 99523
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -9820.06 4370.60 -2.247 0.0248 *
## KIDSDRIV -186.88 318.14 -0.587 0.5570
## AGE 563.78 866.00 0.651 0.5151
## HOMEKIDS 192.10 204.16 0.941 0.3468
## PARENT1Yes 332.02 586.99 0.566 0.5717
## HOME_VAL 59.66 38.15 1.564 0.1180
## MSTATUSYes -859.82 503.16 -1.709 0.0876 .
## SEXM 1216.81 629.40 1.933 0.0533 .
## EDUCATIONHigh School -457.18 504.75 -0.906 0.3652
## EDUCATIONLess than High School 41.75 630.61 0.066 0.9472
## EDUCATIONMasters 542.75 880.47 0.616 0.5377
## EDUCATIONPhD 1653.85 1085.12 1.524 0.1276
## JOBClerical -104.83 576.93 -0.182 0.8558
## JOBDoctor -2798.33 1862.52 -1.502 0.1331
## JOBHome Maker -294.00 764.30 -0.385 0.7005
## JOBLawyer -232.83 1167.74 -0.199 0.8420
## JOBManager -1294.47 900.72 -1.437 0.1508
## JOBOther Job -520.50 1136.08 -0.458 0.6469
## JOBProfessional 499.74 682.04 0.733 0.4638
## JOBStudent 134.49 632.93 0.212 0.8317
## CAR_USEPrivate -323.75 519.14 -0.624 0.5329
## BLUEBOOK 1409.68 325.97 4.325 1.6e-05 ***
## CAR_TYPEPanel Truck -22.29 877.19 -0.025 0.9797
## CAR_TYPEPickup -125.55 594.59 -0.211 0.8328
## CAR_TYPESports Car 997.34 732.87 1.361 0.1737
## CAR_TYPESUV 680.38 641.64 1.060 0.2891
## CAR_TYPEVan 146.89 759.39 0.193 0.8466
## RED_CARyes -200.26 495.87 -0.404 0.6864
## REVOKEDYes -751.21 414.03 -1.814 0.0698 .
## MVR_PTS 120.49 65.11 1.851 0.0644 .
## CAR_AGE -384.91 262.35 -1.467 0.1425
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7683 on 2122 degrees of freedom
## Multiple R-squared: 0.0292, Adjusted R-squared: 0.01547
## F-statistic: 2.127 on 30 and 2122 DF, p-value: 0.0003608##
## Call:
## lm(formula = TARGET_AMT ~ KIDSDRIV + AGE + HOMEKIDS + PARENT1 +
## HOME_VAL + MSTATUS + SEX + EDUCATION + JOB + CAR_USE + BLUEBOOK +
## CAR_TYPE + REVOKED + MVR_PTS + CAR_AGE, data = mlr_crash_transf)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7921 -3209 -1542 438 99449
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -9915.44 4363.36 -2.272 0.0232 *
## KIDSDRIV -184.70 318.03 -0.581 0.5615
## AGE 578.39 865.07 0.669 0.5038
## HOMEKIDS 192.45 204.12 0.943 0.3459
## PARENT1Yes 333.44 586.86 0.568 0.5700
## HOME_VAL 59.81 38.14 1.568 0.1170
## MSTATUSYes -860.83 503.05 -1.711 0.0872 .
## SEXM 1104.16 564.11 1.957 0.0504 .
## EDUCATIONHigh School -450.55 504.38 -0.893 0.3718
## EDUCATIONLess than High School 48.79 630.25 0.077 0.9383
## EDUCATIONMasters 548.71 880.18 0.623 0.5331
## EDUCATIONPhD 1666.91 1084.42 1.537 0.1244
## JOBClerical -97.36 576.52 -0.169 0.8659
## JOBDoctor -2807.36 1862.02 -1.508 0.1318
## JOBHome Maker -292.72 764.14 -0.383 0.7017
## JOBLawyer -234.95 1167.50 -0.201 0.8405
## JOBManager -1300.32 900.42 -1.444 0.1489
## JOBOther Job -535.77 1135.23 -0.472 0.6370
## JOBProfessional 502.88 681.86 0.738 0.4609
## JOBStudent 129.31 632.67 0.204 0.8381
## CAR_USEPrivate -327.47 518.96 -0.631 0.5281
## BLUEBOOK 1412.50 325.83 4.335 1.53e-05 ***
## CAR_TYPEPanel Truck -34.26 876.52 -0.039 0.9688
## CAR_TYPEPickup -129.40 594.40 -0.218 0.8277
## CAR_TYPESports Car 1000.28 732.69 1.365 0.1723
## CAR_TYPESUV 688.83 641.18 1.074 0.2828
## CAR_TYPEVan 142.73 759.17 0.188 0.8509
## REVOKEDYes -748.97 413.91 -1.809 0.0705 .
## MVR_PTS 119.73 65.07 1.840 0.0659 .
## CAR_AGE -383.29 262.26 -1.461 0.1440
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7682 on 2123 degrees of freedom
## Multiple R-squared: 0.02912, Adjusted R-squared: 0.01586
## F-statistic: 2.196 on 29 and 2123 DF, p-value: 0.0002469##
## Call:
## lm(formula = TARGET_AMT ~ KIDSDRIV + AGE + HOMEKIDS + HOME_VAL +
## MSTATUS + SEX + EDUCATION + JOB + CAR_USE + BLUEBOOK + CAR_TYPE +
## REVOKED + MVR_PTS + CAR_AGE, data = mlr_crash_transf)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8001 -3182 -1544 429 99508
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -9645.55 4336.73 -2.224 0.0262 *
## KIDSDRIV -177.34 317.72 -0.558 0.5768
## AGE 522.09 859.24 0.608 0.5435
## HOMEKIDS 244.05 182.77 1.335 0.1819
## HOME_VAL 59.37 38.13 1.557 0.1196
## MSTATUSYes -1008.08 431.08 -2.338 0.0195 *
## SEXM 1101.07 563.99 1.952 0.0510 .
## EDUCATIONHigh School -443.57 504.15 -0.880 0.3791
## EDUCATIONLess than High School 50.65 630.14 0.080 0.9359
## EDUCATIONMasters 533.07 879.61 0.606 0.5446
## EDUCATIONPhD 1656.38 1084.09 1.528 0.1267
## JOBClerical -96.79 576.43 -0.168 0.8667
## JOBDoctor -2822.82 1861.53 -1.516 0.1296
## JOBHome Maker -291.98 764.02 -0.382 0.7024
## JOBLawyer -211.22 1166.57 -0.181 0.8563
## JOBManager -1282.01 899.70 -1.425 0.1543
## JOBOther Job -519.14 1134.67 -0.458 0.6473
## JOBProfessional 518.77 681.18 0.762 0.4464
## JOBStudent 126.15 632.54 0.199 0.8419
## CAR_USEPrivate -322.17 518.79 -0.621 0.5347
## BLUEBOOK 1415.19 325.74 4.345 1.46e-05 ***
## CAR_TYPEPanel Truck -44.90 876.18 -0.051 0.9591
## CAR_TYPEPickup -133.98 594.25 -0.225 0.8216
## CAR_TYPESports Car 1007.48 732.47 1.375 0.1691
## CAR_TYPESUV 690.69 641.06 1.077 0.2814
## CAR_TYPEVan 134.90 758.92 0.178 0.8589
## REVOKEDYes -754.18 413.75 -1.823 0.0685 .
## MVR_PTS 120.97 65.02 1.860 0.0630 .
## CAR_AGE -379.67 262.15 -1.448 0.1477
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7680 on 2124 degrees of freedom
## Multiple R-squared: 0.02898, Adjusted R-squared: 0.01618
## F-statistic: 2.264 on 28 and 2124 DF, p-value: 0.0001746##
## Call:
## lm(formula = TARGET_AMT ~ AGE + HOMEKIDS + HOME_VAL + MSTATUS +
## SEX + EDUCATION + JOB + CAR_USE + BLUEBOOK + CAR_TYPE + REVOKED +
## MVR_PTS + CAR_AGE, data = mlr_crash_transf)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8078 -3178 -1530 459 99524
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -9136.73 4239.16 -2.155 0.0312 *
## AGE 400.50 831.03 0.482 0.6299
## HOMEKIDS 189.67 154.61 1.227 0.2200
## HOME_VAL 59.59 38.12 1.563 0.1181
## MSTATUSYes -1006.39 431.00 -2.335 0.0196 *
## SEXM 1106.98 563.80 1.963 0.0497 *
## EDUCATIONHigh School -436.94 503.93 -0.867 0.3860
## EDUCATIONLess than High School 51.04 630.04 0.081 0.9354
## EDUCATIONMasters 511.06 878.58 0.582 0.5608
## EDUCATIONPhD 1645.52 1083.74 1.518 0.1291
## JOBClerical -88.08 576.12 -0.153 0.8785
## JOBDoctor -2799.95 1860.77 -1.505 0.1325
## JOBHome Maker -279.85 763.59 -0.366 0.7140
## JOBLawyer -190.63 1165.80 -0.164 0.8701
## JOBManager -1314.95 897.62 -1.465 0.1431
## JOBOther Job -510.27 1134.37 -0.450 0.6529
## JOBProfessional 510.66 680.91 0.750 0.4534
## JOBStudent 132.06 632.35 0.209 0.8346
## CAR_USEPrivate -335.48 518.16 -0.647 0.5174
## BLUEBOOK 1409.23 325.51 4.329 1.57e-05 ***
## CAR_TYPEPanel Truck -51.81 875.95 -0.059 0.9528
## CAR_TYPEPickup -139.97 594.06 -0.236 0.8138
## CAR_TYPESports Car 1016.08 732.19 1.388 0.1654
## CAR_TYPESUV 699.27 640.78 1.091 0.2753
## CAR_TYPEVan 143.98 758.63 0.190 0.8495
## REVOKEDYes -765.21 413.21 -1.852 0.0642 .
## MVR_PTS 120.13 64.99 1.848 0.0647 .
## CAR_AGE -374.75 261.96 -1.431 0.1527
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7679 on 2125 degrees of freedom
## Multiple R-squared: 0.02883, Adjusted R-squared: 0.01649
## F-statistic: 2.337 on 27 and 2125 DF, p-value: 0.0001215##
## Call:
## lm(formula = TARGET_AMT ~ HOMEKIDS + HOME_VAL + MSTATUS + SEX +
## EDUCATION + JOB + CAR_USE + BLUEBOOK + CAR_TYPE + REVOKED +
## MVR_PTS + CAR_AGE, data = mlr_crash_transf)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8151 -3184 -1523 459 99553
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -7876.66 3336.17 -2.361 0.0183 *
## HOMEKIDS 160.41 142.16 1.128 0.2593
## HOME_VAL 60.39 38.08 1.586 0.1129
## MSTATUSYes -987.07 429.06 -2.301 0.0215 *
## SEXM 1132.80 561.15 2.019 0.0436 *
## EDUCATIONHigh School -436.65 503.84 -0.867 0.3862
## EDUCATIONLess than High School 58.18 629.75 0.092 0.9264
## EDUCATIONMasters 528.50 877.68 0.602 0.5471
## EDUCATIONPhD 1672.96 1082.05 1.546 0.1222
## JOBClerical -107.99 574.53 -0.188 0.8509
## JOBDoctor -2761.44 1858.72 -1.486 0.1375
## JOBHome Maker -263.45 762.69 -0.345 0.7298
## JOBLawyer -163.91 1164.27 -0.141 0.8881
## JOBManager -1310.21 897.41 -1.460 0.1444
## JOBOther Job -506.24 1134.14 -0.446 0.6554
## JOBProfessional 522.82 680.32 0.768 0.4423
## JOBStudent 129.66 632.22 0.205 0.8375
## CAR_USEPrivate -331.96 518.02 -0.641 0.5217
## BLUEBOOK 1432.35 321.90 4.450 9.04e-06 ***
## CAR_TYPEPanel Truck -68.44 875.11 -0.078 0.9377
## CAR_TYPEPickup -139.29 593.95 -0.235 0.8146
## CAR_TYPESports Car 1045.93 729.43 1.434 0.1517
## CAR_TYPESUV 731.48 637.17 1.148 0.2511
## CAR_TYPEVan 139.25 758.43 0.184 0.8543
## REVOKEDYes -757.71 412.84 -1.835 0.0666 .
## MVR_PTS 119.52 64.97 1.840 0.0660 .
## CAR_AGE -374.56 261.91 -1.430 0.1528
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7678 on 2126 degrees of freedom
## Multiple R-squared: 0.02873, Adjusted R-squared: 0.01685
## F-statistic: 2.419 on 26 and 2126 DF, p-value: 8.117e-05##
## Call:
## lm(formula = TARGET_AMT ~ HOMEKIDS + HOME_VAL + MSTATUS + SEX +
## EDUCATION + JOB + BLUEBOOK + CAR_TYPE + REVOKED + MVR_PTS +
## CAR_AGE, data = mlr_crash_transf)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8303 -3189 -1522 430 99678
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -8109.987 3315.783 -2.446 0.0145 *
## HOMEKIDS 156.882 142.037 1.105 0.2695
## HOME_VAL 61.055 38.057 1.604 0.1088
## MSTATUSYes -991.309 428.947 -2.311 0.0209 *
## SEXM 1125.415 560.949 2.006 0.0450 *
## EDUCATIONHigh School -433.541 503.748 -0.861 0.3895
## EDUCATIONLess than High School -39.142 611.076 -0.064 0.9489
## EDUCATIONMasters 528.314 877.554 0.602 0.5472
## EDUCATIONPhD 1680.341 1081.838 1.553 0.1205
## JOBClerical -274.495 512.351 -0.536 0.5922
## JOBDoctor -3026.832 1811.747 -1.671 0.0949 .
## JOBHome Maker -452.065 703.509 -0.643 0.5206
## JOBLawyer -419.505 1093.662 -0.384 0.7013
## JOBManager -1497.993 848.098 -1.766 0.0775 .
## JOBOther Job -596.233 1125.255 -0.530 0.5963
## JOBProfessional 348.994 623.820 0.559 0.5759
## JOBStudent 80.140 627.392 0.128 0.8984
## BLUEBOOK 1446.868 321.058 4.507 6.95e-06 ***
## CAR_TYPEPanel Truck 121.834 823.083 0.148 0.8823
## CAR_TYPEPickup -7.405 557.076 -0.013 0.9894
## CAR_TYPESports Car 1029.205 728.861 1.412 0.1581
## CAR_TYPESUV 723.797 636.964 1.136 0.2559
## CAR_TYPEVan 263.545 733.104 0.359 0.7193
## REVOKEDYes -747.782 412.490 -1.813 0.0700 .
## MVR_PTS 122.581 64.785 1.892 0.0586 .
## CAR_AGE -376.213 261.859 -1.437 0.1509
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7677 on 2127 degrees of freedom
## Multiple R-squared: 0.02854, Adjusted R-squared: 0.01712
## F-statistic: 2.5 on 25 and 2127 DF, p-value: 5.655e-05##
## Call:
## lm(formula = TARGET_AMT ~ HOMEKIDS + HOME_VAL + MSTATUS + SEX +
## EDUCATION + BLUEBOOK + CAR_TYPE + REVOKED + MVR_PTS + CAR_AGE,
## data = mlr_crash_transf)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8096 -3207 -1527 378 100059
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -8094.118 3197.807 -2.531 0.0114 *
## HOMEKIDS 142.794 141.266 1.011 0.3122
## HOME_VAL 55.348 34.571 1.601 0.1095
## MSTATUSYes -910.378 410.811 -2.216 0.0268 *
## SEXM 1133.015 552.890 2.049 0.0406 *
## EDUCATIONHigh School -427.565 474.626 -0.901 0.3678
## EDUCATIONLess than High School -70.085 567.078 -0.124 0.9017
## EDUCATIONMasters 29.144 556.698 0.052 0.9583
## EDUCATIONPhD 552.367 780.792 0.707 0.4794
## BLUEBOOK 1433.180 313.328 4.574 5.06e-06 ***
## CAR_TYPEPanel Truck 245.320 787.406 0.312 0.7554
## CAR_TYPEPickup -0.581 554.157 -0.001 0.9992
## CAR_TYPESports Car 952.486 727.235 1.310 0.1904
## CAR_TYPESUV 664.736 635.728 1.046 0.2959
## CAR_TYPEVan 281.676 720.588 0.391 0.6959
## REVOKEDYes -681.358 411.172 -1.657 0.0976 .
## MVR_PTS 127.543 64.525 1.977 0.0482 *
## CAR_AGE -365.036 261.332 -1.397 0.1626
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7675 on 2135 degrees of freedom
## Multiple R-squared: 0.02527, Adjusted R-squared: 0.01751
## F-statistic: 3.256 on 17 and 2135 DF, p-value: 7.297e-06##
## Call:
## lm(formula = TARGET_AMT ~ HOMEKIDS + HOME_VAL + MSTATUS + SEX +
## BLUEBOOK + CAR_TYPE + REVOKED + MVR_PTS + CAR_AGE, data = mlr_crash_transf)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7893 -3212 -1557 410 100200
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -8654.216 3095.823 -2.795 0.00523 **
## HOMEKIDS 135.427 140.861 0.961 0.33645
## HOME_VAL 58.351 34.436 1.694 0.09032 .
## MSTATUSYes -963.913 407.931 -2.363 0.01822 *
## SEXM 1116.708 552.118 2.023 0.04324 *
## BLUEBOOK 1452.995 311.031 4.672 3.18e-06 ***
## CAR_TYPEPanel Truck 314.423 783.769 0.401 0.68834
## CAR_TYPEPickup -2.979 553.431 -0.005 0.99571
## CAR_TYPESports Car 959.028 725.935 1.321 0.18661
## CAR_TYPESUV 638.714 634.744 1.006 0.31441
## CAR_TYPEVan 336.811 717.794 0.469 0.63895
## REVOKEDYes -697.721 410.676 -1.699 0.08947 .
## MVR_PTS 129.059 64.464 2.002 0.04541 *
## CAR_AGE -226.895 209.010 -1.086 0.27779
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7671 on 2139 degrees of freedom
## Multiple R-squared: 0.02439, Adjusted R-squared: 0.01846
## F-statistic: 4.114 on 13 and 2139 DF, p-value: 9.195e-07##
## Call:
## lm(formula = TARGET_AMT ~ HOMEKIDS + HOME_VAL + MSTATUS + SEX +
## BLUEBOOK + REVOKED + MVR_PTS + CAR_AGE, data = mlr_crash_transf)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7506 -3167 -1547 392 100397
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -7682.75 2396.42 -3.206 0.00137 **
## HOMEKIDS 126.65 140.53 0.901 0.36755
## HOME_VAL 59.05 34.40 1.717 0.08621 .
## MSTATUSYes -948.00 407.02 -2.329 0.01995 *
## SEXM 666.22 335.54 1.986 0.04721 *
## BLUEBOOK 1410.39 255.13 5.528 3.63e-08 ***
## REVOKEDYes -695.80 409.88 -1.698 0.08973 .
## MVR_PTS 128.90 64.30 2.005 0.04512 *
## CAR_AGE -217.32 208.65 -1.042 0.29775
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7667 on 2144 degrees of freedom
## Multiple R-squared: 0.02321, Adjusted R-squared: 0.01957
## F-statistic: 6.369 on 8 and 2144 DF, p-value: 3.381e-08##
## Call:
## lm(formula = TARGET_AMT ~ HOME_VAL + MSTATUS + SEX + BLUEBOOK +
## REVOKED + MVR_PTS + CAR_AGE, data = mlr_crash_transf)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7364 -3150 -1572 412 100285
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -7400.44 2375.76 -3.115 0.00186 **
## HOME_VAL 57.02 34.32 1.661 0.09682 .
## MSTATUSYes -914.64 405.32 -2.257 0.02413 *
## SEXM 637.15 333.97 1.908 0.05655 .
## BLUEBOOK 1395.31 254.57 5.481 4.73e-08 ***
## REVOKEDYes -677.87 409.37 -1.656 0.09790 .
## MVR_PTS 130.71 64.27 2.034 0.04209 *
## CAR_AGE -227.51 208.34 -1.092 0.27495
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7667 on 2145 degrees of freedom
## Multiple R-squared: 0.02284, Adjusted R-squared: 0.01966
## F-statistic: 7.164 on 7 and 2145 DF, p-value: 1.71e-08##
## Call:
## lm(formula = TARGET_AMT ~ HOME_VAL + MSTATUS + SEX + BLUEBOOK +
## REVOKED + MVR_PTS, data = mlr_crash_transf)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7435 -3176 -1595 386 100375
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -7489.85 2374.46 -3.154 0.00163 **
## HOME_VAL 55.56 34.30 1.620 0.10540
## MSTATUSYes -887.80 404.59 -2.194 0.02832 *
## SEXM 653.55 333.65 1.959 0.05026 .
## BLUEBOOK 1358.16 252.30 5.383 8.12e-08 ***
## REVOKEDYes -682.24 409.37 -1.667 0.09575 .
## MVR_PTS 133.92 64.20 2.086 0.03711 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7667 on 2146 degrees of freedom
## Multiple R-squared: 0.0223, Adjusted R-squared: 0.01957
## F-statistic: 8.158 on 6 and 2146 DF, p-value: 9.631e-09##
## Call:
## lm(formula = TARGET_AMT ~ MSTATUS + SEX + BLUEBOOK + REVOKED +
## MVR_PTS, data = mlr_crash_transf)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7042 -3176 -1561 401 100457
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -7646.12 2373.39 -3.222 0.00129 **
## MSTATUSYes -510.63 331.01 -1.543 0.12306
## SEXM 652.64 333.77 1.955 0.05067 .
## BLUEBOOK 1400.78 251.02 5.580 2.7e-08 ***
## REVOKEDYes -710.83 409.15 -1.737 0.08247 .
## MVR_PTS 128.56 64.14 2.004 0.04516 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7670 on 2147 degrees of freedom
## Multiple R-squared: 0.02111, Adjusted R-squared: 0.01883
## F-statistic: 9.258 on 5 and 2147 DF, p-value: 9.836e-09##
## Call:
## lm(formula = TARGET_AMT ~ SEX + BLUEBOOK + REVOKED + MVR_PTS,
## data = mlr_crash_transf)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7317 -3180 -1617 423 100195
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -8002.80 2362.86 -3.387 0.00072 ***
## SEXM 645.74 333.85 1.934 0.05322 .
## BLUEBOOK 1411.85 251.00 5.625 2.1e-08 ***
## REVOKEDYes -690.94 409.08 -1.689 0.09136 .
## MVR_PTS 129.43 64.16 2.017 0.04378 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7672 on 2148 degrees of freedom
## Multiple R-squared: 0.02002, Adjusted R-squared: 0.0182
## F-statistic: 10.97 on 4 and 2148 DF, p-value: 8.306e-09##
## Call:
## lm(formula = TARGET_AMT ~ SEX + BLUEBOOK + MVR_PTS, data = mlr_crash_transf)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7181 -3173 -1607 348 100329
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -8153.34 2362.20 -3.452 0.000568 ***
## SEXM 648.01 333.99 1.940 0.052483 .
## BLUEBOOK 1412.22 251.11 5.624 2.11e-08 ***
## MVR_PTS 131.00 64.18 2.041 0.041360 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7676 on 2149 degrees of freedom
## Multiple R-squared: 0.01872, Adjusted R-squared: 0.01735
## F-statistic: 13.66 on 3 and 2149 DF, p-value: 7.883e-09##
## Call:
## lm(formula = TARGET_AMT ~ BLUEBOOK + MVR_PTS, data = mlr_crash_transf)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7511 -3151 -1545 328 100673
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -8251.14 2363.18 -3.492 0.00049 ***
## BLUEBOOK 1453.68 250.36 5.806 7.33e-09 ***
## MVR_PTS 130.32 64.22 2.029 0.04256 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7681 on 2150 degrees of freedom
## Multiple R-squared: 0.017, Adjusted R-squared: 0.01609
## F-statistic: 18.59 on 2 and 2150 DF, p-value: 9.889e-09Model 4: Forward Elimination
Now let’s use forward addition to add of variables one at a time.
##
## Call:
## lm(formula = TARGET_AMT ~ BLUEBOOK + MVR_PTS + SEX, data = mlr_crash_transf)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7181 -3173 -1607 348 100329
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -8153.34 2362.20 -3.452 0.000568 ***
## BLUEBOOK 1412.22 251.11 5.624 2.11e-08 ***
## MVR_PTS 131.00 64.18 2.041 0.041360 *
## SEXM 648.01 333.99 1.940 0.052483 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7676 on 2149 degrees of freedom
## Multiple R-squared: 0.01872, Adjusted R-squared: 0.01735
## F-statistic: 13.66 on 3 and 2149 DF, p-value: 7.883e-09##
## Call:
## lm(formula = TARGET_AMT ~ BLUEBOOK + MVR_PTS + SEX + MSTATUS,
## data = mlr_crash_transf)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6912 -3152 -1537 329 100585
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -7813.51 2372.55 -3.293 0.00101 **
## BLUEBOOK 1401.56 251.14 5.581 2.7e-08 ***
## MVR_PTS 130.20 64.16 2.029 0.04256 *
## SEXM 654.74 333.93 1.961 0.05004 .
## MSTATUSYes -492.51 331.00 -1.488 0.13691
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7674 on 2148 degrees of freedom
## Multiple R-squared: 0.01973, Adjusted R-squared: 0.0179
## F-statistic: 10.81 on 4 and 2148 DF, p-value: 1.127e-08##
## Call:
## lm(formula = TARGET_AMT ~ BLUEBOOK + MVR_PTS + SEX + MSTATUS +
## HOME_VAL, data = mlr_crash_transf)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7317 -3147 -1567 342 100494
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -7643.27 2373.65 -3.220 0.0013 **
## BLUEBOOK 1357.01 252.40 5.376 8.43e-08 ***
## MVR_PTS 135.73 64.22 2.113 0.0347 *
## SEXM 655.60 333.78 1.964 0.0496 *
## MSTATUSYes -887.17 404.76 -2.192 0.0285 *
## HOME_VAL 58.03 34.28 1.693 0.0907 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7670 on 2147 degrees of freedom
## Multiple R-squared: 0.02104, Adjusted R-squared: 0.01876
## F-statistic: 9.227 on 5 and 2147 DF, p-value: 1.057e-08##
## Call:
## lm(formula = TARGET_AMT ~ BLUEBOOK + MVR_PTS + SEX + MSTATUS +
## HOME_VAL + REVOKED, data = mlr_crash_transf)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7435 -3176 -1595 386 100375
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -7489.85 2374.46 -3.154 0.00163 **
## BLUEBOOK 1358.16 252.30 5.383 8.12e-08 ***
## MVR_PTS 133.92 64.20 2.086 0.03711 *
## SEXM 653.55 333.65 1.959 0.05026 .
## MSTATUSYes -887.80 404.59 -2.194 0.02832 *
## HOME_VAL 55.56 34.30 1.620 0.10540
## REVOKEDYes -682.24 409.37 -1.667 0.09575 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7667 on 2146 degrees of freedom
## Multiple R-squared: 0.0223, Adjusted R-squared: 0.01957
## F-statistic: 8.158 on 6 and 2146 DF, p-value: 9.631e-09##
## Call:
## lm(formula = TARGET_AMT ~ BLUEBOOK + MVR_PTS + SEX + MSTATUS +
## HOME_VAL + REVOKED + CAR_AGE, data = mlr_crash_transf)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7364 -3150 -1572 412 100285
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -7400.44 2375.76 -3.115 0.00186 **
## BLUEBOOK 1395.31 254.57 5.481 4.73e-08 ***
## MVR_PTS 130.71 64.27 2.034 0.04209 *
## SEXM 637.15 333.97 1.908 0.05655 .
## MSTATUSYes -914.64 405.32 -2.257 0.02413 *
## HOME_VAL 57.02 34.32 1.661 0.09682 .
## REVOKEDYes -677.87 409.37 -1.656 0.09790 .
## CAR_AGE -227.51 208.34 -1.092 0.27495
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7667 on 2145 degrees of freedom
## Multiple R-squared: 0.02284, Adjusted R-squared: 0.01966
## F-statistic: 7.164 on 7 and 2145 DF, p-value: 1.71e-08Model 5: Picking the best model using Leaps
The function, regsubsets(), will go through iterations to find the best model using parameters = 1,2,3,4,… n. Here we see the model with 13 variables (represented by the red dot) had the lowest cp, which indicates the best model. The R^2 remains to be around 3.5% from about 13 variables and higher, which is extremely low.
Model 6:
Using the regsubsets function and our data that includes log transformations, we see it suggests a model with 7 variables is best look at the cp value.
Using the transformed variables, we will choose the model that has 7 parameters since the R^2 value doesn’t change by much as the number of parameters increases. This gives us the following equation:
## (Intercept) MSTATUSYes EDUCATIONPhD JOBDoctor JOBManager
## 4857.7855103 -866.2249453 2008.6181953 -3283.3214513 -1358.0216839
## JOBProfessional BLUEBOOK CAR_AGE
## 1083.6185705 0.1127877 -67.5694404##
## Call:
## lm(formula = TARGET_AMT ~ MSTATUS + JOB + BLUEBOOK + CAR_AGE +
## EDUCATION, data = mlr_crash_transf)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7308 -3123 -1531 374 100678
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -5467.5 2656.6 -2.058 0.0397 *
## MSTATUSYes -491.1 334.2 -1.470 0.1418
## JOBClerical -306.4 510.7 -0.600 0.5486
## JOBDoctor -2863.7 1806.9 -1.585 0.1131
## JOBHome Maker -710.4 681.5 -1.042 0.2973
## JOBLawyer -605.8 1087.2 -0.557 0.5774
## JOBManager -1531.3 845.0 -1.812 0.0701 .
## JOBOther Job -449.7 1104.0 -0.407 0.6838
## JOBProfessional 316.3 622.3 0.508 0.6112
## JOBStudent -279.7 573.6 -0.488 0.6258
## BLUEBOOK 1342.2 268.7 4.996 6.33e-07 ***
## CAR_AGE -439.1 261.4 -1.680 0.0932 .
## EDUCATIONHigh School -539.8 502.5 -1.074 0.2829
## EDUCATIONLess than High School -116.7 609.6 -0.191 0.8482
## EDUCATIONMasters 534.5 877.3 0.609 0.5424
## EDUCATIONPhD 1618.9 1080.7 1.498 0.1343
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7687 on 2137 degrees of freedom
## Multiple R-squared: 0.02142, Adjusted R-squared: 0.01455
## F-statistic: 3.118 on 15 and 2137 DF, p-value: 4.575e-05Model 7
For this model, we used the log transformation of the response variable and a combination of predictors. Here is the model that yielded the best results:
##
## Call:
## lm(formula = log(TARGET_AMT) ~ MSTATUS + SEX + BLUEBOOK + CLM_FREQ +
## MVR_PTS + EDUCATION, data = mlr_crash_transf)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.7062 -0.4084 0.0422 0.4048 3.2688
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.78059 0.25943 26.136 < 2e-16 ***
## MSTATUSYes -0.07614 0.03488 -2.183 0.0292 *
## SEXM 0.05556 0.03503 1.586 0.1128
## BLUEBOOK 0.15326 0.02712 5.652 1.8e-08 ***
## CLM_FREQ -0.02297 0.01457 -1.577 0.1150
## MVR_PTS 0.01766 0.00705 2.505 0.0123 *
## EDUCATIONHigh School 0.06214 0.04575 1.358 0.1745
## EDUCATIONLess than High School 0.06322 0.05455 1.159 0.2466
## EDUCATIONMasters 0.08379 0.05693 1.472 0.1412
## EDUCATIONPhD 0.13885 0.08042 1.726 0.0844 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.804 on 2143 degrees of freedom
## Multiple R-squared: 0.0251, Adjusted R-squared: 0.02101
## F-statistic: 6.131 on 9 and 2143 DF, p-value: 1.473e-08Select Models & Prediction
Binary Logistic Regression
Based on the peformance diagnostics, model 4 or our binned model performs the best. AIC is 5816 and here are the other performance diagnostics:
## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 880 195
## 1 85 134
##
## Accuracy : 0.7836
## 95% CI : (0.7602, 0.8058)
## No Information Rate : 0.7457
## P-Value [Acc > NIR] : 0.0008298
##
## Kappa : 0.3587
##
## Mcnemar's Test P-Value : 7.318e-11
##
## Sensitivity : 0.9119
## Specificity : 0.4073
## Pos Pred Value : 0.8186
## Neg Pred Value : 0.6119
## Prevalence : 0.7457
## Detection Rate : 0.6801
## Detection Prevalence : 0.8308
## Balanced Accuracy : 0.6596
##
## 'Positive' Class : 0
## 
## Multiple Linear Regression
We will look at the diagnostic plot for the two models that had the highest adjusted r^2. Particularly model 1(with all variables minus TARGET_FLAG) and model 7 (log of response variable and a combination of predictors).
Model 1
Model 1 had an adjusted r^2 of 0.02145 and is significant. Here is the diagnostic plot for model 1
The density plot seems skewed and the qq plot deviates quite a bit.
Model 7
Model 7 had an adjusted r^2 of 0.02158 and is significant
The density and qqplot for model 7 seem somewhat normally distributed. The residual plot indicates homoscedasticity.
Prediction
## predicted_flag_bin
## 0 1
## 5337 1111## predicted_amt2
## 0 236.563937331378 236.583059129324 236.586911059253
## 7050 1 1 1
## 236.588374348008 236.618567800217 236.639886586829 236.650517024196
## 1 1 1 1
## 236.666228109109 236.680518823897 236.693942533297 236.694517055668
## 1 1 1 1
## 236.709888189348 236.71217556486 236.73197315084 236.733494351473
## 1 1 1 1
## 236.739001222665 236.746711192303 236.768811369856 236.782809601628
## 1 1 1 1
## 236.786029097308 236.793057169133 236.795152892136 236.813629150445
## 1 1 1 1
## 236.815397804792 236.853934318856 236.859249537539 279.623178522203
## 1 1 1 1
## 305.746405082491 324.062675345335 342.466540605108 365.482545811332
## 1 1 1 1
## 380.696781460324 386.850134888 416.101141301053 417.654884091719
## 1 1 1 1
## 428.276728495385 454.327928747418 498.729564409365 532.402168591273
## 1 1 1 1
## 549.358172460297 552.447608109474 561.498115567589 564.841591548708
## 1 1 1 1
## 581.662040648804 589.206087835678 593.797036191213 604.602223795272
## 1 1 1 1
## 612.095641399929 616.770647501632 619.976025006175 621.326527968014
## 1 1 1 1
## 627.498811976283 635.087741416078 635.097988983583 635.128373653145
## 1 1 1 1
## 638.214441507918 650.492859416711 650.592606486795 665.828997663872
## 1 1 1 1
## 665.858552136897 665.859632555789 666.005199885929 668.878874949939
## 1 1 1 1
## 672.013618417714 679.506844369862 696.418555724399 696.487285255517
## 1 1 1 1
## 696.510450635901 696.521528399944 696.56621943551 711.698116301255
## 1 1 1 1
## 711.767478701776 711.773049594627 711.829819140254 711.836399885403
## 1 1 1 1
## 711.846014360691 711.857234536491 713.396267794833 717.881088658769
## 1 1 1 1
## 727.098551517454 727.187035715922 727.243678065853 734.899133938319
## 1 1 1 1
## 739.413558516032 740.93791775457 742.556011953446 742.561518824638
## 1 1 1 1
## 757.78595868735 757.791082253525 757.793668656989 757.914883470377
## 1 2 1 1
## 762.375507775788 765.448741659593 766.98923820669 770.132090165183
## 1 1 1 1
## 773.106592718168 773.140196883411 773.223174210687 776.218177350495
## 1 1 1 1
## 776.310321826384 782.380506274276 788.480884174377 788.53254536989
## 1 1 1 1
## 788.543360464157 791.423245850874 793.193303017467 803.69298074658
## 1 1 1 1
## 803.705324037088 803.772596824387 803.834440472624 803.896398041239
## 1 1 1 1
## 812.866656987298 812.988745351009 814.48134047314 816.065198072525
## 1 1 1 1
## 819.059562233149 819.11912505081 819.122152236013 819.150632835081
## 1 1 1 1
## 819.173606562957 819.184628525794 819.238733728532 823.848861793891
## 1 1 1 1
## 825.179311495583 829.876019253761 834.394194495739 834.399509714423
## 1 1 1 1
## 834.404882844985 834.481023752944 834.492734609204 834.499762681029
## 1 1 1 1
## 835.973875207211 839.082283697642 843.681908521329 845.110015679882
## 1 1 1 1
## 849.771464331554 849.820189843277 851.348932838298 854.421150760023
## 1 1 1 1
## 855.917981339914 858.965512680623 862.135445971087 864.976980158608
## 1 1 1 1
## 865.10127205592 865.115263742756 865.121467727824 865.121652384724
## 1 1 1 1
## 865.131209398807 865.131273855621 868.140503253403 868.182848343612
## 1 1 1 1
## 877.41811866818 880.435073686818 880.454238180581 880.537215507857
## 1 1 1 1
## 885.004761167618 885.05494342316 886.53773896243 889.759126579838
## 1 1 1 1
## 895.68736105638 895.703306712431 895.713995061676 895.731653570868
## 1 1 1 1
## 895.735320393224 895.743364427128 895.744870411699 895.764241774032
## 1 1 1 1
## 895.808683245212 895.811461301184 895.836530752063 897.290000279666
## 1 1 1 1
## 898.848297747712 898.867669110045 901.718626120345 903.305070123194
## 1 1 1 1
## 903.364818048427 903.481399540946 910.88950908903 911.098235057438
## 1 1 2 1
## 911.104822347522 911.106328332093 911.157797875098 914.191905506406
## 1 1 1 1
## 915.694563088469 918.713549373296 918.717216195652 924.867094453481
## 1 1 1 1
## 926.250775356916 926.286284027808 926.307602814421 926.418869088256
## 1 1 1 1
## 926.446028359652 926.455251309471 926.469002087528 926.479746237979
## 2 1 1 1
## 926.486333528063 926.501590290692 926.505640433583 938.632159831474
## 1 1 1 1
## 941.650136699158 941.659893586203 953.97557593766 957.005640421685
## 1 1 1 1
## 957.051652334249 957.106084605644 957.123302333096 957.202470426259
## 1 1 1 1
## 958.56120907451 959.966400417066 963.199626086428 967.824683845759
## 1 1 1 1
## 972.301396218978 972.418616690681 972.45247042031 976.985526115508
## 1 1 1 1
## 984.687037254324 986.274874232725 987.592475776771 987.729438033248
## 1 1 1 1
## 987.729636246211 987.737595780236 987.776593807652 987.780700707683
## 1 1 1 1
## 987.783543235987 987.783734888496 989.143994737379 989.178679321514
## 1 1 1 1
## 989.291643232429 990.720888721753 992.245964894418 995.38949918588
## 1 1 1 1
## 999.937037248375 1002.90734726223 1003.01348996989 1003.08076275719
## 1 1 1 1
## 1003.11367802901 1003.16905530315 1004.55140011352 1006.23847995284
## 1 1 1 1
## 1009.21537725678 1010.73090341097 1013.75101935544 1018.28222889203
## 1 1 1 1
## 1018.31627383901 1020.02651905871 1021.59551142094 1023.03722739646
## 1 1 1 1
## 1024.39001773381 1024.4477339577 1026.144555468 1029.0835493501
## 1 1 1 1
## 1029.14886816818 1032.07259829204 1032.08659652381 1033.60583219617
## 1 1 1 1
## 1033.66412294243 1033.67070368758 1036.75355204667 1036.76589533718
## 1 1 1 1
## 1046.01702681792 1047.37557381366 1047.44108428426 1047.49342737758
## 1 1 1 1
## 1049.0007026293 1049.03785406294 1053.6050681493 1053.62551993052
## 1 1 1 1
## 1056.6743656033 1064.25817213488 1064.28343323827 1075.16461933853
## 1 1 1 1
## 1076.67120635479 1079.62265724048 1079.68367680196 1082.67018858119
## 1 1 1 1
## 1084.31292010481 1085.64026468188 1085.67596457012 1088.9081742774
## 1 1 1 1
## 1090.19780008952 1090.39696082339 1094.90899021499 1095.09108217811
## 1 1 1 1
## 1099.69145335642 1101.081715005 1107.27697274115 1110.23557844368
## 1 1 1 1
## 1110.26659620546 1110.344557342 1111.74792845597 1114.93355172832
## 1 1 1 1
## 1120.90818098729 1122.48506842673 1122.52589231631 1124.0817166433
## 1 1 1 1
## 1125.63152275077 1125.64772451614 1127.22797974998 1128.59778961734
## 1 1 1 1
## 1133.28221854182 1133.33399993742 1134.87899395409 1136.41101435667
## 1 1 1 1
## 1137.88696693168 1137.90589051667 1139.38001003846 1142.57031543727
## 1 1 1 1
## 1147.06214915697 1147.09335857126 1147.14639855565 1148.65468976945
## 1 1 1 1
## 1150.24963423915 1156.22348210718 1156.26152794079 1160.83633898776
## 1 1 1 1
## 1170.03678231644 1171.67887486088 1171.72620810111 1174.75330287666
## 1 1 1 1
## 1180.78215797361 1186.92304091508 1186.94785469179 1190.1092387098
## 1 1 1 1
## 1191.57437573988 1196.22045391584 1199.22323841977 1202.23406047061
## 1 1 1 1
## 1203.72322988646 1203.77387511989 1211.4651386912 1211.49234721887
## 1 1 1 1
## 1214.55038180125 1217.52196388651 1217.5342427202 1217.68512526903
## 1 1 1 1
## 1219.0521640605 1220.71772691576 1225.27615152495 1225.2963964376
## 1 1 1 1
## 1226.7653209408 1228.32076239793 1232.79658600476 1235.9608904905
## 1 1 1 1
## 1237.37139705174 1242.09366494125 1243.60197180627 1245.24310418983
## 1 1 1 1
## 1246.68691588836 1246.71354989366 1246.74734571141 1249.87620598306
## 1 1 1 1
## 1252.99710017576 1254.31988871341 1255.91994153323 1262.07608823294
## 1 1 1 1
## 1269.75651449832 1271.15848700316 1272.66488870455 1272.82690655788
## 1 1 1 1
## 1274.26240436166 1274.35874094153 1277.38842212054 1280.36127627719
## 1 1 1 1
## 1280.36531942448 1283.46417789643 1289.58557555519 1291.08543986522
## 1 1 1 1
## 1295.79038330981 1295.81765629429 1297.21488810283 1297.30239925784
## 1 1 1 1
## 1301.82330331504 1301.89614088541 1303.42214852028 1303.45746553866
## 1 2 1 1
## 1303.48912227962 1306.50133660195 1311.00487463297 1311.1270274535
## 1 1 1 1
## 1311.20829192763 1314.11607639544 1314.18139521352 1320.27829794378
## 1 1 1 1
## 1321.78177983541 1326.47931168034 1327.90684431653 1327.98190480559
## 1 1 1 1
## 1328.06683610208 1329.40031298898 1331.06031149632 1331.07538360205
## 1 1 1 1
## 1334.06701894746 1340.20993359027 1341.61082567623 1343.19000703611
## 1 1 1 1
## 1344.89873972631 1349.58740345058 1350.8606428249 1350.97853864949
## 1 1 1 1
## 1350.99166333093 1351.05467955745 1353.8956392226 1353.99246582495
## 1 1 1 1
## 1355.6348058231 1357.12418210752 1358.49571137296 1358.49956330289
## 1 1 1 1
## 1360.06893853498 1361.69367793581 1361.71220999533 1363.21100910253
## 1 1 1 1
## 1364.71950718489 1366.21760284058 1370.86773704639 1372.37765727142
## 1 1 1 1
## 1373.78615195157 1375.42152178977 1376.94880149604 1376.9513878995
## 1 1 1 1
## 1386.25822372304 1387.72183955249 1393.89582986896 1396.93980830769
## 1 1 1 1
## 1406.07892715997 1406.10873730716 1409.14729315177 1412.27443402535
## 1 1 1 1
## 1412.33399684301 1413.78513564131 1416.88734014668 1416.89538418058
## 1 1 1 1
## 1417.04031907647 1418.4084805475 1419.95892563415 1421.43487820917
## 1 1 1 1
## 1422.99620940736 1426.04316622569 1426.04329342139 1426.20006007769
## 1 1 1 1
## 1427.49608716096 1428.98747532647 1430.60215881231 1430.61006043446
## 1 1 1 1
## 1433.73974501569 1436.73400180087 1436.77253831493 1438.31455606266
## 1 1 1 1
## 1441.22949579799 1441.28247132556 1441.53075565708 1442.88417908665
## 1 1 1 1
## 1444.27171192001 1446.00493086759 1447.48183666581 1450.53652327403
## 1 2 1 1
## 1456.61905101243 1458.2436053057 1459.76448937439 1462.73880027487
## 1 1 1 1
## 1469.04683026942 1470.47196815465 1478.16645056367 1479.84139398105
## 1 1 1 1
## 1481.19373699172 1484.18810115235 1484.2374164025 1484.39746609994
## 1 1 1 1
## 1488.86310725405 1491.84210028099 1495.08328548438 1496.58056339095
## 1 1 1 1
## 1496.60171125666 1498.08044291704 1499.55366667684 1501.12064715797
## 1 1 1 1
## 1501.17855503437 1501.21366518418 1508.8468448778 1510.45430863931
## 1 1 1 1
## 1511.98114056823 1513.34974981661 1513.38506683499 1514.8240539953
## 1 1 1 1
## 1514.8812708676 1524.06044743458 1527.15544743167 1531.84639918942
## 1 1 1 1
## 1533.42025878569 1536.33062965696 1536.33994576226 1537.86424054399
## 1 1 1 1
## 1537.92272294275 1539.49322128955 1548.57773143399 1548.63202129363
## 1 1 1 1
## 1550.16368475638 1553.23893052127 1554.75810173682 1556.34113502664
## 1 1 1 1
## 1557.80050951136 1562.29551937295 1564.01474008876 1573.03265934371
## 1 1 1 1
## 1576.14184922508 1576.28252756018 1577.78151831989 1579.32196562623
## 1 1 1 1
## 1582.2669137062 1583.86311459609 1588.49835546611 1589.9548094831
## 1 1 1 1
## 1590.02802992333 1591.51044259274 1594.58810292884 1594.68829098796
## 1 1 1 1
## 1597.6869614008 1602.39108010067 1609.93702590622 1611.42134264613
## 1 1 1 1
## 1611.54133528683 1617.65708366265 1617.69000593007 1623.78614903038
## 1 1 1 1
## 1625.18683424776 1628.31461410053 1631.39911740088 1632.81785964854
## 1 1 1 1
## 1632.87468710604 1632.88000232472 1638.98063589899 1639.05912275231
## 1 1 1 1
## 1639.06867277078 1652.73993873163 1654.3548785496 1658.95588216217
## 1 1 1 1
## 1662.09822888211 1663.57492781175 1666.52944112625 1666.58500305729
## 1 1 1 1
## 1666.62353957135 1666.66177705746 1668.15676693055 1669.69486872669
## 1 1 1 1
## 1671.23000081435 1674.24387007794 1674.27588375874 1675.77544904081
## 1 1 1 1
## 1675.79266022333 1678.88874063931 1682.02304332535 1685.08183753767
## 1 1 1 1
## 1686.53024752076 1694.18360767022 1695.76234170343 1695.77341946748
## 1 1 1 1
## 1701.82937111246 1707.9539882669 1708.09772903082 1708.13335141479
## 1 1 1 1
## 1708.17929887054 1711.06879239491 1712.56138751704 1714.05481349368
## 1 1 1 1
## 1717.30013499983 1718.7281001973 1723.31784093825 1723.33037588127
## 1 1 1 1
## 1726.48734763365 1727.94581916531 1729.38899842959 1729.42266050671
## 1 1 1 1
## 1730.97164841439 1738.58988319798 1738.77290662329 1743.25241226854
## 1 1 1 1
## 1751.0240515476 1761.62739884332 1766.20513035802 1766.21284032766
## 1 1 1 1
## 1766.22664690693 1770.83632764561 1770.83891404907 1770.86891584877
## 1 1 1 1
## 1770.93550673826 1772.37000298945 1773.81811394459 1773.87488349021
## 1 1 1 1
## 1777.00620990731 1777.05777794734 1778.49765387403 1780.11906006611
## 1 2 1 1
## 1783.17322795317 1787.70467794786 1789.20980823582 1789.23449481684
## 1 1 1 1
## 1789.30619405644 1790.80088555954 1790.86215423473 1799.89778780008
## 1 1 1 1
## 1800.15373329564 1803.00316256037 1804.68956050187 1807.56671073573
## 1 1 1 1
## 1807.60963034831 1810.63082016674 1812.09449390806 1812.12595899652
## 1 1 1 1
## 1812.26936614684 1821.34981749278 1821.43006600483 1827.49785570177
## 1 1 1 1
## 1827.57765688715 1829.11575868329 1830.64835360824 1835.20336706924
## 1 1 1 1
## 1836.7966474914 1838.30050614312 1838.4375242008 1839.91182837949
## 1 1 1 1
## 1844.38752479063 1846.00430465745 1849.06676569213 1850.56272227102
## 1 1 1 1
## 1850.64790969235 1852.11702584805 1861.37898763912 1861.39683780082
## 1 1 1 1
## 1861.40455476607 1864.39955136094 1870.42076116788 1870.44051540008
## 1 1 1 1
## 1873.5989149287 1873.60170820073 1875.14658195938 1881.46955686396
## 1 1 1 1
## 1887.39671092161 1895.04734225585 1898.0397589922 1899.56494297546
## 1 1 1 1
## 1901.0539207388 1901.13006164676 1907.29747121809 1917.94505311642
## 1 1 1 1
## 1918.06885433327 1924.22601699506 1931.7068996567 1933.29158134284
## 1 1 1 1
## 1939.40216345666 1954.86455624147 1957.76330075636 1962.47879013844
## 1 1 1 1
## 1965.48822640479 1967.21070190598 1971.68499012551 1979.21962970567
## 1 1 1 1
## 1988.44202491317 1990.03822580306 1990.03930622196 1990.06867492944
## 1 1 1 1
## 1991.6061377464 2002.20689863866 2003.86557581833 2008.35659178891
## 1 1 1 1
## 2014.52702920341 2019.16323612127 2020.66695892168 2020.69411819308
## 1 1 1 1
## 2020.79505939514 2022.18208698995 2023.70019954761 2023.84228537026
## 1 1 1 1
## 2025.37488029521 2029.97398639773 2036.07012949804 2037.47038849177
## 1 1 1 1
## 2039.04234401755 2040.67644832929 2040.69410683848 2042.16411176056
## 1 1 1 1
## 2049.82816680421 2051.27988012488 2054.22151832232 2060.52272711362
## 1 1 1 1
## 2063.54728472645 2063.6219619105 2066.74671457806 2068.10867206402
## 1 1 1 1
## 2077.38930832636 2078.90044250362 2081.90329802482 2081.90348967733
## 1 1 1 1
## 2101.98556054598 2103.50752503356 2118.62747712987 2118.87410652013
## 1 1 1 1
## 2120.29113591464 2123.35632576454 2123.47038531041 2129.47184022718
## 1 1 1 1
## 2132.62120802334 2134.1275958707 2135.58753069112 2135.6673318765
## 1 1 1 1
## 2137.21910651127 2140.14209682544 2141.84537188519 2146.28956051206
## 1 1 1 1
## 2150.88791980928 2158.62777515168 2161.72417441587 2161.8573984555
## 1 1 1 1
## 2163.22253274133 2172.29127323101 2172.49835080309 2180.0623379877
## 1 1 1 1
## 2181.44601889113 2183.01943770566 2183.22924409296 2184.5696911398
## 1 1 1 1
## 2189.27664646548 2201.49886935102 2204.5838567869 2209.09823801083
## 1 1 1 1
## 2212.17240335683 2213.71348964236 2213.75992777857 2219.86532186941
## 1 1 1 1
## 2222.86690575436 2222.95202215843 2229.06626454967 2232.20056723571
## 1 1 1 1
## 2233.6693645432 2235.28068677958 2238.25480602755 2241.23873140331
## 1 1 1 1
## 2244.46664185399 2253.50626931035 2258.30633515976 2273.61702764664
## 1 1 1 1
## 2276.5396773516 2282.69342230475 2284.34942692108 2290.42391062558
## 1 1 1 1
## 2291.88607838233 2301.13202184008 2304.18897600357 2304.26784572675
## 1 1 1 1
## 2307.2092343598 2316.51905510788 2319.59638137971 2321.14240001407
## 1 1 1 1
## 2324.19860782293 2333.23671407865 2333.29398886283 2337.93727376676
## 1 1 1 1
## 2339.42791512697 2339.43031687354 2344.01639079213 2350.17734118042
## 1 1 1 1
## 2362.48879436566 2367.10423764971 2368.71708108671 2370.11431289524
## 1 1 1 1
## 2377.71031376065 2382.4033612414 2382.42886557154 2390.06315972426
## 1 1 1 1
## 2393.09455375641 2393.11089093793 2399.21278181821 2400.70455285358
## 1 1 1 1
## 2403.71310689849 2408.30923673208 2411.48525207407 2422.16196222178
## 1 1 1 1
## 2426.77632508693 2429.76556568138 2429.87531075458 2437.4525944529
## 1 1 1 1
## 2439.13327865464 2448.32201178502 2449.75549207414 2451.20423612149
## 1 1 1 1
## 2462.12512299662 2469.75278060299 2471.3736680739 2472.69222181176
## 1 1 1 1
## 2481.86462598107 2482.15739447959 2486.55284237867 2498.72702208545
## 1 1 1 1
## 2505.00119835038 2506.42891609413 2508.09062745462 2509.53645103424
## 1 1 1 1
## 2512.8609471785 2514.17853486851 2515.75770968346 2517.3268936982
## 1 1 1 1
## 2526.46948772032 2532.47557552281 2537.04886536916 2537.14359624851
## 1 1 1 1
## 2544.81076297723 2546.28707903702 2549.42474297252 2552.43676564234
## 1 1 1 1
## 2561.65550057242 2566.32207933521 2567.79549474751 2569.41379581496
## 1 1 1 1
## 2575.55739235559 2578.59170685547 2578.59258040579 2587.6987922067
## 1 1 1 1
## 2589.26948220601 2592.23663783896 2593.80082504806 2599.97556171917
## 1 1 1 1
## 2599.99594904358 2609.13765429932 2612.38429668247 2615.390378037
## 1 1 1 1
## 2620.05411472215 2626.08277816659 2643.01195637781 2655.20252906732
## 1 1 1 1
## 2656.64405339034 2658.35391574018 2659.67943309305 2664.37999278115
## 1 1 1 1
## 2667.54581846752 2675.12430278482 2676.60861130427 2678.09354592033
## 1 1 1 1
## 2678.10828396179 2678.12784697663 2681.14581795735 2682.8266938116
## 1 1 1 1
## 2690.43410650531 2691.9691748247 2699.59012423683 2701.05784112544
## 1 1 1 1
## 2707.27499217057 2708.8460802558 2716.42315708554 2716.4555048306
## 1 1 1 1
## 2725.62316830361 2725.76013056008 2733.30960733669 2742.56151366344
## 1 1 1 1
## 2760.97840454669 2767.09961709788 2771.64105855075 2773.15770781965
## 1 1 1 1
## 2774.72727470424 2776.35030125194 2777.75987635098 2788.51467483093
## 1 1 1 1
## 2797.72151379718 2803.73804081968 2806.80265614721 2809.97164275942
## 1 1 1 1
## 2817.52335111033 2823.93916657529 2826.78891571762 2839.12158122539
## 1 1 1 1
## 2842.18968454741 2843.80821221893 2858.98131076372 2880.50827374979
## 1 1 1 1
## 2883.50151523086 2883.5558050905 2884.93391510108 2886.60493557126
## 1 1 1 1
## 2888.05208047856 2889.60764913138 2891.20721781568 2895.62993869924
## 1 1 1 1
## 2897.32359928371 2898.86487722175 2900.41898258582 2903.54485793293
## 1 1 1 1
## 2906.69226445078 2912.68594597049 2915.78283525717 2917.22713763616
## 1 1 1 1
## 2917.33449617886 2920.44954121565 2923.35473927999 2926.46221630822
## 1 1 1 1
## 2932.46733150241 2937.22662926345 2941.80967599684 2948.00492673738
## 1 1 1 1
## 2951.07163778791 2955.59220823152 2955.63561852456 2958.70169714084
## 1 1 1 1
## 2958.72909732102 2964.76904539807 2964.79055583719 2984.76555253598
## 1 1 1 1
## 2989.31626674037 3004.63411615476 3016.79536939306 3023.0029634241
## 1 1 1 1
## 3039.72068730237 3042.93093924385 3046.03271118793 3047.6063861273
## 1 1 1 1
## 3050.50733417579 3053.50316162517 3056.81625293672 3064.29518162915
## 1 1 1 1
## 3064.39518503137 3065.88333848514 3067.51372671825 3069.12435276763
## 1 1 1 1
## 3073.67371669228 3081.22163102515 3081.30137429865 3085.80322057956
## 1 1 1 1
## 3088.87884964947 3092.06593621058 3093.56657536661 3096.40246027118
## 1 1 1 1
## 3102.76562008616 3111.88524038041 3114.97935161112 3130.2806142796
## 1 1 1 1
## 3133.29282860193 3137.95182459077 3160.99771788361 3174.80903608294
## 1 1 1 1
## 3180.8672687658 3194.67867146501 3199.34998989472 3205.31322817502
## 1 1 1 1
## 3213.0639056073 3217.64404708902 3226.84770991338 3240.73055740287
## 1 1 1 1
## 3243.73985825307 3249.76379621726 3251.31132083618 3255.89949113574
## 1 1 1 1
## 3266.54619948375 3274.32063203485 3277.41904318013 3283.5485981352
## 1 1 1 1
## 3285.01182454985 3288.19086707705 3292.76328337307 3305.08840927892
## 1 1 1 1
## 3305.12555215946 3306.59985633815 3317.24948515389 3331.00367053013
## 1 1 1 1
## 3335.67422841854 3337.16492557995 3338.70196217326 3341.89548706776
## 1 1 1 1
## 3366.30150479334 3380.08461155038 3403.1979627381 3409.20346779776
## 1 1 1 1
## 3409.24986258019 3426.08245675783 3429.18017734969 3430.70745705596
## 1 1 1 1
## 3436.71682881094 3442.97080285902 3445.98574599657 3447.69219719822
## 1 1 1 1
## 3449.13099270601 3452.11491808178 3458.25226794153 3464.4056213692
## 1 1 1 1
## 3464.46815557086 3468.97365390874 3472.25011343469 3473.63372332086
## 1 1 1 1
## 3481.29099120146 3482.7048655571 3484.38486152339 3489.01396942561
## 1 1 1 1
## 3490.45676582003 3498.09397344487 3498.214854194 3502.76846801648
## 1 1 1 1
## 3502.78322690758 3521.18461357449 3521.20245674058 3524.30960015522
## 1 1 1 1
## 3550.08860389005 3564.01732133102 3573.31200551656 3580.76567965053
## 1 1 1 1
## 3582.46390864838 3583.91549522403 3586.94795445901 3590.1975173099
## 1 1 1 1
## 3596.18523666467 3600.76959773013 3603.63581849866 3603.80055098053
## 1 1 1 1
## 3628.33201831929 3632.93643264489 3651.41220401283 3652.89289728416
## 1 1 1 1
## 3656.16042400983 3658.99694200662 3669.79353042398 3680.59182440091
## 1 1 1 1
## 3685.092206689 3686.67808250712 3689.64244486804 3700.32847112106
## 1 1 1 1
## 3712.58176100913 3720.3974518939 3764.9104252821 3781.77472545698
## 1 1 1 1
## 3786.27909411969 3787.90175809398 3790.79902513344 3793.85265308377
## 1 1 1 1
## 3830.72176053978 3835.19208382036 3841.50548694547 3844.40194408485
## 1 1 1 1
## 3856.81206483264 3881.21587902462 3881.29934703236 3901.12898261161
## 1 1 1 1
## 3919.56865557022 3927.31131837133 3928.84011857417 3936.41379125133
## 1 1 1 1
## 3951.79081195792 3965.46265244113 3991.71820864109 3994.67757566092
## 1 1 1 1
## 4034.39353252313 4042.25132527137 4048.40580181375 4056.19143369101
## 1 1 1 1
## 4058.94821404787 4072.92878390171 4075.94561069527 4080.34459730965
## 1 1 1 1
## 4086.70301642832 4123.44739120527 4146.34510206584 4163.17364444059
## 1 1 1 1
## 4181.56586395888 4186.23593116683 4189.28770385227 4210.70174562324
## 1 1 1 1
## 4247.68282198251 4253.82478443151 4256.72833409953 4265.98067319486
## 1 1 1 1
## 4284.24864351166 4284.3681454719 4311.90187859343 4311.9861209965
## 1 1 1 1
## 4324.13581233523 4338.07555173904 4354.92307395065 4370.19604767258
## 1 1 1 1
## 4389.949159474 4431.58358253917 4445.17383944665 4491.30104854334
## 1 1 1 1
## 4535.53864927245 4612.21010817592 4616.94523807711 4633.76447134217
## 1 1 1 1
## 4644.4754246343 4656.79129863827 4670.49953655875 4673.67541816012
## 1 1 1 1
## 4679.66516222063 4710.38434769361 4737.87264445433 4757.97637471879
## 1 1 1 1
## 4764.0976299658 4828.4676972326 4836.07642425837 4875.91984915979
## 1 1 1 1
## 4882.01383142232 4977.1085269479 5081.15205703001 5211.53770115873
## 1 1 1 1
## 5220.89997068822 5249.89471250412 5407.72535576869 5447.52350856724
## 1 1 1 1
## 5524.12232155285 5697.44338458309 5968.56129888332 5997.84034678921
## 1 1 1 1
## 6152.4616121133 6958.67142067345
## 1 1Code Appendix
knitr::opts_chunk$set(echo=FALSE, error=FALSE, warning=FALSE, message=FALSE)
# Libraries
library(stringr)
library(tidyr)
library(DataExplorer)
library(dplyr)
library(visdat)
library(pROC)
library(mice)
library(corrplot)
library(MASS)
library(caret)
library(e1071)
library(rbin)
library(GGally)
library(ggplot2)
library(readr)
library(reshape2)
library(purrr)
library(leaps)
set.seed(2012)
# training data
insurance <- read.csv('https://raw.githubusercontent.com/hillt5/DATA_621/master/HW4/insurance_training_data.csv', stringsAsFactors = FALSE)
# test data
insurance_test <- read.csv('https://raw.githubusercontent.com/hillt5/DATA_621/master/HW4/insurance_training_data.csv')
glimpse(insurance)
head(insurance)
summary(insurance)
insurance_fix <- dplyr::select(insurance, -INDEX)
insurance_fix$HOME_VAL <- substr(insurance_fix$HOME_VAL, 2, nchar(insurance_fix$HOME_VAL)) # remove the dollar sign
insurance_fix$HOME_VAL <- as.numeric(str_remove_all(insurance_fix$HOME_VAL, "[[:punct:]]")) # remove the comma and periods for money
insurance_fix$BLUEBOOK<- substr(insurance_fix$BLUEBOOK , 2, nchar(insurance_fix$BLUEBOOK ))
insurance_fix$BLUEBOOK<- as.numeric(str_remove_all(insurance_fix$BLUEBOOK,"[[:punct:]]"))
insurance_fix$INCOME <- substr(insurance_fix$INCOME, 2, nchar(insurance_fix$INCOME))
insurance_fix$INCOME <- as.numeric(str_remove_all(insurance_fix$INCOME, "[[:punct:]]"))
insurance_fix$OLDCLAIM <- substr(insurance_fix$OLDCLAIM, 2, nchar(insurance_fix$OLDCLAIM))
insurance_fix$OLDCLAIM <- as.numeric(str_remove_all(insurance_fix$OLDCLAIM, "[[:punct:]]"))
insurance_fix$MSTATUS = as.factor(str_remove(insurance_fix$MSTATUS, 'z_')) #several variables have a a recurring typo
insurance_fix$PARENT1 = as.factor(str_remove(insurance_fix$PARENT1, 'z_'))
insurance_fix$EDUCATION = str_replace(insurance_fix$EDUCATION, '<', 'Less than ') #change < to less than symbol to avoid confusion
insurance_fix$SEX= as.factor(str_remove(insurance_fix$SEX, 'z_'))
insurance_fix$EDUCATION = as.factor(str_remove(insurance_fix$EDUCATION, 'z_'))
insurance_fix$JOB[insurance_fix$JOB == ""] <- 'Other Job' #recode blank spaces as 'Other Job'
insurance_fix$JOB = as.factor(str_remove(insurance_fix$JOB, 'z_'))
insurance_fix$CAR_USE = as.factor(str_remove(insurance_fix$CAR_USE, 'z_'))
insurance_fix$CAR_TYPE = as.factor(str_remove(insurance_fix$CAR_TYPE, 'z_'))
insurance_fix$URBANICITY = as.factor(str_remove(insurance_fix$URBANICITY, 'z_'))
insurance_fix$REVOKED = as.factor(str_remove(insurance_fix$REVOKED, 'z_'))
insurance_fix$RED_CAR = as.factor(str_remove(insurance_fix$RED_CAR, 'z_'))
summary(insurance_fix)
insurance_fix$CAR_AGE[insurance_fix$CAR_AGE <1] <- 1
cat_cols = c()
j <- 1
for (i in 4:ncol(insurance_fix)) {
if (class((insurance_fix[,i])) == 'factor') {
print(names(insurance_fix[i]))
print(levels(insurance_fix[,i]))
cat_cols[j]=names(insurance_fix[i])
j <- j+1
}
}
ins_fact <- insurance_fix[cat_cols]
ins_factm <- melt(ins_fact, measure.vars = cat_cols, variable.name = 'metric', value.name = 'value')
ggplot(ins_factm, aes(x = value)) +
geom_bar() +
scale_fill_brewer(palette = "Set1") +
facet_wrap( ~ metric, nrow = 5L, scales = 'free') + coord_flip()
plot_histogram(insurance_fix, geom_histogram_args = list("fill" = "tomato4"))
plot_histogram(insurance_fix, scale_x = "log10", geom_histogram_args = list("fill" = "springgreen4"))
# check columns having missing values
insurance_fix %>% summarise_all(funs(sum(is.na(.)))) %>% select_if(~any(.)>0)
plot_missing(insurance_fix)
round(colSums(is.na(insurance_fix))/nrow(insurance_fix),3)
vis_dat(insurance_fix %>% dplyr:: select(YOJ, INCOME, HOME_VAL, CAR_AGE))
numer_data <- insurance_fix[,c('TARGET_AMT','AGE','YOJ','INCOME','HOME_VAL','TRAVTIME','BLUEBOOK','TIF','OLDCLAIM','CLM_FREQ','MVR_PTS','CAR_AGE')]
AGE_MEDIAN <- median(filter(insurance_fix,AGE > 0)$AGE)
INCOME_MEDIAN <- median(filter(insurance_fix,INCOME > 0)$INCOME)
YOJ_MEDIAN <- median(filter(insurance_fix,YOJ > 0)$YOJ)
HOME_VAL_MEDIAN <- median(filter(insurance_fix,HOME_VAL > 0)$HOME_VAL)
CAR_AGE_MEDIAN <- median(filter(insurance_fix,CAR_AGE > 0)$CAR_AGE)
numer_data <- numer_data %>% dplyr::mutate(AGE = replace_na(AGE,AGE_MEDIAN),
INCOME = replace_na(INCOME,INCOME_MEDIAN),
YOJ = replace_na(YOJ,YOJ_MEDIAN),
HOME_VAL = replace_na(HOME_VAL,HOME_VAL_MEDIAN),
CAR_AGE = replace_na(CAR_AGE,CAR_AGE_MEDIAN))
corrplot(cor(numer_data),type="upper")
mlr_crash <- subset(filter(insurance_fix,TARGET_FLAG==1),select = -c(TARGET_FLAG))
mlr_crash_fix_na <- mlr_crash
AGE_MEDIAN <- median(filter(mlr_crash_fix_na,AGE > 0)$AGE)
INCOME_MEDIAN <- median(filter(mlr_crash_fix_na,INCOME > 0)$INCOME)
YOJ_MEDIAN <- median(filter(mlr_crash_fix_na,YOJ > 0)$YOJ)
HOME_VAL_MEDIAN <- median(filter(mlr_crash_fix_na,HOME_VAL > 0)$HOME_VAL)
CAR_AGE_MEDIAN <- median(filter(mlr_crash_fix_na,CAR_AGE > 0)$CAR_AGE)
mlr_crash_fix_na <- mlr_crash_fix_na %>% dplyr::mutate(AGE = replace_na(AGE,AGE_MEDIAN),
INCOME = replace_na(INCOME,INCOME_MEDIAN),
YOJ = replace_na(YOJ,YOJ_MEDIAN),
HOME_VAL = replace_na(HOME_VAL,HOME_VAL_MEDIAN),
CAR_AGE = replace_na(CAR_AGE,CAR_AGE_MEDIAN))
mlr_crash_transf <- mlr_crash_fix_na
mlr_crash_transf$AGE <- log(mlr_crash_transf$AGE)
mlr_crash_transf$BLUEBOOK <- log(mlr_crash_transf$BLUEBOOK)
mlr_crash_transf$CAR_AGE <- log(mlr_crash_transf$CAR_AGE + 1)
mlr_crash_transf$HOME_VAL <- log(mlr_crash_transf$HOME_VAL + 1)
mlr_crash_transf$INCOME <- log(mlr_crash_transf$INCOME + 1)
mlr_crash_transf$OLDCLAIM <- log(mlr_crash_transf$OLDCLAIM + 1)
mlr_crash_transf$TRAVTIME <- log(mlr_crash_transf$TRAVTIME)
insurance_fix2 <- insurance_fix
insurance_fix2$HOME_VAL <-ifelse(insurance_fix2$HOME_VAL == 0, NA, insurance_fix2$HOME_VAL)
insurance_bins <- insurance_fix %>%
mutate(CAR_AGE_BIN=cut(CAR_AGE, breaks=c(-Inf, 1, 3, 12, Inf), labels=c("New","Like New","Average", 'Old'))) %>% #four level fator for car age
mutate(HOME_VAL_BIN=cut(HOME_VAL, breaks=c(-Inf, 0, 50000, 150000, 250000, Inf), labels=c("Zero", "$0-$50k", "$50k-$150k","$150k-$250k", 'Over $250k'))) %>% #bins for zero, plus four other price ranges
mutate(HAS_HOME_KIDS = as.factor(case_when(HOMEKIDS == 0 ~ 'No kids', HOMEKIDS > 0 ~ ('Has kids')))) %>% #binary variable for whether family has kids
mutate(HAS_KIDSDRIV = as.factor(case_when(KIDSDRIV == 0 ~ 'No kids driving', KIDSDRIV > 0 ~ 'Has kids driving'))) %>% #binary variable for whether family has kids driving
mutate(OLDCLAIM_BIN =cut(OLDCLAIM, breaks=c(-Inf, 0, 3000, 6000, 9000, Inf), labels=c("Zero","$0-$3k", "$3k-$6k", "$6k-$9k",'Over $9k'))) %>% #bins for zero, plus four other price ranges based on quartiles
mutate(TIF_BIN =cut(TIF, breaks=c(-Inf, 0, 1, 4, 7, Inf), labels=c("Zero","Less than 1 year", "1-4 years", "4-7 years",'Over 7 years'))) %>% #bins for zero, plus four other price ranges based on quartiles
mutate(YOJ_BIN =cut(YOJ, breaks=c(-Inf, 0, 10, 15, Inf), labels=c("Zero","Less than 10 years", 'Between 10-15 years', 'Over 15 years'))) %>% #bins for zero, plus three other categories based on quartiles
dplyr::select(-c(CAR_AGE, HOME_VAL, HOMEKIDS, KIDSDRIV, OLDCLAIM, TIF, YOJ)) #drop the binned features
summary(insurance_bins)
head(insurance_bins)
insurance_logistic_model <- glm(insurance_fix, family = 'binomial', formula = TARGET_FLAG~.-TARGET_AMT)
summary(insurance_logistic_model)
get_cv_performance <- function(data_frame, model, split = 0.8) { ### input is dataframe for partitioning, model as generated by 'glm' function, by default 5-fold cross-validation
n <- ncol(data_frame) #number of columns in original dataframe
train_control <- trainControl(method="repeatedcv", number=10, repeats=3)
trainIndex <- createDataPartition(data_frame[,n], p=split, list=FALSE)
data_train <- data_frame[trainIndex,]
data_test <- data_frame[-trainIndex,]
x_test <- data_test[,2:n] #explanatory variables
y_test <- data_test[,1] #response variable
predictions <- predict(model, x_test, type = 'response')
return(confusionMatrix(data = (as.factor(as.numeric(predictions>0.5))), reference = as.factor(y_test)))
return(plot(roc(y_test, predictions),print.auc=TRUE))
}
get_roc <- function(data_frame, model, split = 0.8) { ### input is dataframe for partitioning, model as generated by 'glm' function
n <- ncol(data_frame) #number of columns in original dataframe
train_control <- trainControl(method="repeatedcv", number=10, repeats=3)
trainIndex <- createDataPartition(data_frame[,n], p=split, list=FALSE)
data_train <- data_frame[trainIndex,]
data_test <- data_frame[-trainIndex,]
x_test <- data_test[,2:n] #explanatory variables
y_test <- data_test[,1] #response variable
predictions <- predict(model, x_test, type = 'response')
return(plot(roc(y_test, predictions),print.auc=TRUE))
}
get_cv_performance(insurance_fix, insurance_logistic_model)
get_roc(insurance_fix, insurance_logistic_model)
insurance_impute <- mice(insurance_fix, method = 'cart', m = 1)
imputed_lm <- glm.mids(data = insurance_impute, formula = TARGET_FLAG ~.-TARGET_AMT, family = 'binomial')
imputed_lm
get_cv_performance(insurance_fix, imputed_lm$analyses[[1]])
get_roc(insurance_fix, imputed_lm$analyses[[1]])
insurance_impute2 <- mice(insurance_fix2, method = 'cart', m = 1)
imputed_lm2 <- glm.mids(data = insurance_impute2, formula = TARGET_FLAG ~.-TARGET_AMT, family = 'binomial')
imputed_lm2
get_cv_performance(insurance_fix2, imputed_lm2$analyses[[1]])
get_roc(insurance_fix2, imputed_lm2$analyses[[1]])
binned_lm <- glm(data = insurance_bins, formula = TARGET_FLAG ~.-TARGET_AMT, family = 'binomial')
summary(binned_lm)
get_cv_performance(insurance_bins, binned_lm)
get_roc(insurance_bins, binned_lm)
insurance_binned_impute <- mice(insurance_bins, method = 'cart', m = 1)
binned_imputed_lm <- glm.mids(data = insurance_binned_impute, formula = TARGET_FLAG ~.-TARGET_AMT, family = 'binomial')
binned_imputed_lm
get_cv_performance(insurance_bins, binned_imputed_lm$analyses[[1]])
get_roc(insurance_bins, binned_imputed_lm$analyses[[1]])
mlr<- lm(TARGET_AMT ~ . ,data=mlr_crash)
summary(mlr)
mlr<- lm(TARGET_AMT ~ . ,data=mlr_crash_transf)
summary(mlr)
mlr1 <- lm(TARGET_AMT ~ . ,data=mlr_crash_transf)
summary(mlr1)
mlr2 <- update(mlr1,TARGET_AMT~. - OLDCLAIM)
summary(mlr2)
mlr3 <- update(mlr2,TARGET_AMT~. - YOJ)
summary(mlr3)
mlr4 <- update(mlr3,TARGET_AMT~. - URBANICITY)
summary(mlr4)
mlr5 <- update(mlr4,TARGET_AMT~. - TRAVTIME)
summary(mlr5)
mlr6 <- update(mlr5,TARGET_AMT~. - INCOME)
summary(mlr6)
mlr7 <- update(mlr6,TARGET_AMT~. - CLM_FREQ)
summary(mlr7)
mlr8 <- update(mlr7,TARGET_AMT~. - TIF)
summary(mlr8)
mlr9 <- update(mlr8,TARGET_AMT~. - RED_CAR)
summary(mlr9)
mlr10 <- update(mlr9,TARGET_AMT~. - PARENT1)
summary(mlr10)
mlr11 <- update(mlr10,TARGET_AMT~. - KIDSDRIV)
summary(mlr11)
mlr12 <- update(mlr11,TARGET_AMT~. - AGE)
summary(mlr12)
mlr13 <- update(mlr12,TARGET_AMT~. - CAR_USE)
summary(mlr13)
mlr14 <- update(mlr13,TARGET_AMT~. - JOB)
summary(mlr14)
mlr15 <- update(mlr14,TARGET_AMT~. - EDUCATION)
summary(mlr15)
mlr16 <- update(mlr15,TARGET_AMT~. - CAR_TYPE)
summary(mlr16)
mlr17 <- update(mlr16,TARGET_AMT~. - HOMEKIDS)
summary(mlr17)
mlr18 <- update(mlr17,TARGET_AMT~. - CAR_AGE)
summary(mlr18)
mlr19 <- update(mlr18,TARGET_AMT~. - HOME_VAL)
summary(mlr19)
mlr20 <- update(mlr19,TARGET_AMT~. - MSTATUS)
summary(mlr20)
mlr21 <- update(mlr20,TARGET_AMT~. - REVOKED)
summary(mlr21)
mlr22 <- update(mlr21,TARGET_AMT~. - SEX)
summary(mlr22)
mlr_fwd <- lm(TARGET_AMT ~ BLUEBOOK + MVR_PTS + SEX ,data= mlr_crash_transf)
summary(mlr_fwd)
mlr_fwd <- lm(TARGET_AMT ~ BLUEBOOK + MVR_PTS + SEX + MSTATUS ,data= mlr_crash_transf)
summary(mlr_fwd)
mlr_fwd <- lm(TARGET_AMT ~ BLUEBOOK + MVR_PTS + SEX + MSTATUS + HOME_VAL,data= mlr_crash_transf)
summary(mlr_fwd)
mlr_fwd <- lm(TARGET_AMT ~ BLUEBOOK + MVR_PTS + SEX + MSTATUS + HOME_VAL + REVOKED,data= mlr_crash_transf)
summary(mlr_fwd)
mlr_fwd <- lm(TARGET_AMT ~ BLUEBOOK + MVR_PTS + SEX + MSTATUS + HOME_VAL + REVOKED + CAR_AGE,data= mlr_crash_transf)
summary(mlr_fwd)
mlr_full <- regsubsets(TARGET_AMT ~ . ,data=mlr_crash, nvmax=NULL)
mlr_summary<- summary(mlr_full)
par(mfrow=c(2,2))
plot(mlr_summary$cp,xlab = "# Variables", ylab = "cp - estimate of prediction error")
points(13,mlr_summary$cp[13],pch=20,col="red")
plot(mlr_summary$rsq,xlab = "# Variables", ylab = "R^2")
mlr_full_transf <- regsubsets(TARGET_AMT ~ . ,data=mlr_crash_transf, nvmax=NULL)
mlr_summary_transf <- summary(mlr_full_transf)
par(mfrow=c(1,2))
plot(mlr_summary_transf$cp,xlab = "# Variables", ylab = "cp - estimate of prediction error")
points(7,mlr_summary_transf$cp[7],pch=20,col="red")
plot(mlr_summary_transf$rsq,xlab = "# Variables", ylab = "R^2")
coef(mlr_full,7)
model_6 <- lm(TARGET_AMT ~ MSTATUS +JOB+ BLUEBOOK + CAR_AGE+EDUCATION, data = mlr_crash_transf)
summary(model_6)
model_log <- lm(log(TARGET_AMT) ~ MSTATUS+SEX+ BLUEBOOK + CLM_FREQ + MVR_PTS+EDUCATION, data = mlr_crash_transf)
summary(model_log)
get_cv_performance(insurance_bins, binned_lm)
get_roc(insurance_bins, binned_lm)
res0 <- resid(mlr)
plot(density(res0))
qqnorm(res0)
qqline(res0)
ggplot(data = mlr, aes(x = .fitted, y = .resid)) +
geom_jitter() +
geom_hline(yintercept = 0, linetype = "dashed") +
xlab("Fitted values") +
ylab("Residuals")
res0 <- resid(model_log)
plot(density(res0))
qqnorm(res0)
qqline(res0)
ggplot(data = model_log, aes(x = .fitted, y = .resid)) +
geom_jitter() +
geom_hline(yintercept = 0, linetype = "dashed") +
xlab("Fitted values") +
ylab("Residuals")
insurance_fix3 <- dplyr::select(insurance_test, -INDEX)
insurance_fix3$HOME_VAL <- substr(insurance_fix3$HOME_VAL, 2, nchar(insurance_fix3$HOME_VAL)) # remove the dollar sign
insurance_fix3$HOME_VAL <- as.numeric(str_remove_all(insurance_fix3$HOME_VAL, "[[:punct:]]")) # remove the comma and periods for money
insurance_fix3$BLUEBOOK<- substr(insurance_fix3$BLUEBOOK , 2, nchar(insurance_fix3$BLUEBOOK ))
insurance_fix3$BLUEBOOK<- as.numeric(str_remove_all(insurance_fix3$BLUEBOOK,"[[:punct:]]"))
insurance_fix3$INCOME <- substr(insurance_fix3$INCOME, 2, nchar(insurance_fix3$INCOME))
insurance_fix3$INCOME <- as.numeric(str_remove_all(insurance_fix3$INCOME, "[[:punct:]]"))
insurance_fix3$OLDCLAIM <- substr(insurance_fix3$OLDCLAIM, 2, nchar(insurance_fix3$OLDCLAIM))
insurance_fix3$OLDCLAIM <- as.numeric(str_remove_all(insurance_fix3$OLDCLAIM, "[[:punct:]]"))
insurance_fix3$MSTATUS = as.factor(str_remove(insurance_fix3$MSTATUS, 'z_')) #several variables have a a recurring typo
insurance_fix3$PARENT1 = as.factor(str_remove(insurance_fix3$PARENT1, 'z_'))
insurance_fix3$EDUCATION = str_replace(insurance_fix3$EDUCATION, '<', 'Less than ') #change < to less than symbol to avoid confusion
insurance_fix3$SEX= as.factor(str_remove(insurance_fix3$SEX, 'z_'))
insurance_fix3$EDUCATION = as.factor(str_remove(insurance_fix3$EDUCATION, 'z_'))
insurance_fix3$JOB[insurance_fix3$JOB == ""] <- 'Other Job' #recode blank spaces as 'Other Job'
insurance_fix3$JOB = as.factor(str_remove(insurance_fix3$JOB, 'z_'))
insurance_fix3$CAR_USE = as.factor(str_remove(insurance_fix3$CAR_USE, 'z_'))
insurance_fix3$CAR_TYPE = as.factor(str_remove(insurance_fix3$CAR_TYPE, 'z_'))
insurance_fix3$URBANICITY = as.factor(str_remove(insurance_fix3$URBANICITY, 'z_'))
insurance_fix3$REVOKED = as.factor(str_remove(insurance_fix3$REVOKED, 'z_'))
insurance_fix3$RED_CAR = as.factor(str_remove(insurance_fix3$RED_CAR, 'z_'))
insurance_fix3$CAR_AGE[insurance_fix3$CAR_AGE <1] <- 1
insurance_bins2 <- insurance_fix3 %>%
mutate(CAR_AGE_BIN=cut(CAR_AGE, breaks=c(-Inf, 1, 3, 12, Inf), labels=c("New","Like New","Average", 'Old'))) %>% #four level fator for car age
mutate(HOME_VAL_BIN=cut(HOME_VAL, breaks=c(-Inf, 0, 50000, 150000, 250000, Inf), labels=c("Zero", "$0-$50k", "$50k-$150k","$150k-$250k", 'Over $250k'))) %>% #bins for zero, plus four other price ranges
mutate(HAS_HOME_KIDS = as.factor(case_when(HOMEKIDS == 0 ~ 'No kids', HOMEKIDS > 0 ~ ('Has kids')))) %>% #binary variable for whether family has kids
mutate(HAS_KIDSDRIV = as.factor(case_when(KIDSDRIV == 0 ~ 'No kids driving', KIDSDRIV > 0 ~ 'Has kids driving'))) %>% #binary variable for whether family has kids driving
mutate(OLDCLAIM_BIN =cut(OLDCLAIM, breaks=c(-Inf, 0, 3000, 6000, 9000, Inf), labels=c("Zero","$0-$3k", "$3k-$6k", "$6k-$9k",'Over $9k'))) %>% #bins for zero, plus four other price ranges based on quartiles
mutate(TIF_BIN =cut(TIF, breaks=c(-Inf, 0, 1, 4, 7, Inf), labels=c("Zero","Less than 1 year", "1-4 years", "4-7 years",'Over 7 years'))) %>% #bins for zero, plus four other price ranges based on quartiles
mutate(YOJ_BIN =cut(YOJ, breaks=c(-Inf, 0, 10, 15, Inf), labels=c("Zero","Less than 10 years", 'Between 10-15 years', 'Over 15 years'))) %>% #bins for zero, plus three other categories based on quartiles
dplyr::select(-c(CAR_AGE, HOME_VAL, HOMEKIDS, KIDSDRIV, OLDCLAIM, TIF, YOJ)) #drop the binned features
mlr_crash2 <- subset(filter(insurance_fix2,TARGET_FLAG==1),select = -c(TARGET_FLAG))
mlr_crash_fix_na2 <- mlr_crash2
AGE_MEDIAN <- median(filter(mlr_crash_fix_na2,AGE > 0)$AGE)
INCOME_MEDIAN <- median(filter(mlr_crash_fix_na2,INCOME > 0)$INCOME)
YOJ_MEDIAN <- median(filter(mlr_crash_fix_na2,YOJ > 0)$YOJ)
HOME_VAL_MEDIAN <- median(filter(mlr_crash_fix_na2,HOME_VAL > 0)$HOME_VAL)
CAR_AGE_MEDIAN <- median(filter(mlr_crash_fix_na2,CAR_AGE > 0)$CAR_AGE)
mlr_crash_fix_na2 <- mlr_crash_fix_na2 %>% dplyr::mutate(AGE = replace_na(AGE,AGE_MEDIAN),
INCOME = replace_na(INCOME,INCOME_MEDIAN),
YOJ = replace_na(YOJ,YOJ_MEDIAN),
HOME_VAL = replace_na(HOME_VAL,HOME_VAL_MEDIAN),
CAR_AGE = replace_na(CAR_AGE,CAR_AGE_MEDIAN))
mlr_crash_transf2 <- mlr_crash_fix_na2
mlr_crash_transf2$AGE <- log(mlr_crash_transf2$AGE)
mlr_crash_transf2$BLUEBOOK <- log(mlr_crash_transf2$BLUEBOOK)
mlr_crash_transf2$CAR_AGE <- log(mlr_crash_transf2$CAR_AGE + 1)
mlr_crash_transf2$HOME_VAL <- log(mlr_crash_transf2$HOME_VAL + 1)
mlr_crash_transf2$INCOME <- log(mlr_crash_transf2$INCOME + 1)
mlr_crash_transf2$OLDCLAIM <- log(mlr_crash_transf2$OLDCLAIM + 1)
mlr_crash_transf2$TRAVTIME <- log(mlr_crash_transf2$TRAVTIME)
predicted_amt <- predict(model_log, insurance_bins2)
predicted_amt2 = predicted_amt
predicted_amt2[] = 0
predicted_flag = predict(binned_lm, insurance_bins2, type = "response")
predicted_flag_bin = ifelse(predicted_flag > 0.5, 1, 0)
for (i in 1:length(predicted_amt)) {
if(predicted_flag_bin[i] == 0 | is.na(predicted_flag_bin[i])) {
predicted_amt2[i] = 0
} else {
predicted_amt2[i] = predicted_amt[i]
}
}
table(predicted_flag_bin)
table(predicted_amt2)