Download Fraud1.csv here
fraud <- read.csv("Fraud1.csv")
str(fraud)
## 'data.frame': 5175 obs. of 33 variables:
## $ Month : num 7 7 7 11 11 11 11 11 12 12 ...
## $ WeekOfMonth : num 1 3 4 2 2 3 4 5 1 1 ...
## $ DayOfWeek : num 6 7 6 4 5 2 4 1 5 1 ...
## $ Make : num 7 7 7 7 18 3 1 10 7 18 ...
## $ AccidentArea : num 2 1 2 2 2 2 1 2 1 1 ...
## $ DayOfWeekClaimed : num 2 3 3 5 2 3 2 3 5 2 ...
## $ MonthClaimed : num 9 1 8 1 1 1 1 12 12 5 ...
## $ WeekOfMonthClaimed : num 4 4 2 3 1 2 2 1 3 3 ...
## $ Sex : num 1 1 1 1 1 1 1 1 1 1 ...
## $ MaritalStatus : num 1 2 2 1 2 2 2 1 1 2 ...
## $ Age : num 0 21 50 34 38 31 56 68 0 39 ...
## $ Fault : num 1 1 1 1 1 1 1 1 1 1 ...
## $ PolicyType : num 1 5 2 5 2 7 7 1 1 1 ...
## $ VehicleCategory : num 1 2 1 2 1 3 3 1 1 1 ...
## $ VehiclePrice : num 6 6 1 6 1 6 6 1 6 2 ...
## $ FraudFound : num 1 1 1 1 1 1 1 1 1 1 ...
## $ PolicyNumber : num 29 53 54 95 97 101 114 119 120 148 ...
## $ RepNumber : num 9 4 13 7 7 2 10 9 7 1 ...
## $ Deductible : num 400 400 400 400 400 400 400 400 400 400 ...
## $ DriverRating : num 1 4 1 3 2 1 2 3 3 3 ...
## $ Days.Policy.Accident: num 5 5 5 5 5 5 5 5 5 5 ...
## $ Days.Policy.Claim : num 5 5 5 5 5 5 5 5 5 5 ...
## $ PastNumberOfClaims : num 0 0 0 0 1 3 0 2 0 0 ...
## $ AgeOfVehicle : num 1 4 8 7 7 7 8 5 1 8 ...
## $ AgeOfPolicyHolder : num 1 4 7 5 6 5 8 9 1 6 ...
## $ PoliceReportFiled : num 0 0 0 0 0 0 0 0 0 0 ...
## $ WitnessPresent : num 0 0 0 0 0 0 0 0 0 0 ...
## $ AgentType : num 1 1 1 1 1 1 1 1 1 1 ...
## $ NumberOfSuppliments : num 0 2 2 2 0 3 0 0 0 3 ...
## $ AddressChange.Claim : num 0 0 0 0 0 0 0 0 0 1 ...
## $ NumberOfCars : num 1 1 1 1 1 1 1 1 1 2 ...
## $ Year : num 0 0 0 0 0 0 0 0 0 0 ...
## $ BasePolicy : num 1 2 2 2 2 1 1 1 1 1 ...
table(fraud$FraudFound)
##
## 0 1
## 4252 923
fraud$PolicyNumber <- NULL
fit <- glm(FraudFound ~ ., family = "binomial", data = fraud)
summary(fit)
##
## Call:
## glm(formula = FraudFound ~ ., family = "binomial", data = fraud)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.5295 -0.7575 -0.2523 -0.1849 3.4550
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.6798679 1.8734010 0.363 0.716675
## Month -0.0186249 0.0190395 -0.978 0.327964
## WeekOfMonth -0.0355307 0.0322003 -1.103 0.269842
## DayOfWeek 0.0092370 0.0202374 0.456 0.648078
## Make -0.0080926 0.0078994 -1.024 0.305620
## AccidentArea -0.1350649 0.1173466 -1.151 0.249736
## DayOfWeekClaimed 0.0181823 0.0278706 0.652 0.514156
## MonthClaimed -0.0158506 0.0193188 -0.820 0.411946
## WeekOfMonthClaimed 0.0303371 0.0333776 0.909 0.363400
## Sex 0.2048348 0.1247042 1.643 0.100473
## MaritalStatus 0.0734411 0.0952873 0.771 0.440865
## Age -0.0105968 0.0130398 -0.813 0.416416
## Fault 2.6445394 0.1744383 15.160 < 2e-16 ***
## PolicyType 0.6570563 0.0795770 8.257 < 2e-16 ***
## VehicleCategory -2.0707754 0.2142786 -9.664 < 2e-16 ***
## VehiclePrice 0.0468513 0.0258990 1.809 0.070451 .
## RepNumber -0.0146515 0.0087868 -1.667 0.095428 .
## Deductible 0.0018522 0.0008554 2.165 0.030369 *
## DriverRating 0.0290115 0.0359580 0.807 0.419773
## Days.Policy.Accident -0.2070811 0.1283182 -1.614 0.106569
## Days.Policy.Claim -0.1621159 0.3838761 -0.422 0.672796
## PastNumberOfClaims -0.0040028 0.0428002 -0.094 0.925489
## AgeOfVehicle -0.0648867 0.0436543 -1.486 0.137180
## AgeOfPolicyHolder 0.0576097 0.1351392 0.426 0.669890
## PoliceReportFiled -0.5822621 0.2915118 -1.997 0.045783 *
## WitnessPresent -0.0646361 0.6987097 -0.093 0.926295
## AgentType 0.8104724 0.5377146 1.507 0.131746
## NumberOfSuppliments -0.0425643 0.0341325 -1.247 0.212385
## AddressChange.Claim 0.1756352 0.0479342 3.664 0.000248 ***
## NumberOfCars -0.1408564 0.1181647 -1.192 0.233248
## Year -0.0927106 0.0510623 -1.816 0.069426 .
## BasePolicy -1.1778804 0.0781402 -15.074 < 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: 4853 on 5174 degrees of freedom
## Residual deviance: 3835 on 5143 degrees of freedom
## AIC: 3899
##
## Number of Fisher Scoring iterations: 6
backwards <- step(fit)
## Start: AIC=3899.05
## FraudFound ~ Month + WeekOfMonth + DayOfWeek + Make + AccidentArea +
## DayOfWeekClaimed + MonthClaimed + WeekOfMonthClaimed + Sex +
## MaritalStatus + Age + Fault + PolicyType + VehicleCategory +
## VehiclePrice + RepNumber + Deductible + DriverRating + Days.Policy.Accident +
## Days.Policy.Claim + PastNumberOfClaims + AgeOfVehicle + AgeOfPolicyHolder +
## PoliceReportFiled + WitnessPresent + AgentType + NumberOfSuppliments +
## AddressChange.Claim + NumberOfCars + Year + BasePolicy
##
## Df Deviance AIC
## - WitnessPresent 1 3835.1 3897.1
## - PastNumberOfClaims 1 3835.1 3897.1
## - Days.Policy.Claim 1 3835.2 3897.2
## - AgeOfPolicyHolder 1 3835.2 3897.2
## - DayOfWeek 1 3835.3 3897.3
## - DayOfWeekClaimed 1 3835.5 3897.5
## - MaritalStatus 1 3835.6 3897.6
## - DriverRating 1 3835.7 3897.7
## - Age 1 3835.7 3897.7
## - MonthClaimed 1 3835.7 3897.7
## - WeekOfMonthClaimed 1 3835.9 3897.9
## - Month 1 3836.0 3898.0
## - Make 1 3836.1 3898.1
## - WeekOfMonth 1 3836.3 3898.3
## - AccidentArea 1 3836.4 3898.4
## - NumberOfCars 1 3836.5 3898.5
## - NumberOfSuppliments 1 3836.6 3898.6
## <none> 3835.0 3899.0
## - AgeOfVehicle 1 3837.2 3899.2
## - Days.Policy.Accident 1 3837.6 3899.6
## - Sex 1 3837.8 3899.8
## - AgentType 1 3837.8 3899.8
## - RepNumber 1 3837.8 3899.8
## - VehiclePrice 1 3838.3 3900.3
## - Year 1 3838.4 3900.4
## - PoliceReportFiled 1 3839.5 3901.5
## - Deductible 1 3839.5 3901.5
## - AddressChange.Claim 1 3848.3 3910.3
## - PolicyType 1 3910.7 3972.7
## - VehicleCategory 1 3947.1 4009.1
## - BasePolicy 1 4102.7 4164.7
## - Fault 1 4280.9 4342.9
##
## Step: AIC=3897.06
## FraudFound ~ Month + WeekOfMonth + DayOfWeek + Make + AccidentArea +
## DayOfWeekClaimed + MonthClaimed + WeekOfMonthClaimed + Sex +
## MaritalStatus + Age + Fault + PolicyType + VehicleCategory +
## VehiclePrice + RepNumber + Deductible + DriverRating + Days.Policy.Accident +
## Days.Policy.Claim + PastNumberOfClaims + AgeOfVehicle + AgeOfPolicyHolder +
## PoliceReportFiled + AgentType + NumberOfSuppliments + AddressChange.Claim +
## NumberOfCars + Year + BasePolicy
##
## Df Deviance AIC
## - PastNumberOfClaims 1 3835.1 3895.1
## - Days.Policy.Claim 1 3835.2 3895.2
## - AgeOfPolicyHolder 1 3835.2 3895.2
## - DayOfWeek 1 3835.3 3895.3
## - DayOfWeekClaimed 1 3835.5 3895.5
## - MaritalStatus 1 3835.6 3895.6
## - DriverRating 1 3835.7 3895.7
## - Age 1 3835.7 3895.7
## - MonthClaimed 1 3835.7 3895.7
## - WeekOfMonthClaimed 1 3835.9 3895.9
## - Month 1 3836.0 3896.0
## - Make 1 3836.1 3896.1
## - WeekOfMonth 1 3836.3 3896.3
## - AccidentArea 1 3836.4 3896.4
## - NumberOfCars 1 3836.5 3896.5
## - NumberOfSuppliments 1 3836.6 3896.6
## <none> 3835.1 3897.1
## - AgeOfVehicle 1 3837.2 3897.2
## - Days.Policy.Accident 1 3837.6 3897.6
## - Sex 1 3837.8 3897.8
## - AgentType 1 3837.8 3897.8
## - RepNumber 1 3837.8 3897.8
## - VehiclePrice 1 3838.3 3898.3
## - Year 1 3838.4 3898.4
## - Deductible 1 3839.6 3899.6
## - PoliceReportFiled 1 3839.7 3899.7
## - AddressChange.Claim 1 3848.3 3908.3
## - PolicyType 1 3910.8 3970.8
## - VehicleCategory 1 3947.2 4007.2
## - BasePolicy 1 4102.7 4162.7
## - Fault 1 4281.3 4341.3
##
## Step: AIC=3895.07
## FraudFound ~ Month + WeekOfMonth + DayOfWeek + Make + AccidentArea +
## DayOfWeekClaimed + MonthClaimed + WeekOfMonthClaimed + Sex +
## MaritalStatus + Age + Fault + PolicyType + VehicleCategory +
## VehiclePrice + RepNumber + Deductible + DriverRating + Days.Policy.Accident +
## Days.Policy.Claim + AgeOfVehicle + AgeOfPolicyHolder + PoliceReportFiled +
## AgentType + NumberOfSuppliments + AddressChange.Claim + NumberOfCars +
## Year + BasePolicy
##
## Df Deviance AIC
## - AgeOfPolicyHolder 1 3835.2 3893.2
## - Days.Policy.Claim 1 3835.2 3893.2
## - DayOfWeek 1 3835.3 3893.3
## - DayOfWeekClaimed 1 3835.5 3893.5
## - MaritalStatus 1 3835.7 3893.7
## - DriverRating 1 3835.7 3893.7
## - Age 1 3835.7 3893.7
## - MonthClaimed 1 3835.7 3893.7
## - WeekOfMonthClaimed 1 3835.9 3893.9
## - Month 1 3836.0 3894.0
## - Make 1 3836.1 3894.1
## - WeekOfMonth 1 3836.3 3894.3
## - AccidentArea 1 3836.4 3894.4
## - NumberOfCars 1 3836.5 3894.5
## - NumberOfSuppliments 1 3836.7 3894.7
## <none> 3835.1 3895.1
## - AgeOfVehicle 1 3837.3 3895.3
## - Days.Policy.Accident 1 3837.6 3895.6
## - Sex 1 3837.8 3895.8
## - AgentType 1 3837.8 3895.8
## - RepNumber 1 3837.8 3895.8
## - VehiclePrice 1 3838.3 3896.3
## - Year 1 3838.4 3896.4
## - Deductible 1 3839.6 3897.6
## - PoliceReportFiled 1 3839.7 3897.7
## - AddressChange.Claim 1 3848.3 3906.3
## - PolicyType 1 3911.6 3969.6
## - VehicleCategory 1 3948.8 4006.8
## - BasePolicy 1 4117.9 4175.9
## - Fault 1 4281.5 4339.5
##
## Step: AIC=3893.24
## FraudFound ~ Month + WeekOfMonth + DayOfWeek + Make + AccidentArea +
## DayOfWeekClaimed + MonthClaimed + WeekOfMonthClaimed + Sex +
## MaritalStatus + Age + Fault + PolicyType + VehicleCategory +
## VehiclePrice + RepNumber + Deductible + DriverRating + Days.Policy.Accident +
## Days.Policy.Claim + AgeOfVehicle + PoliceReportFiled + AgentType +
## NumberOfSuppliments + AddressChange.Claim + NumberOfCars +
## Year + BasePolicy
##
## Df Deviance AIC
## - Days.Policy.Claim 1 3835.4 3891.4
## - DayOfWeek 1 3835.4 3891.4
## - DayOfWeekClaimed 1 3835.7 3891.7
## - DriverRating 1 3835.9 3891.9
## - MonthClaimed 1 3835.9 3891.9
## - MaritalStatus 1 3835.9 3891.9
## - WeekOfMonthClaimed 1 3836.1 3892.1
## - Month 1 3836.2 3892.2
## - Make 1 3836.3 3892.3
## - WeekOfMonth 1 3836.5 3892.5
## - AccidentArea 1 3836.6 3892.6
## - NumberOfCars 1 3836.7 3892.7
## - Age 1 3836.8 3892.8
## - NumberOfSuppliments 1 3836.9 3892.9
## <none> 3835.2 3893.2
## - AgeOfVehicle 1 3837.3 3893.3
## - Days.Policy.Accident 1 3837.8 3893.8
## - Sex 1 3837.9 3893.9
## - RepNumber 1 3838.0 3894.0
## - AgentType 1 3838.0 3894.0
## - VehiclePrice 1 3838.4 3894.4
## - Year 1 3838.5 3894.5
## - Deductible 1 3839.7 3895.7
## - PoliceReportFiled 1 3839.8 3895.8
## - AddressChange.Claim 1 3848.5 3904.5
## - PolicyType 1 3912.1 3968.1
## - VehicleCategory 1 3949.0 4005.0
## - BasePolicy 1 4118.3 4174.3
## - Fault 1 4281.7 4337.7
##
## Step: AIC=3891.42
## FraudFound ~ Month + WeekOfMonth + DayOfWeek + Make + AccidentArea +
## DayOfWeekClaimed + MonthClaimed + WeekOfMonthClaimed + Sex +
## MaritalStatus + Age + Fault + PolicyType + VehicleCategory +
## VehiclePrice + RepNumber + Deductible + DriverRating + Days.Policy.Accident +
## AgeOfVehicle + PoliceReportFiled + AgentType + NumberOfSuppliments +
## AddressChange.Claim + NumberOfCars + Year + BasePolicy
##
## Df Deviance AIC
## - DayOfWeek 1 3835.6 3889.6
## - DayOfWeekClaimed 1 3835.8 3889.8
## - MonthClaimed 1 3836.1 3890.1
## - DriverRating 1 3836.1 3890.1
## - MaritalStatus 1 3836.1 3890.1
## - WeekOfMonthClaimed 1 3836.2 3890.2
## - Month 1 3836.4 3890.4
## - Make 1 3836.5 3890.5
## - WeekOfMonth 1 3836.6 3890.6
## - AccidentArea 1 3836.8 3890.8
## - NumberOfCars 1 3836.8 3890.8
## - Age 1 3837.0 3891.0
## - NumberOfSuppliments 1 3837.1 3891.1
## <none> 3835.4 3891.4
## - AgeOfVehicle 1 3837.5 3891.5
## - Sex 1 3838.1 3892.1
## - RepNumber 1 3838.2 3892.2
## - AgentType 1 3838.2 3892.2
## - VehiclePrice 1 3838.5 3892.5
## - Year 1 3838.7 3892.7
## - Days.Policy.Accident 1 3839.8 3893.8
## - Deductible 1 3839.9 3893.9
## - PoliceReportFiled 1 3840.0 3894.0
## - AddressChange.Claim 1 3848.6 3902.6
## - PolicyType 1 3912.3 3966.3
## - VehicleCategory 1 3949.2 4003.2
## - BasePolicy 1 4118.3 4172.3
## - Fault 1 4281.7 4335.7
##
## Step: AIC=3889.61
## FraudFound ~ Month + WeekOfMonth + Make + AccidentArea + DayOfWeekClaimed +
## MonthClaimed + WeekOfMonthClaimed + Sex + MaritalStatus +
## Age + Fault + PolicyType + VehicleCategory + VehiclePrice +
## RepNumber + Deductible + DriverRating + Days.Policy.Accident +
## AgeOfVehicle + PoliceReportFiled + AgentType + NumberOfSuppliments +
## AddressChange.Claim + NumberOfCars + Year + BasePolicy
##
## Df Deviance AIC
## - DayOfWeekClaimed 1 3836.0 3888.0
## - MonthClaimed 1 3836.3 3888.3
## - DriverRating 1 3836.3 3888.3
## - MaritalStatus 1 3836.3 3888.3
## - WeekOfMonthClaimed 1 3836.4 3888.4
## - Month 1 3836.6 3888.6
## - Make 1 3836.7 3888.7
## - WeekOfMonth 1 3836.9 3888.9
## - AccidentArea 1 3837.0 3889.0
## - NumberOfCars 1 3837.1 3889.1
## - NumberOfSuppliments 1 3837.2 3889.2
## - Age 1 3837.2 3889.2
## <none> 3835.6 3889.6
## - AgeOfVehicle 1 3837.7 3889.7
## - Sex 1 3838.3 3890.3
## - RepNumber 1 3838.4 3890.4
## - AgentType 1 3838.4 3890.4
## - VehiclePrice 1 3838.7 3890.7
## - Year 1 3838.8 3890.8
## - Days.Policy.Accident 1 3840.0 3892.0
## - Deductible 1 3840.1 3892.1
## - PoliceReportFiled 1 3840.2 3892.2
## - AddressChange.Claim 1 3848.9 3900.9
## - PolicyType 1 3912.7 3964.7
## - VehicleCategory 1 3950.4 4002.4
## - BasePolicy 1 4118.7 4170.7
## - Fault 1 4282.3 4334.3
##
## Step: AIC=3887.99
## FraudFound ~ Month + WeekOfMonth + Make + AccidentArea + MonthClaimed +
## WeekOfMonthClaimed + Sex + MaritalStatus + Age + Fault +
## PolicyType + VehicleCategory + VehiclePrice + RepNumber +
## Deductible + DriverRating + Days.Policy.Accident + AgeOfVehicle +
## PoliceReportFiled + AgentType + NumberOfSuppliments + AddressChange.Claim +
## NumberOfCars + Year + BasePolicy
##
## Df Deviance AIC
## - MonthClaimed 1 3836.6 3886.6
## - DriverRating 1 3836.7 3886.7
## - MaritalStatus 1 3836.7 3886.7
## - WeekOfMonthClaimed 1 3836.8 3886.8
## - Month 1 3837.0 3887.0
## - Make 1 3837.1 3887.1
## - WeekOfMonth 1 3837.3 3887.3
## - AccidentArea 1 3837.4 3887.4
## - NumberOfCars 1 3837.5 3887.5
## - Age 1 3837.6 3887.6
## - NumberOfSuppliments 1 3837.6 3887.6
## <none> 3836.0 3888.0
## - AgeOfVehicle 1 3838.0 3888.0
## - AgentType 1 3838.8 3888.8
## - Sex 1 3838.8 3888.8
## - RepNumber 1 3838.8 3888.8
## - VehiclePrice 1 3839.1 3889.1
## - Year 1 3839.2 3889.2
## - Days.Policy.Accident 1 3840.5 3890.5
## - Deductible 1 3840.5 3890.5
## - PoliceReportFiled 1 3840.6 3890.6
## - AddressChange.Claim 1 3849.3 3899.3
## - PolicyType 1 3913.2 3963.2
## - VehicleCategory 1 3950.8 4000.8
## - BasePolicy 1 4119.6 4169.6
## - Fault 1 4283.0 4333.0
##
## Step: AIC=3886.6
## FraudFound ~ Month + WeekOfMonth + Make + AccidentArea + WeekOfMonthClaimed +
## Sex + MaritalStatus + Age + Fault + PolicyType + VehicleCategory +
## VehiclePrice + RepNumber + Deductible + DriverRating + Days.Policy.Accident +
## AgeOfVehicle + PoliceReportFiled + AgentType + NumberOfSuppliments +
## AddressChange.Claim + NumberOfCars + Year + BasePolicy
##
## Df Deviance AIC
## - DriverRating 1 3837.3 3885.3
## - MaritalStatus 1 3837.3 3885.3
## - WeekOfMonthClaimed 1 3837.4 3885.4
## - Make 1 3837.6 3885.6
## - WeekOfMonth 1 3837.8 3885.8
## - AccidentArea 1 3837.9 3885.9
## - NumberOfCars 1 3838.1 3886.1
## - Age 1 3838.3 3886.3
## - NumberOfSuppliments 1 3838.3 3886.3
## <none> 3836.6 3886.6
## - AgeOfVehicle 1 3838.7 3886.7
## - Sex 1 3839.4 3887.4
## - AgentType 1 3839.4 3887.4
## - RepNumber 1 3839.4 3887.4
## - VehiclePrice 1 3839.8 3887.8
## - Year 1 3840.0 3888.0
## - Days.Policy.Accident 1 3841.0 3889.0
## - Deductible 1 3841.1 3889.1
## - PoliceReportFiled 1 3841.3 3889.3
## - Month 1 3843.5 3891.5
## - AddressChange.Claim 1 3850.0 3898.0
## - PolicyType 1 3913.5 3961.5
## - VehicleCategory 1 3951.0 3999.0
## - BasePolicy 1 4121.5 4169.5
## - Fault 1 4283.3 4331.3
##
## Step: AIC=3885.26
## FraudFound ~ Month + WeekOfMonth + Make + AccidentArea + WeekOfMonthClaimed +
## Sex + MaritalStatus + Age + Fault + PolicyType + VehicleCategory +
## VehiclePrice + RepNumber + Deductible + Days.Policy.Accident +
## AgeOfVehicle + PoliceReportFiled + AgentType + NumberOfSuppliments +
## AddressChange.Claim + NumberOfCars + Year + BasePolicy
##
## Df Deviance AIC
## - MaritalStatus 1 3838.0 3884.0
## - WeekOfMonthClaimed 1 3838.0 3884.0
## - Make 1 3838.3 3884.3
## - WeekOfMonth 1 3838.6 3884.6
## - AccidentArea 1 3838.6 3884.6
## - NumberOfCars 1 3838.8 3884.8
## - NumberOfSuppliments 1 3838.9 3884.9
## - Age 1 3838.9 3884.9
## <none> 3837.3 3885.3
## - AgeOfVehicle 1 3839.4 3885.4
## - AgentType 1 3840.0 3886.0
## - RepNumber 1 3840.1 3886.1
## - Sex 1 3840.1 3886.1
## - VehiclePrice 1 3840.4 3886.4
## - Year 1 3840.7 3886.7
## - Days.Policy.Accident 1 3841.7 3887.7
## - Deductible 1 3841.7 3887.7
## - PoliceReportFiled 1 3841.9 3887.9
## - Month 1 3844.1 3890.1
## - AddressChange.Claim 1 3850.6 3896.6
## - PolicyType 1 3914.1 3960.1
## - VehicleCategory 1 3951.6 3997.6
## - BasePolicy 1 4122.2 4168.2
## - Fault 1 4284.0 4330.0
##
## Step: AIC=3883.98
## FraudFound ~ Month + WeekOfMonth + Make + AccidentArea + WeekOfMonthClaimed +
## Sex + Age + Fault + PolicyType + VehicleCategory + VehiclePrice +
## RepNumber + Deductible + Days.Policy.Accident + AgeOfVehicle +
## PoliceReportFiled + AgentType + NumberOfSuppliments + AddressChange.Claim +
## NumberOfCars + Year + BasePolicy
##
## Df Deviance AIC
## - WeekOfMonthClaimed 1 3838.8 3882.8
## - Make 1 3839.0 3883.0
## - AccidentArea 1 3839.3 3883.3
## - WeekOfMonth 1 3839.3 3883.3
## - Age 1 3839.3 3883.3
## - NumberOfCars 1 3839.5 3883.5
## - AgeOfVehicle 1 3839.7 3883.7
## - NumberOfSuppliments 1 3839.7 3883.7
## <none> 3838.0 3884.0
## - AgentType 1 3840.6 3884.6
## - RepNumber 1 3840.8 3884.8
## - Sex 1 3840.8 3884.8
## - VehiclePrice 1 3841.3 3885.3
## - Year 1 3841.5 3885.5
## - Days.Policy.Accident 1 3842.4 3886.4
## - Deductible 1 3842.4 3886.4
## - PoliceReportFiled 1 3842.6 3886.6
## - Month 1 3844.7 3888.7
## - AddressChange.Claim 1 3851.2 3895.2
## - PolicyType 1 3914.7 3958.7
## - VehicleCategory 1 3952.7 3996.7
## - BasePolicy 1 4122.6 4166.6
## - Fault 1 4284.8 4328.8
##
## Step: AIC=3882.77
## FraudFound ~ Month + WeekOfMonth + Make + AccidentArea + Sex +
## Age + Fault + PolicyType + VehicleCategory + VehiclePrice +
## RepNumber + Deductible + Days.Policy.Accident + AgeOfVehicle +
## PoliceReportFiled + AgentType + NumberOfSuppliments + AddressChange.Claim +
## NumberOfCars + Year + BasePolicy
##
## Df Deviance AIC
## - WeekOfMonth 1 3839.7 3881.7
## - Make 1 3839.9 3881.9
## - AccidentArea 1 3840.0 3882.0
## - Age 1 3840.1 3882.1
## - NumberOfCars 1 3840.2 3882.2
## - NumberOfSuppliments 1 3840.5 3882.5
## - AgeOfVehicle 1 3840.5 3882.5
## <none> 3838.8 3882.8
## - AgentType 1 3841.4 3883.4
## - RepNumber 1 3841.5 3883.5
## - Sex 1 3841.6 3883.6
## - VehiclePrice 1 3842.1 3884.1
## - Year 1 3842.2 3884.2
## - Days.Policy.Accident 1 3843.0 3885.0
## - Deductible 1 3843.2 3885.2
## - PoliceReportFiled 1 3843.4 3885.4
## - Month 1 3845.4 3887.4
## - AddressChange.Claim 1 3851.9 3893.9
## - PolicyType 1 3915.5 3957.5
## - VehicleCategory 1 3953.4 3995.4
## - BasePolicy 1 4123.1 4165.1
## - Fault 1 4284.9 4326.9
##
## Step: AIC=3881.71
## FraudFound ~ Month + Make + AccidentArea + Sex + Age + Fault +
## PolicyType + VehicleCategory + VehiclePrice + RepNumber +
## Deductible + Days.Policy.Accident + AgeOfVehicle + PoliceReportFiled +
## AgentType + NumberOfSuppliments + AddressChange.Claim + NumberOfCars +
## Year + BasePolicy
##
## Df Deviance AIC
## - Make 1 3840.7 3880.7
## - AccidentArea 1 3841.0 3881.0
## - Age 1 3841.0 3881.0
## - NumberOfCars 1 3841.1 3881.1
## - AgeOfVehicle 1 3841.4 3881.4
## - NumberOfSuppliments 1 3841.5 3881.5
## <none> 3839.7 3881.7
## - AgentType 1 3842.3 3882.3
## - RepNumber 1 3842.5 3882.5
## - Sex 1 3842.6 3882.6
## - Year 1 3843.1 3883.1
## - VehiclePrice 1 3843.1 3883.1
## - Days.Policy.Accident 1 3843.8 3883.8
## - PoliceReportFiled 1 3844.4 3884.4
## - Deductible 1 3844.4 3884.4
## - Month 1 3846.4 3886.4
## - AddressChange.Claim 1 3852.8 3892.8
## - PolicyType 1 3916.5 3956.5
## - VehicleCategory 1 3954.6 3994.6
## - BasePolicy 1 4123.5 4163.5
## - Fault 1 4287.0 4327.0
##
## Step: AIC=3880.75
## FraudFound ~ Month + AccidentArea + Sex + Age + Fault + PolicyType +
## VehicleCategory + VehiclePrice + RepNumber + Deductible +
## Days.Policy.Accident + AgeOfVehicle + PoliceReportFiled +
## AgentType + NumberOfSuppliments + AddressChange.Claim + NumberOfCars +
## Year + BasePolicy
##
## Df Deviance AIC
## - AccidentArea 1 3842.0 3880.0
## - Age 1 3842.1 3880.1
## - NumberOfCars 1 3842.3 3880.3
## - AgeOfVehicle 1 3842.4 3880.4
## - NumberOfSuppliments 1 3842.6 3880.6
## <none> 3840.7 3880.7
## - AgentType 1 3843.4 3881.4
## - RepNumber 1 3843.6 3881.6
## - Sex 1 3843.7 3881.7
## - Year 1 3844.1 3882.1
## - Days.Policy.Accident 1 3844.8 3882.8
## - VehiclePrice 1 3845.2 3883.2
## - PoliceReportFiled 1 3845.4 3883.4
## - Deductible 1 3845.4 3883.4
## - Month 1 3847.6 3885.6
## - AddressChange.Claim 1 3854.0 3892.0
## - PolicyType 1 3918.9 3956.9
## - VehicleCategory 1 3955.7 3993.7
## - BasePolicy 1 4125.5 4163.5
## - Fault 1 4288.2 4326.2
##
## Step: AIC=3880.01
## FraudFound ~ Month + Sex + Age + Fault + PolicyType + VehicleCategory +
## VehiclePrice + RepNumber + Deductible + Days.Policy.Accident +
## AgeOfVehicle + PoliceReportFiled + AgentType + NumberOfSuppliments +
## AddressChange.Claim + NumberOfCars + Year + BasePolicy
##
## Df Deviance AIC
## - Age 1 3843.3 3879.3
## - NumberOfCars 1 3843.5 3879.5
## - AgeOfVehicle 1 3843.8 3879.8
## - NumberOfSuppliments 1 3843.8 3879.8
## <none> 3842.0 3880.0
## - AgentType 1 3844.7 3880.7
## - RepNumber 1 3844.8 3880.8
## - Sex 1 3845.0 3881.0
## - Year 1 3845.5 3881.5
## - Days.Policy.Accident 1 3846.0 3882.0
## - VehiclePrice 1 3846.4 3882.4
## - Deductible 1 3846.6 3882.6
## - PoliceReportFiled 1 3846.8 3882.8
## - Month 1 3848.8 3884.8
## - AddressChange.Claim 1 3855.4 3891.4
## - PolicyType 1 3921.0 3957.0
## - VehicleCategory 1 3958.1 3994.1
## - BasePolicy 1 4127.6 4163.6
## - Fault 1 4291.2 4327.2
##
## Step: AIC=3879.34
## FraudFound ~ Month + Sex + Fault + PolicyType + VehicleCategory +
## VehiclePrice + RepNumber + Deductible + Days.Policy.Accident +
## AgeOfVehicle + PoliceReportFiled + AgentType + NumberOfSuppliments +
## AddressChange.Claim + NumberOfCars + Year + BasePolicy
##
## Df Deviance AIC
## - NumberOfCars 1 3844.9 3878.9
## - NumberOfSuppliments 1 3845.2 3879.2
## <none> 3843.3 3879.3
## - AgentType 1 3846.1 3880.1
## - RepNumber 1 3846.1 3880.1
## - Sex 1 3846.4 3880.4
## - Year 1 3847.0 3881.0
## - Days.Policy.Accident 1 3847.4 3881.4
## - VehiclePrice 1 3847.6 3881.6
## - Deductible 1 3847.9 3881.9
## - PoliceReportFiled 1 3848.1 3882.1
## - Month 1 3850.1 3884.1
## - AgeOfVehicle 1 3851.8 3885.8
## - AddressChange.Claim 1 3856.8 3890.8
## - PolicyType 1 3923.1 3957.1
## - VehicleCategory 1 3960.7 3994.7
## - BasePolicy 1 4127.7 4161.7
## - Fault 1 4292.6 4326.6
##
## Step: AIC=3878.89
## FraudFound ~ Month + Sex + Fault + PolicyType + VehicleCategory +
## VehiclePrice + RepNumber + Deductible + Days.Policy.Accident +
## AgeOfVehicle + PoliceReportFiled + AgentType + NumberOfSuppliments +
## AddressChange.Claim + Year + BasePolicy
##
## Df Deviance AIC
## - NumberOfSuppliments 1 3846.7 3878.7
## <none> 3844.9 3878.9
## - RepNumber 1 3847.5 3879.5
## - AgentType 1 3847.7 3879.7
## - Sex 1 3847.9 3879.9
## - Year 1 3848.6 3880.6
## - Days.Policy.Accident 1 3848.8 3880.8
## - VehiclePrice 1 3849.2 3881.2
## - PoliceReportFiled 1 3849.6 3881.6
## - Deductible 1 3849.8 3881.8
## - Month 1 3851.6 3883.6
## - AgeOfVehicle 1 3853.7 3885.7
## - AddressChange.Claim 1 3857.0 3889.0
## - PolicyType 1 3924.5 3956.5
## - VehicleCategory 1 3962.2 3994.2
## - BasePolicy 1 4128.6 4160.6
## - Fault 1 4292.6 4324.6
##
## Step: AIC=3878.74
## FraudFound ~ Month + Sex + Fault + PolicyType + VehicleCategory +
## VehiclePrice + RepNumber + Deductible + Days.Policy.Accident +
## AgeOfVehicle + PoliceReportFiled + AgentType + AddressChange.Claim +
## Year + BasePolicy
##
## Df Deviance AIC
## <none> 3846.7 3878.7
## - RepNumber 1 3849.4 3879.4
## - AgentType 1 3849.7 3879.7
## - Sex 1 3849.9 3879.9
## - Year 1 3850.7 3880.7
## - VehiclePrice 1 3851.0 3881.0
## - Days.Policy.Accident 1 3851.1 3881.1
## - PoliceReportFiled 1 3851.6 3881.6
## - Deductible 1 3851.8 3881.8
## - Month 1 3853.5 3883.5
## - AgeOfVehicle 1 3857.1 3887.1
## - AddressChange.Claim 1 3858.9 3888.9
## - PolicyType 1 3927.2 3957.2
## - VehicleCategory 1 3964.3 3994.3
## - BasePolicy 1 4133.7 4163.7
## - Fault 1 4294.9 4324.9
summary(backwards)
##
## Call:
## glm(formula = FraudFound ~ Month + Sex + Fault + PolicyType +
## VehicleCategory + VehiclePrice + RepNumber + Deductible +
## Days.Policy.Accident + AgeOfVehicle + PoliceReportFiled +
## AgentType + AddressChange.Claim + Year + BasePolicy, family = "binomial",
## data = fraud)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.5684 -0.7649 -0.2526 -0.1891 3.3457
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.2714784 0.8896975 -0.305 0.760263
## Month -0.0303647 0.0117194 -2.591 0.009570 **
## Sex 0.2174556 0.1239603 1.754 0.079390 .
## Fault 2.6372820 0.1739285 15.163 < 2e-16 ***
## PolicyType 0.6700298 0.0789213 8.490 < 2e-16 ***
## VehicleCategory -2.0958253 0.2125361 -9.861 < 2e-16 ***
## VehiclePrice 0.0518040 0.0250283 2.070 0.038469 *
## RepNumber -0.0143179 0.0087470 -1.637 0.101652
## Deductible 0.0019536 0.0008462 2.309 0.020958 *
## Days.Policy.Accident -0.2329156 0.1101513 -2.115 0.034472 *
## AgeOfVehicle -0.0901743 0.0279337 -3.228 0.001246 **
## PoliceReportFiled -0.5951474 0.2854399 -2.085 0.037068 *
## AgentType 0.8264800 0.5360805 1.542 0.123144
## AddressChange.Claim 0.1478784 0.0415144 3.562 0.000368 ***
## Year -0.1003819 0.0507061 -1.980 0.047739 *
## BasePolicy -1.1798653 0.0761750 -15.489 < 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: 4853.0 on 5174 degrees of freedom
## Residual deviance: 3846.7 on 5159 degrees of freedom
## AIC: 3878.7
##
## Number of Fisher Scoring iterations: 6
str(backwards)
## List of 31
## $ coefficients : Named num [1:16] -0.2715 -0.0304 0.2175 2.6373 0.67 ...
## ..- attr(*, "names")= chr [1:16] "(Intercept)" "Month" "Sex" "Fault" ...
## $ residuals : Named num [1:5175] 1.74 2.64 4.18 3.53 4.01 ...
## ..- attr(*, "names")= chr [1:5175] "1" "2" "3" "4" ...
## $ fitted.values : Named num [1:5175] 0.574 0.379 0.239 0.283 0.249 ...
## ..- attr(*, "names")= chr [1:5175] "1" "2" "3" "4" ...
## $ effects : Named num [1:5175] 25.28 3.01 -2.7 -13.86 -3.49 ...
## ..- attr(*, "names")= chr [1:5175] "(Intercept)" "Month" "Sex" "Fault" ...
## $ R : num [1:16, 1:16] -25 0 0 0 0 ...
## ..- attr(*, "dimnames")=List of 2
## .. ..$ : chr [1:16] "(Intercept)" "Month" "Sex" "Fault" ...
## .. ..$ : chr [1:16] "(Intercept)" "Month" "Sex" "Fault" ...
## $ rank : int 16
## $ qr :List of 5
## ..$ qr : num [1:5175, 1:16] -24.9606 0.0194 0.0171 0.018 0.0173 ...
## .. ..- attr(*, "dimnames")=List of 2
## .. .. ..$ : chr [1:5175] "1" "2" "3" "4" ...
## .. .. ..$ : chr [1:16] "(Intercept)" "Month" "Sex" "Fault" ...
## ..$ rank : int 16
## ..$ qraux: num [1:16] 1.02 1 1.01 1 1 ...
## ..$ pivot: int [1:16] 1 2 3 4 5 6 7 8 9 10 ...
## ..$ tol : num 1e-11
## ..- attr(*, "class")= chr "qr"
## $ family :List of 12
## ..$ family : chr "binomial"
## ..$ link : chr "logit"
## ..$ linkfun :function (mu)
## ..$ linkinv :function (eta)
## ..$ variance :function (mu)
## ..$ dev.resids:function (y, mu, wt)
## ..$ aic :function (y, n, mu, wt, dev)
## ..$ mu.eta :function (eta)
## ..$ initialize: expression({ if (NCOL(y) == 1) { if (is.factor(y)) y <- y != levels(y)[1L] n <- rep.int(1, nobs) y[weights == 0] <- 0 if (any(y < 0 | y > 1)) stop("y values must be 0 <= y <= 1") mustart <- (weights * y + 0.5)/(weights + 1) m <- weights * y if (any(abs(m - round(m)) > 0.001)) warning("non-integer #successes in a binomial glm!") } else if (NCOL(y) == 2) { if (any(abs(y - round(y)) > 0.001)) warning("non-integer counts in a binomial glm!") n <- y[, 1] + y[, 2] y <- ifelse(n == 0, 0, y[, 1]/n) weights <- weights * n mustart <- (n * y + 0.5)/(n + 1) } else stop("for the 'binomial' family, y must be a vector of 0 and 1's\nor a 2 column matrix where col 1 is no. successes and col 2 is no. failures") })
## ..$ validmu :function (mu)
## ..$ valideta :function (eta)
## ..$ simulate :function (object, nsim)
## ..- attr(*, "class")= chr "family"
## $ linear.predictors: Named num [1:5175] 0.3 -0.494 -1.157 -0.929 -1.103 ...
## ..- attr(*, "names")= chr [1:5175] "1" "2" "3" "4" ...
## $ deviance : num 3847
## $ aic : num 3879
## $ null.deviance : num 4853
## $ iter : int 6
## $ weights : Named num [1:5175] 0.244 0.235 0.182 0.203 0.187 ...
## ..- attr(*, "names")= chr [1:5175] "1" "2" "3" "4" ...
## $ prior.weights : Named num [1:5175] 1 1 1 1 1 1 1 1 1 1 ...
## ..- attr(*, "names")= chr [1:5175] "1" "2" "3" "4" ...
## $ df.residual : int 5159
## $ df.null : int 5174
## $ y : Named num [1:5175] 1 1 1 1 1 1 1 1 1 1 ...
## ..- attr(*, "names")= chr [1:5175] "1" "2" "3" "4" ...
## $ converged : logi TRUE
## $ boundary : logi FALSE
## $ model :'data.frame': 5175 obs. of 16 variables:
## ..$ FraudFound : num [1:5175] 1 1 1 1 1 1 1 1 1 1 ...
## ..$ Month : num [1:5175] 7 7 7 11 11 11 11 11 12 12 ...
## ..$ Sex : num [1:5175] 1 1 1 1 1 1 1 1 1 1 ...
## ..$ Fault : num [1:5175] 1 1 1 1 1 1 1 1 1 1 ...
## ..$ PolicyType : num [1:5175] 1 5 2 5 2 7 7 1 1 1 ...
## ..$ VehicleCategory : num [1:5175] 1 2 1 2 1 3 3 1 1 1 ...
## ..$ VehiclePrice : num [1:5175] 6 6 1 6 1 6 6 1 6 2 ...
## ..$ RepNumber : num [1:5175] 9 4 13 7 7 2 10 9 7 1 ...
## ..$ Deductible : num [1:5175] 400 400 400 400 400 400 400 400 400 400 ...
## ..$ Days.Policy.Accident: num [1:5175] 5 5 5 5 5 5 5 5 5 5 ...
## ..$ AgeOfVehicle : num [1:5175] 1 4 8 7 7 7 8 5 1 8 ...
## ..$ PoliceReportFiled : num [1:5175] 0 0 0 0 0 0 0 0 0 0 ...
## ..$ AgentType : num [1:5175] 1 1 1 1 1 1 1 1 1 1 ...
## ..$ AddressChange.Claim : num [1:5175] 0 0 0 0 0 0 0 0 0 1 ...
## ..$ Year : num [1:5175] 0 0 0 0 0 0 0 0 0 0 ...
## ..$ BasePolicy : num [1:5175] 1 2 2 2 2 1 1 1 1 1 ...
## ..- attr(*, "terms")=Classes 'terms', 'formula' language FraudFound ~ Month + Sex + Fault + PolicyType + VehicleCategory + VehiclePrice + RepNumber + Deductible + Days.Policy.Accident + ...
## .. .. ..- attr(*, "variables")= language list(FraudFound, Month, Sex, Fault, PolicyType, VehicleCategory, VehiclePrice, RepNumber, Deductible, Days.Policy.Accident, AgeOfVehicle, PoliceReportFiled, ...
## .. .. ..- attr(*, "factors")= int [1:16, 1:15] 0 1 0 0 0 0 0 0 0 0 ...
## .. .. .. ..- attr(*, "dimnames")=List of 2
## .. .. .. .. ..$ : chr [1:16] "FraudFound" "Month" "Sex" "Fault" ...
## .. .. .. .. ..$ : chr [1:15] "Month" "Sex" "Fault" "PolicyType" ...
## .. .. ..- attr(*, "term.labels")= chr [1:15] "Month" "Sex" "Fault" "PolicyType" ...
## .. .. ..- attr(*, "order")= int [1:15] 1 1 1 1 1 1 1 1 1 1 ...
## .. .. ..- attr(*, "intercept")= int 1
## .. .. ..- attr(*, "response")= int 1
## .. .. ..- attr(*, ".Environment")=<environment: R_GlobalEnv>
## .. .. ..- attr(*, "predvars")= language list(FraudFound, Month, Sex, Fault, PolicyType, VehicleCategory, VehiclePrice, RepNumber, Deductible, Days.Policy.Accident, AgeOfVehicle, PoliceReportFiled, ...
## .. .. ..- attr(*, "dataClasses")= Named chr [1:16] "numeric" "numeric" "numeric" "numeric" ...
## .. .. .. ..- attr(*, "names")= chr [1:16] "FraudFound" "Month" "Sex" "Fault" ...
## $ call : language glm(formula = FraudFound ~ Month + Sex + Fault + PolicyType + VehicleCategory + VehiclePrice + RepNumber + Deductible + Days.Policy.Accident + ...
## $ formula :Class 'formula' language FraudFound ~ Month + Sex + Fault + PolicyType + VehicleCategory + VehiclePrice + RepNumber + Deductible + Days.Policy.Accident + ...
## .. ..- attr(*, ".Environment")=<environment: R_GlobalEnv>
## $ terms :Classes 'terms', 'formula' language FraudFound ~ Month + Sex + Fault + PolicyType + VehicleCategory + VehiclePrice + RepNumber + Deductible + Days.Policy.Accident + ...
## .. ..- attr(*, "variables")= language list(FraudFound, Month, Sex, Fault, PolicyType, VehicleCategory, VehiclePrice, RepNumber, Deductible, Days.Policy.Accident, AgeOfVehicle, PoliceReportFiled, ...
## .. ..- attr(*, "factors")= int [1:16, 1:15] 0 1 0 0 0 0 0 0 0 0 ...
## .. .. ..- attr(*, "dimnames")=List of 2
## .. .. .. ..$ : chr [1:16] "FraudFound" "Month" "Sex" "Fault" ...
## .. .. .. ..$ : chr [1:15] "Month" "Sex" "Fault" "PolicyType" ...
## .. ..- attr(*, "term.labels")= chr [1:15] "Month" "Sex" "Fault" "PolicyType" ...
## .. ..- attr(*, "order")= int [1:15] 1 1 1 1 1 1 1 1 1 1 ...
## .. ..- attr(*, "intercept")= int 1
## .. ..- attr(*, "response")= int 1
## .. ..- attr(*, ".Environment")=<environment: R_GlobalEnv>
## .. ..- attr(*, "predvars")= language list(FraudFound, Month, Sex, Fault, PolicyType, VehicleCategory, VehiclePrice, RepNumber, Deductible, Days.Policy.Accident, AgeOfVehicle, PoliceReportFiled, ...
## .. ..- attr(*, "dataClasses")= Named chr [1:16] "numeric" "numeric" "numeric" "numeric" ...
## .. .. ..- attr(*, "names")= chr [1:16] "FraudFound" "Month" "Sex" "Fault" ...
## $ data :'data.frame': 5175 obs. of 32 variables:
## ..$ Month : num [1:5175] 7 7 7 11 11 11 11 11 12 12 ...
## ..$ WeekOfMonth : num [1:5175] 1 3 4 2 2 3 4 5 1 1 ...
## ..$ DayOfWeek : num [1:5175] 6 7 6 4 5 2 4 1 5 1 ...
## ..$ Make : num [1:5175] 7 7 7 7 18 3 1 10 7 18 ...
## ..$ AccidentArea : num [1:5175] 2 1 2 2 2 2 1 2 1 1 ...
## ..$ DayOfWeekClaimed : num [1:5175] 2 3 3 5 2 3 2 3 5 2 ...
## ..$ MonthClaimed : num [1:5175] 9 1 8 1 1 1 1 12 12 5 ...
## ..$ WeekOfMonthClaimed : num [1:5175] 4 4 2 3 1 2 2 1 3 3 ...
## ..$ Sex : num [1:5175] 1 1 1 1 1 1 1 1 1 1 ...
## ..$ MaritalStatus : num [1:5175] 1 2 2 1 2 2 2 1 1 2 ...
## ..$ Age : num [1:5175] 0 21 50 34 38 31 56 68 0 39 ...
## ..$ Fault : num [1:5175] 1 1 1 1 1 1 1 1 1 1 ...
## ..$ PolicyType : num [1:5175] 1 5 2 5 2 7 7 1 1 1 ...
## ..$ VehicleCategory : num [1:5175] 1 2 1 2 1 3 3 1 1 1 ...
## ..$ VehiclePrice : num [1:5175] 6 6 1 6 1 6 6 1 6 2 ...
## ..$ FraudFound : num [1:5175] 1 1 1 1 1 1 1 1 1 1 ...
## ..$ RepNumber : num [1:5175] 9 4 13 7 7 2 10 9 7 1 ...
## ..$ Deductible : num [1:5175] 400 400 400 400 400 400 400 400 400 400 ...
## ..$ DriverRating : num [1:5175] 1 4 1 3 2 1 2 3 3 3 ...
## ..$ Days.Policy.Accident: num [1:5175] 5 5 5 5 5 5 5 5 5 5 ...
## ..$ Days.Policy.Claim : num [1:5175] 5 5 5 5 5 5 5 5 5 5 ...
## ..$ PastNumberOfClaims : num [1:5175] 0 0 0 0 1 3 0 2 0 0 ...
## ..$ AgeOfVehicle : num [1:5175] 1 4 8 7 7 7 8 5 1 8 ...
## ..$ AgeOfPolicyHolder : num [1:5175] 1 4 7 5 6 5 8 9 1 6 ...
## ..$ PoliceReportFiled : num [1:5175] 0 0 0 0 0 0 0 0 0 0 ...
## ..$ WitnessPresent : num [1:5175] 0 0 0 0 0 0 0 0 0 0 ...
## ..$ AgentType : num [1:5175] 1 1 1 1 1 1 1 1 1 1 ...
## ..$ NumberOfSuppliments : num [1:5175] 0 2 2 2 0 3 0 0 0 3 ...
## ..$ AddressChange.Claim : num [1:5175] 0 0 0 0 0 0 0 0 0 1 ...
## ..$ NumberOfCars : num [1:5175] 1 1 1 1 1 1 1 1 1 2 ...
## ..$ Year : num [1:5175] 0 0 0 0 0 0 0 0 0 0 ...
## ..$ BasePolicy : num [1:5175] 1 2 2 2 2 1 1 1 1 1 ...
## $ offset : NULL
## $ control :List of 3
## ..$ epsilon: num 1e-08
## ..$ maxit : num 25
## ..$ trace : logi FALSE
## $ method : chr "glm.fit"
## $ contrasts : NULL
## $ xlevels : Named list()
## $ anova :'data.frame': 17 obs. of 6 variables:
## ..$ Step :Class 'AsIs' chr [1:17] "" "- WitnessPresent" "- PastNumberOfClaims" "- AgeOfPolicyHolder" ...
## ..$ Df : num [1:17] NA 1 1 1 1 1 1 1 1 1 ...
## ..$ Deviance : num [1:17] NA 0.00864 0.00893 0.17809 0.1731 ...
## ..$ Resid. Df : num [1:17] 5143 5144 5145 5146 5147 ...
## ..$ Resid. Dev: num [1:17] 3835 3835 3835 3835 3835 ...
## ..$ AIC : num [1:17] 3899 3897 3895 3893 3891 ...
## ..- attr(*, "heading")= chr [1:15] "Stepwise Model Path \nAnalysis of Deviance Table" "\nInitial Model:" "FraudFound ~ Month + WeekOfMonth + DayOfWeek + Make + AccidentArea + " " DayOfWeekClaimed + MonthClaimed + WeekOfMonthClaimed + Sex + " ...
## - attr(*, "class")= chr [1:2] "glm" "lm"
# backwards$fit is the probability
fraud$prob <- backwards$fit
fraud$pred <- ifelse(fraud$prob > 0.18, 1, 0)
t <- table(fraud$FraudFound, fraud$pred)
t <- data.frame(Predicted.No = t[,1], Predicted.Yes = t[,2], row.names = c("True.No","True.Yes"))
t
## Predicted.No Predicted.Yes
## True.No 2529 1723
## True.Yes 83 840