Homework5
Starter code for German credit scoring
Refer to http://archive.ics.uci.edu/ml/datasets/Statlog+(German+Credit+Data))
for variable description. The response variable is Class
and all others are predictors.
Only run the following code once to install the package
caret. The German credit scoring data in
provided in that package.
if (!require(package_name, quietly = TRUE)) {
install.packages("caret")
}Task1: Data Preparation
1. Load the caret package and the GermanCredit dataset.
library(caret) #this package contains the german data with its numeric format
data(GermanCredit)
GermanCredit$Class <- GermanCredit$Class == "Good" # use this code to convert `Class` into True or False (equivalent to 1 or 0)
str(GermanCredit)## 'data.frame': 1000 obs. of 62 variables:
## $ Duration : int 6 48 12 42 24 36 24 36 12 30 ...
## $ Amount : int 1169 5951 2096 7882 4870 9055 2835 6948 3059 5234 ...
## $ InstallmentRatePercentage : int 4 2 2 2 3 2 3 2 2 4 ...
## $ ResidenceDuration : int 4 2 3 4 4 4 4 2 4 2 ...
## $ Age : int 67 22 49 45 53 35 53 35 61 28 ...
## $ NumberExistingCredits : int 2 1 1 1 2 1 1 1 1 2 ...
## $ NumberPeopleMaintenance : int 1 1 2 2 2 2 1 1 1 1 ...
## $ Telephone : num 0 1 1 1 1 0 1 0 1 1 ...
## $ ForeignWorker : num 1 1 1 1 1 1 1 1 1 1 ...
## $ Class : logi TRUE FALSE TRUE TRUE FALSE TRUE ...
## $ CheckingAccountStatus.lt.0 : num 1 0 0 1 1 0 0 0 0 0 ...
## $ CheckingAccountStatus.0.to.200 : num 0 1 0 0 0 0 0 1 0 1 ...
## $ CheckingAccountStatus.gt.200 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ CheckingAccountStatus.none : num 0 0 1 0 0 1 1 0 1 0 ...
## $ CreditHistory.NoCredit.AllPaid : num 0 0 0 0 0 0 0 0 0 0 ...
## $ CreditHistory.ThisBank.AllPaid : num 0 0 0 0 0 0 0 0 0 0 ...
## $ CreditHistory.PaidDuly : num 0 1 0 1 0 1 1 1 1 0 ...
## $ CreditHistory.Delay : num 0 0 0 0 1 0 0 0 0 0 ...
## $ CreditHistory.Critical : num 1 0 1 0 0 0 0 0 0 1 ...
## $ Purpose.NewCar : num 0 0 0 0 1 0 0 0 0 1 ...
## $ Purpose.UsedCar : num 0 0 0 0 0 0 0 1 0 0 ...
## $ Purpose.Furniture.Equipment : num 0 0 0 1 0 0 1 0 0 0 ...
## $ Purpose.Radio.Television : num 1 1 0 0 0 0 0 0 1 0 ...
## $ Purpose.DomesticAppliance : num 0 0 0 0 0 0 0 0 0 0 ...
## $ Purpose.Repairs : num 0 0 0 0 0 0 0 0 0 0 ...
## $ Purpose.Education : num 0 0 1 0 0 1 0 0 0 0 ...
## $ Purpose.Vacation : num 0 0 0 0 0 0 0 0 0 0 ...
## $ Purpose.Retraining : num 0 0 0 0 0 0 0 0 0 0 ...
## $ Purpose.Business : num 0 0 0 0 0 0 0 0 0 0 ...
## $ Purpose.Other : num 0 0 0 0 0 0 0 0 0 0 ...
## $ SavingsAccountBonds.lt.100 : num 0 1 1 1 1 0 0 1 0 1 ...
## $ SavingsAccountBonds.100.to.500 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ SavingsAccountBonds.500.to.1000 : num 0 0 0 0 0 0 1 0 0 0 ...
## $ SavingsAccountBonds.gt.1000 : num 0 0 0 0 0 0 0 0 1 0 ...
## $ SavingsAccountBonds.Unknown : num 1 0 0 0 0 1 0 0 0 0 ...
## $ EmploymentDuration.lt.1 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ EmploymentDuration.1.to.4 : num 0 1 0 0 1 1 0 1 0 0 ...
## $ EmploymentDuration.4.to.7 : num 0 0 1 1 0 0 0 0 1 0 ...
## $ EmploymentDuration.gt.7 : num 1 0 0 0 0 0 1 0 0 0 ...
## $ EmploymentDuration.Unemployed : num 0 0 0 0 0 0 0 0 0 1 ...
## $ Personal.Male.Divorced.Seperated : num 0 0 0 0 0 0 0 0 1 0 ...
## $ Personal.Female.NotSingle : num 0 1 0 0 0 0 0 0 0 0 ...
## $ Personal.Male.Single : num 1 0 1 1 1 1 1 1 0 0 ...
## $ Personal.Male.Married.Widowed : num 0 0 0 0 0 0 0 0 0 1 ...
## $ Personal.Female.Single : num 0 0 0 0 0 0 0 0 0 0 ...
## $ OtherDebtorsGuarantors.None : num 1 1 1 0 1 1 1 1 1 1 ...
## $ OtherDebtorsGuarantors.CoApplicant : num 0 0 0 0 0 0 0 0 0 0 ...
## $ OtherDebtorsGuarantors.Guarantor : num 0 0 0 1 0 0 0 0 0 0 ...
## $ Property.RealEstate : num 1 1 1 0 0 0 0 0 1 0 ...
## $ Property.Insurance : num 0 0 0 1 0 0 1 0 0 0 ...
## $ Property.CarOther : num 0 0 0 0 0 0 0 1 0 1 ...
## $ Property.Unknown : num 0 0 0 0 1 1 0 0 0 0 ...
## $ OtherInstallmentPlans.Bank : num 0 0 0 0 0 0 0 0 0 0 ...
## $ OtherInstallmentPlans.Stores : num 0 0 0 0 0 0 0 0 0 0 ...
## $ OtherInstallmentPlans.None : num 1 1 1 1 1 1 1 1 1 1 ...
## $ Housing.Rent : num 0 0 0 0 0 0 0 1 0 0 ...
## $ Housing.Own : num 1 1 1 0 0 0 1 0 1 1 ...
## $ Housing.ForFree : num 0 0 0 1 1 1 0 0 0 0 ...
## $ Job.UnemployedUnskilled : num 0 0 0 0 0 0 0 0 0 0 ...
## $ Job.UnskilledResident : num 0 0 1 0 0 1 0 0 1 0 ...
## $ Job.SkilledEmployee : num 1 1 0 1 1 0 1 0 0 0 ...
## $ Job.Management.SelfEmp.HighlyQualified: num 0 0 0 0 0 0 0 1 0 1 ...Your observation: There are 1000 observations and 62 variables. The data contains information that classifies people as either good or bad credit risks.
#This is an optional code that drop variables that provide no information in the data
GermanCredit = GermanCredit[,-c(14,19,27,30,35,40,44,45,48,52,55,58,62)] #don't run this code twice!! Think about why.2. Explore the dataset to understand its structure.
(1) How many observations and variables are there? (2 pts)
str(GermanCredit)## 'data.frame': 1000 obs. of 49 variables:
## $ Duration : int 6 48 12 42 24 36 24 36 12 30 ...
## $ Amount : int 1169 5951 2096 7882 4870 9055 2835 6948 3059 5234 ...
## $ InstallmentRatePercentage : int 4 2 2 2 3 2 3 2 2 4 ...
## $ ResidenceDuration : int 4 2 3 4 4 4 4 2 4 2 ...
## $ Age : int 67 22 49 45 53 35 53 35 61 28 ...
## $ NumberExistingCredits : int 2 1 1 1 2 1 1 1 1 2 ...
## $ NumberPeopleMaintenance : int 1 1 2 2 2 2 1 1 1 1 ...
## $ Telephone : num 0 1 1 1 1 0 1 0 1 1 ...
## $ ForeignWorker : num 1 1 1 1 1 1 1 1 1 1 ...
## $ Class : logi TRUE FALSE TRUE TRUE FALSE TRUE ...
## $ CheckingAccountStatus.lt.0 : num 1 0 0 1 1 0 0 0 0 0 ...
## $ CheckingAccountStatus.0.to.200 : num 0 1 0 0 0 0 0 1 0 1 ...
## $ CheckingAccountStatus.gt.200 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ CreditHistory.NoCredit.AllPaid : num 0 0 0 0 0 0 0 0 0 0 ...
## $ CreditHistory.ThisBank.AllPaid : num 0 0 0 0 0 0 0 0 0 0 ...
## $ CreditHistory.PaidDuly : num 0 1 0 1 0 1 1 1 1 0 ...
## $ CreditHistory.Delay : num 0 0 0 0 1 0 0 0 0 0 ...
## $ Purpose.NewCar : num 0 0 0 0 1 0 0 0 0 1 ...
## $ Purpose.UsedCar : num 0 0 0 0 0 0 0 1 0 0 ...
## $ Purpose.Furniture.Equipment : num 0 0 0 1 0 0 1 0 0 0 ...
## $ Purpose.Radio.Television : num 1 1 0 0 0 0 0 0 1 0 ...
## $ Purpose.DomesticAppliance : num 0 0 0 0 0 0 0 0 0 0 ...
## $ Purpose.Repairs : num 0 0 0 0 0 0 0 0 0 0 ...
## $ Purpose.Education : num 0 0 1 0 0 1 0 0 0 0 ...
## $ Purpose.Retraining : num 0 0 0 0 0 0 0 0 0 0 ...
## $ Purpose.Business : num 0 0 0 0 0 0 0 0 0 0 ...
## $ SavingsAccountBonds.lt.100 : num 0 1 1 1 1 0 0 1 0 1 ...
## $ SavingsAccountBonds.100.to.500 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ SavingsAccountBonds.500.to.1000 : num 0 0 0 0 0 0 1 0 0 0 ...
## $ SavingsAccountBonds.gt.1000 : num 0 0 0 0 0 0 0 0 1 0 ...
## $ EmploymentDuration.lt.1 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ EmploymentDuration.1.to.4 : num 0 1 0 0 1 1 0 1 0 0 ...
## $ EmploymentDuration.4.to.7 : num 0 0 1 1 0 0 0 0 1 0 ...
## $ EmploymentDuration.gt.7 : num 1 0 0 0 0 0 1 0 0 0 ...
## $ Personal.Male.Divorced.Seperated : num 0 0 0 0 0 0 0 0 1 0 ...
## $ Personal.Female.NotSingle : num 0 1 0 0 0 0 0 0 0 0 ...
## $ Personal.Male.Single : num 1 0 1 1 1 1 1 1 0 0 ...
## $ OtherDebtorsGuarantors.None : num 1 1 1 0 1 1 1 1 1 1 ...
## $ OtherDebtorsGuarantors.CoApplicant: num 0 0 0 0 0 0 0 0 0 0 ...
## $ Property.RealEstate : num 1 1 1 0 0 0 0 0 1 0 ...
## $ Property.Insurance : num 0 0 0 1 0 0 1 0 0 0 ...
## $ Property.CarOther : num 0 0 0 0 0 0 0 1 0 1 ...
## $ OtherInstallmentPlans.Bank : num 0 0 0 0 0 0 0 0 0 0 ...
## $ OtherInstallmentPlans.Stores : num 0 0 0 0 0 0 0 0 0 0 ...
## $ Housing.Rent : num 0 0 0 0 0 0 0 1 0 0 ...
## $ Housing.Own : num 1 1 1 0 0 0 1 0 1 1 ...
## $ Job.UnemployedUnskilled : num 0 0 0 0 0 0 0 0 0 0 ...
## $ Job.UnskilledResident : num 0 0 1 0 0 1 0 0 1 0 ...
## $ Job.SkilledEmployee : num 1 1 0 1 1 0 1 0 0 0 ...head(GermanCredit)## Duration Amount InstallmentRatePercentage ResidenceDuration Age
## 1 6 1169 4 4 67
## 2 48 5951 2 2 22
## 3 12 2096 2 3 49
## 4 42 7882 2 4 45
## 5 24 4870 3 4 53
## 6 36 9055 2 4 35
## NumberExistingCredits NumberPeopleMaintenance Telephone ForeignWorker Class
## 1 2 1 0 1 TRUE
## 2 1 1 1 1 FALSE
## 3 1 2 1 1 TRUE
## 4 1 2 1 1 TRUE
## 5 2 2 1 1 FALSE
## 6 1 2 0 1 TRUE
## CheckingAccountStatus.lt.0 CheckingAccountStatus.0.to.200
## 1 1 0
## 2 0 1
## 3 0 0
## 4 1 0
## 5 1 0
## 6 0 0
## CheckingAccountStatus.gt.200 CreditHistory.NoCredit.AllPaid
## 1 0 0
## 2 0 0
## 3 0 0
## 4 0 0
## 5 0 0
## 6 0 0
## CreditHistory.ThisBank.AllPaid CreditHistory.PaidDuly CreditHistory.Delay
## 1 0 0 0
## 2 0 1 0
## 3 0 0 0
## 4 0 1 0
## 5 0 0 1
## 6 0 1 0
## Purpose.NewCar Purpose.UsedCar Purpose.Furniture.Equipment
## 1 0 0 0
## 2 0 0 0
## 3 0 0 0
## 4 0 0 1
## 5 1 0 0
## 6 0 0 0
## Purpose.Radio.Television Purpose.DomesticAppliance Purpose.Repairs
## 1 1 0 0
## 2 1 0 0
## 3 0 0 0
## 4 0 0 0
## 5 0 0 0
## 6 0 0 0
## Purpose.Education Purpose.Retraining Purpose.Business
## 1 0 0 0
## 2 0 0 0
## 3 1 0 0
## 4 0 0 0
## 5 0 0 0
## 6 1 0 0
## SavingsAccountBonds.lt.100 SavingsAccountBonds.100.to.500
## 1 0 0
## 2 1 0
## 3 1 0
## 4 1 0
## 5 1 0
## 6 0 0
## SavingsAccountBonds.500.to.1000 SavingsAccountBonds.gt.1000
## 1 0 0
## 2 0 0
## 3 0 0
## 4 0 0
## 5 0 0
## 6 0 0
## EmploymentDuration.lt.1 EmploymentDuration.1.to.4 EmploymentDuration.4.to.7
## 1 0 0 0
## 2 0 1 0
## 3 0 0 1
## 4 0 0 1
## 5 0 1 0
## 6 0 1 0
## EmploymentDuration.gt.7 Personal.Male.Divorced.Seperated
## 1 1 0
## 2 0 0
## 3 0 0
## 4 0 0
## 5 0 0
## 6 0 0
## Personal.Female.NotSingle Personal.Male.Single OtherDebtorsGuarantors.None
## 1 0 1 1
## 2 1 0 1
## 3 0 1 1
## 4 0 1 0
## 5 0 1 1
## 6 0 1 1
## OtherDebtorsGuarantors.CoApplicant Property.RealEstate Property.Insurance
## 1 0 1 0
## 2 0 1 0
## 3 0 1 0
## 4 0 0 1
## 5 0 0 0
## 6 0 0 0
## Property.CarOther OtherInstallmentPlans.Bank OtherInstallmentPlans.Stores
## 1 0 0 0
## 2 0 0 0
## 3 0 0 0
## 4 0 0 0
## 5 0 0 0
## 6 0 0 0
## Housing.Rent Housing.Own Job.UnemployedUnskilled Job.UnskilledResident
## 1 0 1 0 0
## 2 0 1 0 0
## 3 0 1 0 1
## 4 0 0 0 0
## 5 0 0 0 0
## 6 0 0 0 1
## Job.SkilledEmployee
## 1 1
## 2 1
## 3 0
## 4 1
## 5 1
## 6 0summary(GermanCredit)## Duration Amount InstallmentRatePercentage ResidenceDuration
## Min. : 4.0 Min. : 250 Min. :1.000 Min. :1.000
## 1st Qu.:12.0 1st Qu.: 1366 1st Qu.:2.000 1st Qu.:2.000
## Median :18.0 Median : 2320 Median :3.000 Median :3.000
## Mean :20.9 Mean : 3271 Mean :2.973 Mean :2.845
## 3rd Qu.:24.0 3rd Qu.: 3972 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :72.0 Max. :18424 Max. :4.000 Max. :4.000
## Age NumberExistingCredits NumberPeopleMaintenance Telephone
## Min. :19.00 Min. :1.000 Min. :1.000 Min. :0.000
## 1st Qu.:27.00 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:0.000
## Median :33.00 Median :1.000 Median :1.000 Median :1.000
## Mean :35.55 Mean :1.407 Mean :1.155 Mean :0.596
## 3rd Qu.:42.00 3rd Qu.:2.000 3rd Qu.:1.000 3rd Qu.:1.000
## Max. :75.00 Max. :4.000 Max. :2.000 Max. :1.000
## ForeignWorker Class CheckingAccountStatus.lt.0
## Min. :0.000 Mode :logical Min. :0.000
## 1st Qu.:1.000 FALSE:300 1st Qu.:0.000
## Median :1.000 TRUE :700 Median :0.000
## Mean :0.963 Mean :0.274
## 3rd Qu.:1.000 3rd Qu.:1.000
## Max. :1.000 Max. :1.000
## CheckingAccountStatus.0.to.200 CheckingAccountStatus.gt.200
## Min. :0.000 Min. :0.000
## 1st Qu.:0.000 1st Qu.:0.000
## Median :0.000 Median :0.000
## Mean :0.269 Mean :0.063
## 3rd Qu.:1.000 3rd Qu.:0.000
## Max. :1.000 Max. :1.000
## CreditHistory.NoCredit.AllPaid CreditHistory.ThisBank.AllPaid
## Min. :0.00 Min. :0.000
## 1st Qu.:0.00 1st Qu.:0.000
## Median :0.00 Median :0.000
## Mean :0.04 Mean :0.049
## 3rd Qu.:0.00 3rd Qu.:0.000
## Max. :1.00 Max. :1.000
## CreditHistory.PaidDuly CreditHistory.Delay Purpose.NewCar Purpose.UsedCar
## Min. :0.00 Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:0.00 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.000
## Median :1.00 Median :0.000 Median :0.000 Median :0.000
## Mean :0.53 Mean :0.088 Mean :0.234 Mean :0.103
## 3rd Qu.:1.00 3rd Qu.:0.000 3rd Qu.:0.000 3rd Qu.:0.000
## Max. :1.00 Max. :1.000 Max. :1.000 Max. :1.000
## Purpose.Furniture.Equipment Purpose.Radio.Television Purpose.DomesticAppliance
## Min. :0.000 Min. :0.00 Min. :0.000
## 1st Qu.:0.000 1st Qu.:0.00 1st Qu.:0.000
## Median :0.000 Median :0.00 Median :0.000
## Mean :0.181 Mean :0.28 Mean :0.012
## 3rd Qu.:0.000 3rd Qu.:1.00 3rd Qu.:0.000
## Max. :1.000 Max. :1.00 Max. :1.000
## Purpose.Repairs Purpose.Education Purpose.Retraining Purpose.Business
## Min. :0.000 Min. :0.00 Min. :0.000 Min. :0.000
## 1st Qu.:0.000 1st Qu.:0.00 1st Qu.:0.000 1st Qu.:0.000
## Median :0.000 Median :0.00 Median :0.000 Median :0.000
## Mean :0.022 Mean :0.05 Mean :0.009 Mean :0.097
## 3rd Qu.:0.000 3rd Qu.:0.00 3rd Qu.:0.000 3rd Qu.:0.000
## Max. :1.000 Max. :1.00 Max. :1.000 Max. :1.000
## SavingsAccountBonds.lt.100 SavingsAccountBonds.100.to.500
## Min. :0.000 Min. :0.000
## 1st Qu.:0.000 1st Qu.:0.000
## Median :1.000 Median :0.000
## Mean :0.603 Mean :0.103
## 3rd Qu.:1.000 3rd Qu.:0.000
## Max. :1.000 Max. :1.000
## SavingsAccountBonds.500.to.1000 SavingsAccountBonds.gt.1000
## Min. :0.000 Min. :0.000
## 1st Qu.:0.000 1st Qu.:0.000
## Median :0.000 Median :0.000
## Mean :0.063 Mean :0.048
## 3rd Qu.:0.000 3rd Qu.:0.000
## Max. :1.000 Max. :1.000
## EmploymentDuration.lt.1 EmploymentDuration.1.to.4 EmploymentDuration.4.to.7
## Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.000
## Median :0.000 Median :0.000 Median :0.000
## Mean :0.172 Mean :0.339 Mean :0.174
## 3rd Qu.:0.000 3rd Qu.:1.000 3rd Qu.:0.000
## Max. :1.000 Max. :1.000 Max. :1.000
## EmploymentDuration.gt.7 Personal.Male.Divorced.Seperated
## Min. :0.000 Min. :0.00
## 1st Qu.:0.000 1st Qu.:0.00
## Median :0.000 Median :0.00
## Mean :0.253 Mean :0.05
## 3rd Qu.:1.000 3rd Qu.:0.00
## Max. :1.000 Max. :1.00
## Personal.Female.NotSingle Personal.Male.Single OtherDebtorsGuarantors.None
## Min. :0.00 Min. :0.000 Min. :0.000
## 1st Qu.:0.00 1st Qu.:0.000 1st Qu.:1.000
## Median :0.00 Median :1.000 Median :1.000
## Mean :0.31 Mean :0.548 Mean :0.907
## 3rd Qu.:1.00 3rd Qu.:1.000 3rd Qu.:1.000
## Max. :1.00 Max. :1.000 Max. :1.000
## OtherDebtorsGuarantors.CoApplicant Property.RealEstate Property.Insurance
## Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.000
## Median :0.000 Median :0.000 Median :0.000
## Mean :0.041 Mean :0.282 Mean :0.232
## 3rd Qu.:0.000 3rd Qu.:1.000 3rd Qu.:0.000
## Max. :1.000 Max. :1.000 Max. :1.000
## Property.CarOther OtherInstallmentPlans.Bank OtherInstallmentPlans.Stores
## Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.000
## Median :0.000 Median :0.000 Median :0.000
## Mean :0.332 Mean :0.139 Mean :0.047
## 3rd Qu.:1.000 3rd Qu.:0.000 3rd Qu.:0.000
## Max. :1.000 Max. :1.000 Max. :1.000
## Housing.Rent Housing.Own Job.UnemployedUnskilled Job.UnskilledResident
## Min. :0.000 Min. :0.000 Min. :0.000 Min. :0.0
## 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:0.0
## Median :0.000 Median :1.000 Median :0.000 Median :0.0
## Mean :0.179 Mean :0.713 Mean :0.022 Mean :0.2
## 3rd Qu.:0.000 3rd Qu.:1.000 3rd Qu.:0.000 3rd Qu.:0.0
## Max. :1.000 Max. :1.000 Max. :1.000 Max. :1.0
## Job.SkilledEmployee
## Min. :0.00
## 1st Qu.:0.00
## Median :1.00
## Mean :0.63
## 3rd Qu.:1.00
## Max. :1.00?GermanCreditYour observation: With the above variables dropped, there are 49 variables with 1000 observations each. There are 7 integer type variables, 41 numeric type variables, and 1 logical variable (class). Overall, the data set includes predictors like checking account status, employment duration, age, and other personal information, which may shape an individual’s credit worthiness.
(2) Please make a frequency table of variable class
(use table() function). How many observations are classed
as “good” and how many are “bad”? (2 pts)
table(GermanCredit$Class)##
## FALSE TRUE
## 300 700Your observation: Since TRUE corresponds with “good” and FALSE corresponds with “bad”, there are 700 observations that are good and 300 that are bad.
(3) Please make a barplot of of response variable
class. Please add titles and labels to axis. (2 pts)
library(ggplot2)
ggplot(GermanCredit, aes(x = factor(Class, labels = c("Bad", "Good")))) +
geom_bar() +
labs(title = "Frequency of Credit Classes (Bad vs. Good)",
x = "Credit Class",
y = "Count")
3. Split the dataset into training and test set. A
random seed of 2025 is set for reproducibility. Please
comment on what is the split proportion you choose for training and
testing data? (2 pts)
set.seed(2025) # set random seed for reproducibility.
# split dataset into 80% training and 20% testing
train_ind <-sample(1:nrow(GermanCredit), 0.8 * nrow(GermanCredit))
# creating training and testing datasets
GermanCredit_train <- GermanCredit[train_ind, ]
GermanCredit_test <- GermanCredit[-train_ind,]
# test dimensions
dim(GermanCredit_train)## [1] 800 49dim(GermanCredit_test)## [1] 200 49# how many "good" and "bad" risks in data:
table(GermanCredit_train$Class)##
## FALSE TRUE
## 246 554table(GermanCredit_test$Class)##
## FALSE TRUE
## 54 146Your comment: I chose to randomly select 80% of the rows for training data. The other 20% was used for testing data. The set seed ensures that anyone else running the code will get the same split each time. In the training data, there are 246 bad risks and 554 good risks. In the testing data, there are 54 bad risks and 146 good risks.
Task 2: Model Fitting
1. Fit a logistic regression model using the training set. Please use all variables, but make sure the variable types are right. (2 pts)
# fitting logistic model
# note: I used Class as response variable since this indicates credit risk (good or bad)
model_GermanCredit <- glm(Class ~ ., data = GermanCredit_train, family = "binomial")2. Summarize the model and interpret the coefficients. What is the
estimated coefficients for variable
InstallmentRatePercentage? Is it significant, and why? (2
pts)
# examining fitted model:
summary(model_GermanCredit)##
## Call:
## glm(formula = Class ~ ., family = "binomial", data = GermanCredit_train)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 8.815e+00 1.594e+00 5.529 3.22e-08 ***
## Duration -2.643e-02 1.027e-02 -2.573 0.010068 *
## Amount -1.355e-04 4.957e-05 -2.734 0.006253 **
## InstallmentRatePercentage -2.925e-01 9.747e-02 -3.001 0.002693 **
## ResidenceDuration -4.893e-02 9.689e-02 -0.505 0.613531
## Age 1.355e-02 1.020e-02 1.329 0.183763
## NumberExistingCredits -3.599e-01 2.175e-01 -1.654 0.098027 .
## NumberPeopleMaintenance -3.644e-01 2.712e-01 -1.344 0.178951
## Telephone -2.654e-01 2.276e-01 -1.166 0.243564
## ForeignWorker -1.454e+00 7.181e-01 -2.025 0.042862 *
## CheckingAccountStatus.lt.0 -1.775e+00 2.635e-01 -6.735 1.64e-11 ***
## CheckingAccountStatus.0.to.200 -1.393e+00 2.596e-01 -5.365 8.09e-08 ***
## CheckingAccountStatus.gt.200 -9.145e-01 4.225e-01 -2.165 0.030425 *
## CreditHistory.NoCredit.AllPaid -1.232e+00 4.874e-01 -2.528 0.011465 *
## CreditHistory.ThisBank.AllPaid -1.570e+00 4.829e-01 -3.252 0.001147 **
## CreditHistory.PaidDuly -9.374e-01 2.907e-01 -3.224 0.001262 **
## CreditHistory.Delay -5.626e-01 3.728e-01 -1.509 0.131283
## Purpose.NewCar -1.417e+00 8.247e-01 -1.718 0.085814 .
## Purpose.UsedCar 2.976e-01 8.684e-01 0.343 0.731867
## Purpose.Furniture.Equipment -5.842e-01 8.330e-01 -0.701 0.483148
## Purpose.Radio.Television -4.791e-01 8.311e-01 -0.576 0.564284
## Purpose.DomesticAppliance -7.999e-01 1.209e+00 -0.661 0.508314
## Purpose.Repairs -1.601e+00 1.011e+00 -1.585 0.113077
## Purpose.Education -1.304e+00 9.075e-01 -1.436 0.150873
## Purpose.Retraining 3.610e-01 1.500e+00 0.241 0.809867
## Purpose.Business -6.988e-01 8.558e-01 -0.817 0.414159
## SavingsAccountBonds.lt.100 -1.065e+00 3.092e-01 -3.444 0.000573 ***
## SavingsAccountBonds.100.to.500 -8.837e-01 3.957e-01 -2.233 0.025519 *
## SavingsAccountBonds.500.to.1000 -9.486e-01 5.005e-01 -1.896 0.058026 .
## SavingsAccountBonds.gt.1000 1.460e-01 5.940e-01 0.246 0.805829
## EmploymentDuration.lt.1 9.279e-02 4.634e-01 0.200 0.841281
## EmploymentDuration.1.to.4 2.090e-01 4.443e-01 0.470 0.638077
## EmploymentDuration.4.to.7 9.869e-01 4.882e-01 2.021 0.043232 *
## EmploymentDuration.gt.7 1.785e-01 4.568e-01 0.391 0.695924
## Personal.Male.Divorced.Seperated -1.288e-01 5.011e-01 -0.257 0.797124
## Personal.Female.NotSingle -2.033e-01 3.478e-01 -0.584 0.558947
## Personal.Male.Single 3.802e-01 3.481e-01 1.092 0.274710
## OtherDebtorsGuarantors.None -7.408e-01 4.667e-01 -1.587 0.112448
## OtherDebtorsGuarantors.CoApplicant -1.220e+00 6.317e-01 -1.931 0.053423 .
## Property.RealEstate 3.867e-01 4.875e-01 0.793 0.427607
## Property.Insurance 1.635e-01 4.784e-01 0.342 0.732464
## Property.CarOther 1.796e-01 4.596e-01 0.391 0.695959
## OtherInstallmentPlans.Bank -7.233e-01 2.617e-01 -2.764 0.005716 **
## OtherInstallmentPlans.Stores -1.929e-01 4.246e-01 -0.454 0.649608
## Housing.Rent -4.468e-01 5.415e-01 -0.825 0.409294
## Housing.Own -2.017e-01 5.184e-01 -0.389 0.697127
## Job.UnemployedUnskilled 5.206e-01 7.212e-01 0.722 0.470322
## Job.UnskilledResident -2.015e-02 3.833e-01 -0.053 0.958079
## Job.SkilledEmployee -6.640e-02 3.153e-01 -0.211 0.833214
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 987.34 on 799 degrees of freedom
## Residual deviance: 728.49 on 751 degrees of freedom
## AIC: 826.49
##
## Number of Fisher Scoring iterations: 5Your comment: Some predictors in the model are not significant since they have a p value greater than 0.05 (ex: residence duration, telephone, housing). Here are my interpretations of the first several variables in the model: - Duration: As duration increases, class is more likely to be good. - Amount: As loan amount decreases, class is less likely to be good. Installment rate has an estimate of -0.2925, indicating that as the installment rate increases by 1, the log-odds of having good credit worthiness decrease by 0.2925 on average, provided that other variables are held constant. In other words, a higher installation rate reduces the odds of being identified as a good credit risk. The level of significance for this variable is 0.002693; because this is lower than the threshold of 0.05, this suggests that installment rate is statistically significant. In summary, having more income go towards installment payments generally makes people less likely to have good credit.
3. Please interpret this number in detail (please calculate the corresponding odds ratio, and interpret it). (2 pts)
# Calculate odds ratio for a specific coefficient (example: InstallmentRatePercentage)
exp(-0.2925)## [1] 0.7463952# Show change in odds ratio
exp(-0.2925)-1## [1] -0.2536048Your comment: The odds ratio is 0.7464, which indicates that as the installment rate percentage increases by 1 unit, the odds of having good credit decrease by ~25% when all other variables are held constant.
Task 3: Model Evaluation (Part I)
1. Use the training set to obtain predicted probabilities. (2 pts)
# predicted probabilities on training set:
pred_prob_train <- predict(model_GermanCredit, newdata = GermanCredit_train, type = "response")
# summarize predicted probabilities
summary(pred_prob_train)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.05173 0.50798 0.76807 0.69250 0.91225 0.999192. Using the probability cut-off of 0.5, generate confusion matrix and obtain MR (misclassification rate) for the the training set. (3 pts)
actual_value_train <- GermanCredit_train$Class * 1 # * 1 converts TRUE/FALSE to numeric 1/0
pred_value_train <- 1 * (pred_prob_train > 0.5)
confusion_matrix_train <- table(actual_value_train, pred_value_train)
# false positives and false negatives
FP_train <- sum(actual_value_train == 0 & pred_value_train == 1)
FN_train <- sum(actual_value_train == 1 & pred_value_train == 0)
# misclassification rate - 2 ways
MR_train1 <- (FP_train + FN_train) / sum(confusion_matrix_train)
MR_train2 <- 1 - sum(diag(confusion_matrix_train))/sum(confusion_matrix_train)
# showing confusion matrix and misclassification rate
confusion_matrix_train## pred_value_train
## actual_value_train 0 1
## 0 134 112
## 1 62 492MR_train1## [1] 0.2175MR_train2## [1] 0.2175# accuracy
sum(diag(confusion_matrix_train)) / sum(confusion_matrix_train)## [1] 0.7825Your comment: Based on the confusion matrix, there are 134 true negatives (model predicted bad credit and the individual actually had bad credit), 112 false positives (the model predicted good credit but the individual actually had bad credit), 62 false negatives (the model predicted bad credit but the individual actually had good credit), and 492 true positives (the model predicted good credit and the individual actually had good credit). I also computed the accuracy rate, which indicates that 78.25% of the training cases were predicted correctly. The misclassification rate is 0.2175, which represents the number of false postives plus the false negatives divided by the total number of observations. This indicates that 21.75% of the predictions made by the model are incorrect.
3. Find the optimal probability cut-off point using the MR. Please draw a plot of MR vs. cut-off probability, and comment on optimal cut-off probability. (3 pts)
# note: used training data for this
# create a sequence of cut-off probabilities (go from 0 to 1 by increments of 0.01)
pcut_seq <- seq(from = 0, to = 1, by = 0.01)
# vector to store MR rate
MR_seq <- rep(0, length(pcut_seq))
for(i in 1:length(pcut_seq)) {
pcut <- pcut_seq[i]
pred_value <- 1 * (pred_prob_train > pcut) # converts predicted probabilities to binary predictions
confusion_matrix_train <- table(actual = actual_value_train, predict = pred_value)
FP_train <- sum(actual_value_train == 0 & pred_value == 1) # false positives
FN_train <- sum(actual_value_train == 1 & pred_value == 0) # false negatives
MR_seq[i] <- (FP_train + FN_train) / length(pred_value) # misclassification rate
}
plot(MR_seq ~ pcut_seq)
Your comment: The misclassification rate decreases as the cut-off probability changes. It reaches its lowest point near a cut-off around ~0.5. This indicates that this cut-off could lead to the best classification performance for the training data.
4. Please generate the ROC curve and calculate the AUC for the training set. Please comment on this AUC. (2 pts)
library(pROC)## Type 'citation("pROC")' for a citation.##
## Attaching package: 'pROC'## The following objects are masked from 'package:stats':
##
## cov, smooth, var# generate ROC curve
roc_obj_train <- roc(actual_value_train, pred_prob_train)## Setting levels: control = 0, case = 1## Setting direction: controls < casesplot(roc_obj_train)
# calculate AUC
auc_train <- auc(actual_value_train, pred_prob_train)## Setting levels: control = 0, case = 1
## Setting direction: controls < cases# view AUC
auc_train## Area under the curve: 0.8312Your comment: The area under the curve is 0.8312, which represents an aggregate measure of the model’s performance across all possible classification thresholds. In this case, it specifically indicates the model’s ability to differentiate between good and bad credit worthiness across different cut-off probabilities. An AUC of 1 indicates a perfect model, while an AUC of 0.5 indicates a model that is no better than random guessing. Since this model’s AUC falls between 0.5 and 1, it indicates a fairly strong model.
Task 4: Model Evaluation (Part II)
1. Use the testing set to obtain predicted probabilities. (2 pts)
pred_prob_test <- predict(model_GermanCredit, newdata = GermanCredit_test, type = "response")
summary(pred_prob_test)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.1150 0.6116 0.7922 0.7398 0.9312 0.99562. Using the probability cut-off of 0.5, generate confusion matrix and obtain MR (misclassification rate) for the the training set. (2 pts)
Note: I calculated the confusion matrix and MR for the testing set here, since I already generated these values for the training set above.
actual_value_test <- GermanCredit_test$Class * 1 # * 1 converts TRUE/FALSE to numeric 1/0
pred_value_test <- 1 * (pred_prob_test > 0.5)
confusion_matrix_test <- table(actual_value_test, pred_value_test)
# false positives and false negatives
FP_test <- sum(actual_value_test == 0 & pred_value_test == 1)
FN_test <- sum(actual_value_test == 1 & pred_value_test == 0)
# misclassification rate - 2 ways
MR_test1 <- (FP_test + FN_test) / sum(confusion_matrix_test)
MR_test2 <- 1 - sum(diag(confusion_matrix_test))/sum(confusion_matrix_test)
# showing confusion matrix and misclassification rate
confusion_matrix_test## pred_value_test
## actual_value_test 0 1
## 0 21 33
## 1 12 134MR_test1## [1] 0.225MR_test2## [1] 0.225# accuracyYour comment: Based on the confusion matrix, there are 21 true negatives (model predicted bad credit and the individual actually had bad credit), 33 false positives (the model predicted good credit but the individual actually had bad credit), 12 false negatives (the model predicted bad credit but the individual actually had good credit), and 134 true positives (the model predicted good credit and the individual actually had good credit). I also computed the accuracy rate, which indicates that 78.25% of the test cases were predicted correctly. The misclassification rate is 0.225, which represents the number of false positives plus the false negatives divided by the total number of observations. This means that 22.5% of the predictions made by the model are incorrect. This test model has a slightly higher misclassification rate than the training model.
2. Please generate the ROC curve and calculate the AUC for the test set. Please comment on this AUC. (2 pts)
# generate ROC curve
roc_obj_test <- roc(actual_value_test, pred_prob_test)## Setting levels: control = 0, case = 1## Setting direction: controls < casesplot(roc_obj_test)
# calculate AUC
auc_test <- auc(actual_value_test, pred_prob_test)## Setting levels: control = 0, case = 1
## Setting direction: controls < cases# view AUC
auc_test## Area under the curve: 0.8182Comment: The AUC for the test set is 0.6533, which represents an aggregate measure of the model’s performance across all possible classification thresholds. In this case, it specifically indicates the model’s ability to differentiate between good and bad credit worthiness across different cut-off probabilities. An AUC of 1 indicates a perfect model, while an AUC of 0.5 indicates a model that is no better than random guessing. Since this model’s AUC falls between 0.5 and 1, it indicates a moderately strong predictive model, though not as strong as the model for the training set.