# Create the dataset (numeric columns only)
data <- data.frame(
Age = c(30.83, 58.67, 24.50, 27.83, 20.17),
Debt = c(0.000, 4.460, 0.500, 1.540, 5.625),
YearsEmployed = c(1.25, 3.04, 1.50, 3.75, 1.71),
PriorDefault = c(1, 1, 1, 1, 1),
Employed = c(1, 0, 0, 0, 0),
CreditScore = c(1, 6, 0, 5, 0),
DriversLicense = c(0, 0, 0, 1, 0),
ZipCode = c(202, 43, 280, 100, 120),
Income = c(0, 560, 824, 3, 0),
Approved = c(1, 0, 1, 1, 1)
)
# Compute Eigenvalues and Eigenvectors
eigen_result <- eigen(cov(data))
print("Eigenvalues:")
## [1] "Eigenvalues:"
print(eigen_result$values)
## [1] 1.529992e+05 7.738448e+03 7.510682e+01 4.711088e+00 1.044619e-12
## [6] 6.669169e-16 -1.336583e-18 -3.742133e-16 -3.245420e-12 -8.696304e-12
print("Eigenvectors:")
## [1] "Eigenvectors:"
print(eigen_result$vectors)
## [,1] [,2] [,3] [,4] [,5]
## [1,] -1.289709e-02 -1.315582e-01 0.97843164 1.276634e-01 0.0000000000
## [2,] 8.188101e-04 -1.960534e-02 -0.12762331 6.329455e-01 0.1225411638
## [3,] 3.179433e-04 -9.024713e-03 -0.01854659 -3.291788e-01 0.6629357695
## [4,] 5.421011e-20 1.734723e-18 0.00000000 1.110223e-16 -0.0001933776
## [5,] 4.444488e-04 2.426767e-03 0.03996726 2.996410e-02 0.5058179010
## [6,] 3.494784e-05 -2.713520e-02 0.08359503 -6.639822e-01 -0.0510799635
## [7,] 4.535468e-04 -8.272648e-04 -0.01336967 -1.783218e-01 -0.4637822510
## [8,] -8.349345e-02 9.873686e-01 0.12800222 8.073894e-03 0.0065793483
## [9,] -9.964242e-01 -8.104919e-02 -0.02349427 -2.019687e-03 -0.0003464269
## [10,] 4.462058e-04 4.237608e-03 -0.01841268 -3.294375e-02 -0.2681445422
## [,6] [,7] [,8] [,9] [,10]
## [1,] 0.0000000000 0.000000e+00 0.0000000000 9.433819e-02 0.000000e+00
## [2,] 0.0002317823 8.961608e-05 0.0016607465 4.398860e-01 -6.117094e-01
## [3,] -0.0009849804 2.421517e-03 -0.0161448382 6.252767e-01 2.459543e-01
## [4,] 0.9544420336 -2.781433e-01 -0.1080586763 -1.110223e-16 -1.121145e-05
## [5,] 0.1281844941 5.843865e-01 -0.3728906377 -4.516258e-01 -2.017296e-01
## [6,] -0.0022520500 -7.271480e-02 0.1674424427 -6.309641e-03 -7.179309e-01
## [7,] -0.0171834526 2.309699e-01 -0.7454617318 3.788866e-01 -4.139027e-03
## [8,] -0.0015253873 -6.220167e-03 0.0025288204 2.700337e-02 -2.936666e-02
## [9,] 0.0002973823 1.208974e-03 -0.0004848184 -2.843811e-03 1.960321e-03
## [10,] 0.2688965565 7.228058e-01 0.5150297912 2.415195e-01 9.118760e-02
# Compute Variance-Covariance Matrix
cov_matrix <- cov(data)
print("Variance-Covariance Matrix:")
## [1] "Variance-Covariance Matrix:"
print(cov_matrix)
## Age Debt YearsEmployed PriorDefault Employed
## Age 231.361400 9.345663 6.999375 0 -0.39250
## Debt 9.345663 6.187675 0.605225 0 -0.60625
## YearsEmployed 6.999375 0.605225 1.182050 0 -0.25000
## PriorDefault 0.000000 0.000000 0.000000 0 0.00000
## Employed -0.392500 -0.606250 -0.250000 0 0.20000
## CreditScore 33.300000 1.340000 2.810000 0 -0.35000
## DriversLicense -1.142500 -0.221250 0.375000 0 -0.05000
## ZipCode -831.032500 -161.461250 -73.207500 0 13.25000
## Income 2046.972500 -112.313750 -42.775000 0 -69.35000
## Approved -6.567500 -0.508750 -0.197500 0 0.05000
## CreditScore DriversLicense ZipCode Income Approved
## Age 33.30 -1.14250 -831.0325 2046.9725 -6.56750
## Debt 1.34 -0.22125 -161.4613 -112.3137 -0.50875
## YearsEmployed 2.81 0.37500 -73.2075 -42.7750 -0.19750
## PriorDefault 0.00 0.00000 0.0000 0.0000 0.00000
## Employed -0.35 -0.05000 13.2500 -69.3500 0.05000
## CreditScore 8.30 0.65000 -207.0000 11.5500 -0.90000
## DriversLicense 0.65 0.20000 -12.2500 -68.6000 0.05000
## ZipCode -207.00 -12.25000 8612.0000 12109.2500 26.50000
## Income 11.55 -68.60000 12109.2500 151957.8000 -70.65000
## Approved -0.90 0.05000 26.5000 -70.6500 0.20000
# Compute Correlation Matrix
cor_matrix <- cor(data)
## Warning in cor(data): the standard deviation is zero
print("Correlation Matrix:")
## [1] "Correlation Matrix:"
print(cor_matrix)
## Age Debt YearsEmployed PriorDefault Employed
## Age 1.00000000 0.2470022 0.4232489 NA -0.05770045
## Debt 0.24700224 1.0000000 0.2237872 NA -0.54497052
## YearsEmployed 0.42324895 0.2237872 1.0000000 NA -0.51417042
## PriorDefault NA NA NA 1 NA
## Employed -0.05770045 -0.5449705 -0.5141704 NA 1.00000000
## CreditScore 0.75990576 0.1869829 0.8971175 NA -0.27165268
## DriversLicense -0.16795609 -0.1988861 0.7712556 NA -0.25000000
## ZipCode -0.58873594 -0.6994434 -0.7255806 NA 0.31926321
## Income 0.34522724 -0.1158264 -0.1009278 NA -0.39780475
## Approved -0.96547189 -0.4573258 -0.4061946 NA 0.25000000
## CreditScore DriversLicense ZipCode Income Approved
## Age 0.75990576 -0.1679561 -0.5887359 0.34522724 -0.9654719
## Debt 0.18698295 -0.1988861 -0.6994434 -0.11582643 -0.4573258
## YearsEmployed 0.89711754 0.7712556 -0.7255806 -0.10092775 -0.4061946
## PriorDefault NA NA NA NA NA
## Employed -0.27165268 -0.2500000 0.3192632 -0.39780475 0.2500000
## CreditScore 1.00000000 0.5044978 -0.7742466 0.01028446 -0.6985355
## DriversLicense 0.50449784 1.0000000 -0.2951679 -0.39350261 0.2500000
## ZipCode -0.77424657 -0.2951679 1.0000000 0.33473701 0.6385264
## Income 0.01028446 -0.3935026 0.3347370 1.00000000 -0.4052618
## Approved -0.69853547 0.2500000 0.6385264 -0.40526180 1.0000000