Perhitungan Eigen value, eigen vector, Variance, Covariance Matrix, Correlation Matrix dengan R.
data <- data.frame(
Gender = c(0, 1, 0, 1, 1),
Age = c(30.83, 58.67, 24.50, 27.83, 20.17),
Debt = c(0.000, 4.460, 0.500, 1.540, 5.625),
Married = c(1, 1, 1, 1, 1),
BankCustomer = c(1, 1, 1, 1, 1),
YearsEmployed = c(1.25, 3.04, 1.50, 3.75, 1.71),
PriorDefault = c(1, 1, 1, 1, 1),
Employed = c(1, 1, 0, 1, 0),
CreditScore = c(1, 1, 0, 1, 0),
DriversLicense = c(1, 6, 0, 5, 0),
ZipCode = c(202, 43, 280, 100, 120),
Income = c(0, 560, 824, 3, 0),
Approved = c(1, 1, 1, 1, 1)
)# Variance-Covariance Matrix
cov_matrix <- cov(data)
# Eigenvalues dan Eigenvectors
eigen_result <- eigen(cov_matrix)print(eigen_result$values)## [1] 1.529992e+05 7.738576e+03 7.531000e+01 4.676731e+00 1.039317e-13
## [6] 6.163538e-14 2.955816e-15 1.594150e-16 1.339176e-17 7.657497e-31
## [11] 0.000000e+00 -4.413988e-16 -8.349156e-15print(eigen_result$vectors)## [,1] [,2] [,3] [,4] [,5]
## [1,] -4.632102e-04 -0.005211269 -2.742947e-02 -8.669831e-03 0.0000000000
## [2,] 1.289702e-02 -0.131558350 9.769654e-01 1.431920e-01 -0.0740696735
## [3,] -8.188158e-04 -0.019604797 -1.280577e-01 6.333180e-01 -0.6359855744
## [4,] 0.000000e+00 0.000000000 3.330669e-16 -1.405126e-14 0.0127883345
## [5,] 0.000000e+00 0.000000000 0.000000e+00 0.000000e+00 -0.0000988402
## [6,] -3.179469e-04 -0.009024728 -1.820789e-02 -3.306622e-01 -0.6270593846
## [7,] 0.000000e+00 0.000000000 0.000000e+00 0.000000e+00 0.0000000000
## [8,] -4.517914e-04 -0.002638175 4.505918e-02 -1.151453e-01 0.1712609343
## [9,] -4.517914e-04 -0.002638175 4.505918e-02 -1.151453e-01 0.1712410029
## [10,] -3.496005e-05 -0.027135313 8.411290e-02 -6.651158e-01 -0.3696218245
## [11,] 8.349383e-02 0.987359655 1.279472e-01 9.497448e-03 -0.0371849215
## [12,] 9.964241e-01 -0.081056246 -2.344628e-02 -2.366064e-03 0.0034941755
## [13,] 0.000000e+00 0.000000000 0.000000e+00 0.000000e+00 0.0000000000
## [,6] [,7] [,8] [,9] [,10]
## [1,] 0.0000000000 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [2,] -0.0362743881 -8.506743e-04 1.421209e-04 7.227101e-06 9.376342e-18
## [3,] 0.4190113965 -1.849049e-02 1.450571e-05 -2.399919e-05 -1.144322e-16
## [4,] 0.0386845061 -8.229939e-01 8.659246e-02 5.309228e-03 1.036037e-15
## [5,] -0.0011608561 7.539007e-02 9.920724e-01 9.068823e-02 3.808671e-14
## [6,] -0.5094450596 -2.963527e-01 4.949860e-03 -9.064455e-05 -3.700425e-16
## [7,] 0.0000000000 2.664535e-15 4.329870e-14 -5.606626e-14 -1.000000e+00
## [8,] 0.3883016027 -2.939215e-01 6.679869e-02 -7.044117e-01 4.180277e-14
## [9,] 0.3882861432 -2.976905e-01 -6.161545e-02 7.039542e-01 -4.301843e-14
## [10,] 0.5102106799 2.319864e-01 -3.313929e-03 1.029918e-04 2.874837e-16
## [11,] 0.0149083040 1.565397e-03 -1.250969e-05 1.229105e-06 1.745740e-19
## [12,] -0.0002279255 -4.900218e-04 3.033955e-06 -4.490065e-07 -8.892056e-19
## [13,] 0.0000000000 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
## [,11] [,12] [,13]
## [1,] 0 0.000000e+00 9.995725e-01
## [2,] 0 2.925563e-03 2.737119e-02
## [3,] 0 -4.160475e-02 1.876463e-03
## [4,] 0 5.599059e-01 -1.179612e-16
## [5,] 0 -4.339255e-02 0.000000e+00
## [6,] 0 -3.868470e-01 -3.414856e-03
## [7,] 0 -2.498002e-16 0.000000e+00
## [8,] 0 -4.664202e-01 2.237975e-04
## [9,] 0 -4.654533e-01 2.237975e-04
## [10,] 0 3.146947e-01 -3.602235e-03
## [11,] 0 2.122145e-03 8.779689e-03
## [12,] 0 -7.847975e-04 -6.247516e-04
## [13,] 1 0.000000e+00 0.000000e+00print(cov_matrix)## Gender Age Debt Married BankCustomer
## Gender 0.3000 2.367500 1.087500 0 0
## Age 2.3675 231.361400 9.345663 0 0
## Debt 1.0875 9.345663 6.187675 0 0
## Married 0.0000 0.000000 0.000000 0 0
## BankCustomer 0.0000 0.000000 0.000000 0 0
## YearsEmployed 0.4375 6.999375 0.605225 0 0
## PriorDefault 0.0000 0.000000 0.000000 0 0
## Employed 0.0500 5.032500 -0.318750 0 0
## CreditScore 0.0500 5.032500 -0.318750 0 0
## DriversLicense 0.9500 33.300000 1.340000 0 0
## ZipCode -46.0000 -831.032500 -161.461250 0 0
## Income -67.3000 2046.972500 -112.313750 0 0
## Approved 0.0000 0.000000 0.000000 0 0
## YearsEmployed PriorDefault Employed CreditScore DriversLicense
## Gender 0.437500 0 0.05000 0.05000 0.95
## Age 6.999375 0 5.03250 5.03250 33.30
## Debt 0.605225 0 -0.31875 -0.31875 1.34
## Married 0.000000 0 0.00000 0.00000 0.00
## BankCustomer 0.000000 0 0.00000 0.00000 0.00
## YearsEmployed 1.182050 0 0.32250 0.32250 2.81
## PriorDefault 0.000000 0 0.00000 0.00000 0.00
## Employed 0.322500 0 0.30000 0.30000 1.20
## CreditScore 0.322500 0 0.30000 0.30000 1.20
## DriversLicense 2.810000 0 1.20000 1.20000 8.30
## ZipCode -73.207500 0 -25.50000 -25.50000 -207.00
## Income -42.775000 0 -67.30000 -67.30000 11.55
## Approved 0.000000 0 0.00000 0.00000 0.00
## ZipCode Income Approved
## Gender -46.0000 -67.3000 0
## Age -831.0325 2046.9725 0
## Debt -161.4613 -112.3137 0
## Married 0.0000 0.0000 0
## BankCustomer 0.0000 0.0000 0
## YearsEmployed -73.2075 -42.7750 0
## PriorDefault 0.0000 0.0000 0
## Employed -25.5000 -67.3000 0
## CreditScore -25.5000 -67.3000 0
## DriversLicense -207.0000 11.5500 0
## ZipCode 8612.0000 12109.2500 0
## Income 12109.2500 151957.8000 0
## Approved 0.0000 0.0000 0cor_matrix <- cor(data)## Warning in cor(data): the standard deviation is zeroprint(cor_matrix)## Gender Age Debt Married BankCustomer
## Gender 1.0000000 0.2841737 0.7981874 NA NA
## Age 0.2841737 1.0000000 0.2470022 NA NA
## Debt 0.7981874 0.2470022 1.0000000 NA NA
## Married NA NA NA 1 NA
## BankCustomer NA NA NA NA 1
## YearsEmployed 0.7346822 0.4232489 0.2237872 NA NA
## PriorDefault NA NA NA NA NA
## Employed 0.1666667 0.6040567 -0.2339515 NA NA
## CreditScore 0.1666667 0.6040567 -0.2339515 NA NA
## DriversLicense 0.6020380 0.7599058 0.1869829 NA NA
## ZipCode -0.9049929 -0.5887359 -0.6994434 NA NA
## Income -0.3152049 0.3452272 -0.1158264 NA NA
## Approved NA NA NA NA NA
## YearsEmployed PriorDefault Employed CreditScore DriversLicense
## Gender 0.7346822 NA 0.1666667 0.1666667 0.60203804
## Age 0.4232489 NA 0.6040567 0.6040567 0.75990576
## Debt 0.2237872 NA -0.2339515 -0.2339515 0.18698295
## Married NA NA NA NA NA
## BankCustomer NA NA NA NA NA
## YearsEmployed 1.0000000 NA 0.5415657 0.5415657 0.89711754
## PriorDefault NA 1 NA NA NA
## Employed 0.5415657 NA 1.0000000 1.0000000 0.76046910
## CreditScore 0.5415657 NA 1.0000000 1.0000000 0.76046910
## DriversLicense 0.8971175 NA 0.7604691 0.7604691 1.00000000
## ZipCode -0.7255806 NA -0.5016809 -0.5016809 -0.77424657
## Income -0.1009278 NA -0.3152049 -0.3152049 0.01028446
## Approved NA NA NA NA NA
## ZipCode Income Approved
## Gender -0.9049929 -0.31520488 NA
## Age -0.5887359 0.34522724 NA
## Debt -0.6994434 -0.11582643 NA
## Married NA NA NA
## BankCustomer NA NA NA
## YearsEmployed -0.7255806 -0.10092775 NA
## PriorDefault NA NA NA
## Employed -0.5016809 -0.31520488 NA
## CreditScore -0.5016809 -0.31520488 NA
## DriversLicense -0.7742466 0.01028446 NA
## ZipCode 1.0000000 0.33473701 NA
## Income 0.3347370 1.00000000 NA
## Approved NA NA 1