data <- data.frame(
Gender = c(1,0,0,1,1),
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),
Industry = c("Industrials", "Materials", "Materials", "Industrials", "Industrials"),
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, 6, 0, 5, 0),
DriverLicense = c(0, 0, 0, 1, 0),
Citizen = c("ByBirth", "ByBirth", "ByBirth", "ByBirth", "ByOtherMeans"),
ZipCode = c(202, 43, 280, 100, 200),
Income = c(0, 560, 824, 3, 0),
Approved = c(1, 1, 1, 1, 1)
)
print(data)
## Gender Age Debt Married BankCustomer Industry YearsEmployed
## 1 1 30.83 0.000 1 1 Industrials 1.25
## 2 0 58.67 4.460 1 1 Materials 3.04
## 3 0 24.50 0.500 1 1 Materials 1.50
## 4 1 27.83 1.540 1 1 Industrials 3.75
## 5 1 20.17 5.625 1 1 Industrials 1.71
## PriorDefault Employed CreditScore DriverLicense Citizen ZipCode Income
## 1 1 1 1 0 ByBirth 202 0
## 2 1 1 6 0 ByBirth 43 560
## 3 1 0 0 0 ByBirth 280 824
## 4 1 1 5 1 ByBirth 100 3
## 5 1 0 0 0 ByOtherMeans 200 0
## Approved
## 1 1
## 2 1
## 3 1
## 4 1
## 5 1
# Konversi kategorikal menjadi numerik
data$Industry <- ifelse(data$Industry == "Industrials", 1, 2)
data$Citizen <- ifelse(data$Citizen == "ByBirth", 1, 2)
# Melihat data setelah konversi
print(data)
## Gender Age Debt Married BankCustomer Industry YearsEmployed PriorDefault
## 1 1 30.83 0.000 1 1 1 1.25 1
## 2 0 58.67 4.460 1 1 2 3.04 1
## 3 0 24.50 0.500 1 1 2 1.50 1
## 4 1 27.83 1.540 1 1 1 3.75 1
## 5 1 20.17 5.625 1 1 1 1.71 1
## Employed CreditScore DriverLicense Citizen ZipCode Income Approved
## 1 1 1 0 1 202 0 1
## 2 1 6 0 1 43 560 1
## 3 0 0 0 1 280 824 1
## 4 1 5 1 1 100 3 1
## 5 0 0 0 2 200 0 1
# Menggunakan semua data
data_num <- data
# Variance covariance matrix
cov_matrix <- cov(data_num)
# a) Eigen Values dan Eigen Vectors
eigen_values_vectors <- eigen(cov_matrix)
cat("Eigen Values:\n")
## Eigen Values:
print(eigen_values_vectors$values)
## [1] 1.522847e+05 8.604341e+03 4.326422e+01 5.823647e+00 3.422712e-13
## [6] 2.623138e-16 2.161620e-16 4.267156e-17 4.321305e-33 0.000000e+00
## [11] -2.235751e-17 -5.068396e-16 -1.123648e-15 -1.216216e-15 -2.300090e-13
cat("\nEigen Vectors:\n")
##
## Eigen Vectors:
print(eigen_values_vectors$vectors)
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1.359610e-03 0.001319120 7.274702e-03 1.455566e-02 0.0000000000
## [2,] -1.312477e-02 -0.137774563 -9.829297e-01 -2.264025e-02 -0.0731839253
## [3,] 7.650770e-04 -0.010798966 4.818303e-02 -9.260962e-01 -0.3720935912
## [4,] -1.355253e-20 0.000000000 -1.110223e-16 3.330669e-16 0.0007191097
## [5,] 0.000000e+00 0.000000000 0.000000e+00 0.000000e+00 0.0002880034
## [6,] -1.359610e-03 -0.001319120 -7.274702e-03 -1.455566e-02 0.0294359290
## [7,] 3.051069e-04 -0.009564355 8.739913e-02 9.293379e-02 -0.2533959625
## [8,] 0.000000e+00 0.000000000 0.000000e+00 0.000000e+00 0.0000000000
## [9,] 4.522227e-04 -0.004056268 -2.691879e-02 1.283498e-01 -0.2664127092
## [10,] -2.333447e-06 -0.029934496 5.062775e-02 2.867877e-01 -0.7441606960
## [11,] 4.549263e-04 -0.001506625 4.718909e-02 9.504761e-02 -0.2262784721
## [12,] 4.525352e-04 0.001405043 1.195153e-02 -1.581447e-01 0.3368587965
## [13,] -4.555716e-02 0.988946221 -1.332714e-01 -2.838211e-03 -0.0410078738
## [14,] -9.988730e-01 -0.043303531 1.909161e-02 -1.853130e-04 0.0023601291
## [15,] 0.000000e+00 0.000000000 0.000000e+00 0.000000e+00 0.0000000000
## [,6] [,7] [,8] [,9] [,10]
## [1,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0
## [2,] -7.131846e-04 -5.579001e-04 -6.309562e-04 4.430008e-18 0
## [3,] 3.111273e-03 1.770120e-03 7.441045e-04 -1.410697e-17 0
## [4,] 4.206137e-01 -8.882191e-01 1.704558e-02 4.395445e-16 0
## [5,] 3.897192e-02 1.861133e-01 -2.492221e-01 2.894621e-15 0
## [6,] 8.048605e-01 3.902005e-01 3.059233e-01 -2.337652e-15 0
## [7,] 5.408865e-03 1.270400e-02 4.864138e-01 -8.834866e-15 0
## [8,] 8.153200e-17 3.538836e-16 -1.254032e-14 -1.000000e+00 0
## [9,] 2.301632e-01 4.185930e-02 -2.988398e-02 -6.339192e-15 0
## [10,] -1.077354e-01 -6.488077e-02 -9.886059e-02 1.739907e-15 0
## [11,] 3.170182e-01 1.259495e-01 -6.831082e-01 1.062555e-14 0
## [12,] 9.295956e-02 -4.670419e-02 -3.606987e-01 -4.973859e-16 0
## [13,] -9.383848e-04 -9.673655e-04 1.353892e-03 -4.435752e-17 0
## [14,] -7.483749e-04 -4.191263e-04 -8.085448e-04 4.177263e-18 0
## [15,] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 1
## [,11] [,12] [,13] [,14] [,15]
## [1,] 0.000000e+00 0.000000e+00 0.000000000 9.998658e-01 0.0000000000
## [2,] -2.586579e-04 3.228009e-04 0.001789562 7.680680e-03 0.0936115386
## [3,] 5.181558e-04 1.808780e-03 0.023982656 1.314439e-02 -0.0262383784
## [4,] 1.592502e-02 -1.802545e-01 0.033356413 -1.734723e-18 -0.0013841020
## [5,] -3.739802e-01 -8.702142e-01 0.067801578 0.000000e+00 0.0006227185
## [6,] 1.488610e-01 -5.391849e-02 -0.279891666 2.684131e-04 -0.0425796973
## [7,] -2.959364e-01 1.161877e-02 0.261165427 -1.976579e-03 0.7257478722
## [8,] 8.975459e-15 -3.348884e-15 0.000000000 0.000000e+00 0.0000000000
## [9,] -6.504157e-01 3.315114e-01 0.315719098 -1.667878e-03 -0.4728289170
## [10,] 2.882809e-02 -4.789753e-02 -0.575807525 -4.503800e-03 -0.0151246427
## [11,] 2.799530e-01 1.463020e-01 0.380942806 -1.725630e-03 0.3311127701
## [12,] -4.978854e-01 2.712777e-01 -0.520256904 2.212784e-03 0.3581779578
## [13,] -3.378284e-03 -1.290681e-04 -0.012103334 -2.318079e-04 0.0172428294
## [14,] -5.277364e-04 4.197013e-04 0.001089695 1.279184e-03 -0.0016578535
## [15,] 0.000000e+00 0.000000e+00 0.000000000 0.000000e+00 0.0000000000
# b) Variance covariance matrix
cat("Variance-Covariance Matrix:\n")
## Variance-Covariance Matrix:
print(cov_matrix)
## Gender Age Debt Married BankCustomer Industry
## Gender 0.3000 -4.592500 -0.027500 0 0 -0.3000
## Age -4.5925 231.361400 9.345663 0 0 4.5925
## Debt -0.0275 9.345663 6.187675 0 0 0.0275
## Married 0.0000 0.000000 0.000000 0 0 0.0000
## BankCustomer 0.0000 0.000000 0.000000 0 0 0.0000
## Industry -0.3000 4.592500 0.027500 0 0 0.3000
## YearsEmployed -0.0100 6.999375 0.605225 0 0 0.0100
## PriorDefault 0.0000 0.000000 0.000000 0 0 0.0000
## Employed 0.0500 5.032500 -0.318750 0 0 -0.0500
## CreditScore -0.3000 33.300000 1.340000 0 0 0.3000
## DriverLicense 0.1000 -1.142500 -0.221250 0 0 -0.1000
## Citizen 0.1000 -3.057500 0.800000 0 0 -0.1000
## ZipCode 1.7500 -1075.632500 -97.461250 0 0 -1.7500
## Income -207.3000 2046.972500 -112.313750 0 0 207.3000
## Approved 0.0000 0.000000 0.000000 0 0 0.0000
## YearsEmployed PriorDefault Employed CreditScore DriverLicense
## Gender -0.010000 0 0.05000 -0.30 0.10000
## Age 6.999375 0 5.03250 33.30 -1.14250
## Debt 0.605225 0 -0.31875 1.34 -0.22125
## Married 0.000000 0 0.00000 0.00 0.00000
## BankCustomer 0.000000 0 0.00000 0.00 0.00000
## Industry 0.010000 0 -0.05000 0.30 -0.10000
## YearsEmployed 1.182050 0 0.32250 2.81 0.37500
## PriorDefault 0.000000 0 0.00000 0.00 0.00000
## Employed 0.322500 0 0.30000 1.20 0.10000
## CreditScore 2.810000 0 1.20000 8.30 0.65000
## DriverLicense 0.375000 0 0.10000 0.65 0.20000
## Citizen -0.135000 0 -0.15000 -0.60 -0.05000
## ZipCode -84.007500 0 -37.50000 -255.00 -16.25000
## Income -42.775000 0 -67.30000 11.55 -68.60000
## Approved 0.000000 0 0.00000 0.00 0.00000
## Citizen ZipCode Income Approved
## Gender 0.1000 1.75000 -207.3000 0
## Age -3.0575 -1075.63250 2046.9725 0
## Debt 0.8000 -97.46125 -112.3137 0
## Married 0.0000 0.00000 0.0000 0
## BankCustomer 0.0000 0.00000 0.0000 0
## Industry -0.1000 -1.75000 207.3000 0
## YearsEmployed -0.1350 -84.00750 -42.7750 0
## PriorDefault 0.0000 0.00000 0.0000 0
## Employed -0.1500 -37.50000 -67.3000 0
## CreditScore -0.6000 -255.00000 11.5500 0
## DriverLicense -0.0500 -16.25000 -68.6000 0
## Citizen 0.2000 8.75000 -69.3500 0
## ZipCode 8.7500 8732.00000 6561.2500 0
## Income -69.3500 6561.25000 151957.8000 0
## Approved 0.0000 0.00000 0.0000 0
# c) Correlation Matrix
cor_matrix <- cor(data_num)
## Warning in cor(data_num): the standard deviation is zero
cat("Correlation Matrix:\n")
## Correlation Matrix:
print(cor_matrix)
## Gender Age Debt Married BankCustomer
## Gender 1.00000000 -0.5512430 -0.02018405 NA NA
## Age -0.55124300 1.0000000 0.24700224 NA NA
## Debt -0.02018405 0.2470022 1.00000000 NA NA
## Married NA NA NA 1 NA
## BankCustomer NA NA NA NA 1
## Industry -1.00000000 0.5512430 0.02018405 NA NA
## YearsEmployed -0.01679274 0.4232489 0.22378717 NA NA
## PriorDefault NA NA NA NA NA
## Employed 0.16666667 0.6040567 -0.23395149 NA NA
## CreditScore -0.19011728 0.7599058 0.18698295 NA NA
## DriverLicense 0.40824829 -0.1679561 -0.19888615 NA NA
## Citizen 0.40824829 -0.4494755 0.71913635 NA NA
## ZipCode 0.03419169 -0.7567660 -0.41928697 NA NA
## Income -0.97090598 0.3452272 -0.11582643 NA NA
## Approved NA NA NA NA NA
## Industry YearsEmployed PriorDefault Employed CreditScore
## Gender -1.00000000 -0.01679274 NA 0.1666667 -0.19011728
## Age 0.55124300 0.42324895 NA 0.6040567 0.75990576
## Debt 0.02018405 0.22378717 NA -0.2339515 0.18698295
## Married NA NA NA NA NA
## BankCustomer NA NA NA NA NA
## Industry 1.00000000 0.01679274 NA -0.1666667 0.19011728
## YearsEmployed 0.01679274 1.00000000 NA 0.5415657 0.89711754
## PriorDefault NA NA 1 NA NA
## Employed -0.16666667 0.54156572 NA 1.0000000 0.76046910
## CreditScore 0.19011728 0.89711754 NA 0.7604691 1.00000000
## DriverLicense -0.40824829 0.77125563 NA 0.4082483 0.50449784
## Citizen -0.40824829 -0.27765203 NA -0.6123724 -0.46569032
## ZipCode -0.03419169 -0.82688150 NA -0.7326791 -0.94720563
## Income 0.97090598 -0.10092775 NA -0.3152049 0.01028446
## Approved NA NA NA NA NA
## DriverLicense Citizen ZipCode Income Approved
## Gender 0.4082483 0.4082483 0.03419169 -0.97090598 NA
## Age -0.1679561 -0.4494755 -0.75676598 0.34522724 NA
## Debt -0.1988861 0.7191364 -0.41928697 -0.11582643 NA
## Married NA NA NA NA NA
## BankCustomer NA NA NA NA NA
## Industry -0.4082483 -0.4082483 -0.03419169 0.97090598 NA
## YearsEmployed 0.7712556 -0.2776520 -0.82688150 -0.10092775 NA
## PriorDefault NA NA NA NA NA
## Employed 0.4082483 -0.6123724 -0.73267906 -0.31520488 NA
## CreditScore 0.5044978 -0.4656903 -0.94720563 0.01028446 NA
## DriverLicense 1.0000000 -0.2500000 -0.38884946 -0.39350261 NA
## Citizen -0.2500000 1.0000000 0.20938048 -0.39780475 NA
## ZipCode -0.3888495 0.2093805 1.00000000 0.18012261 NA
## Income -0.3935026 -0.3978048 0.18012261 1.00000000 NA
## Approved NA NA NA NA 1