data <- data.frame(
  Gender =c(1, 0, 0, 1, 1),
  Age =c(30.83, 58.67, 24.50, 27.83, 20.17),
  Dept =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, 0, 0, 1, 0),
  CreditStore =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, 120),
  Income =c(0, 560, 824, 3, 0),
  Approved =c(1, 1, 1, 1, 1),
  Industry =c("Industrials", "Materials", "Materials", "Industrials", "Industrials")
)
print(data)
##   Gender   Age  Dept Married BankCustomer YearsEmployed PriorDefault Employed
## 1      1 30.83 0.000       1            1          1.25            1        1
## 2      0 58.67 4.460       1            1          3.04            1        0
## 3      0 24.50 0.500       1            1          1.50            1        0
## 4      1 27.83 1.540       1            1          3.75            1        1
## 5      1 20.17 5.625       1            1          1.71            1        0
##   CreditStore DriverLicense      Citizen ZipCode Income Approved    Industry
## 1           1             0      ByBIrth     202      0        1 Industrials
## 2           6             0      ByBirth      43    560        1   Materials
## 3           0             0      ByBirth     280    824        1   Materials
## 4           5             1      ByBirth     100      3        1 Industrials
## 5           0             0 ByOtherMeans     120      0        1 Industrials
#Memilih kolom numerik
data_numeric <- data[, sapply(data, is.numeric)]
print(data_numeric)
##   Gender   Age  Dept Married BankCustomer YearsEmployed PriorDefault Employed
## 1      1 30.83 0.000       1            1          1.25            1        1
## 2      0 58.67 4.460       1            1          3.04            1        0
## 3      0 24.50 0.500       1            1          1.50            1        0
## 4      1 27.83 1.540       1            1          3.75            1        1
## 5      1 20.17 5.625       1            1          1.71            1        0
##   CreditStore DriverLicense ZipCode Income Approved
## 1           1             0     202      0        1
## 2           6             0      43    560        1
## 3           0             0     280    824        1
## 4           5             1     100      3        1
## 5           0             0     120      0        1
#Kovarians matriks
cov_matrix <- cov(data_numeric)
print(cov_matrix)
##                  Gender         Age        Dept Married BankCustomer
## Gender           0.3000   -4.592500   -0.027500       0            0
## Age             -4.5925  231.361400    9.345663       0            0
## Dept            -0.0275    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   -0.0100    6.999375    0.605225       0            0
## PriorDefault     0.0000    0.000000    0.000000       0            0
## Employed         0.2000   -1.535000   -0.827500       0            0
## CreditStore     -0.3000   33.300000    1.340000       0            0
## DriverLicense    0.1000   -1.142500   -0.221250       0            0
## ZipCode         -6.2500 -831.032500 -161.461250       0            0
## Income        -207.3000 2046.972500 -112.313750       0            0
## Approved         0.0000    0.000000    0.000000       0            0
##               YearsEmployed PriorDefault  Employed CreditStore DriverLicense
## Gender            -0.010000            0    0.2000       -0.30       0.10000
## Age                6.999375            0   -1.5350       33.30      -1.14250
## Dept               0.605225            0   -0.8275        1.34      -0.22125
## Married            0.000000            0    0.0000        0.00       0.00000
## BankCustomer       0.000000            0    0.0000        0.00       0.00000
## YearsEmployed      1.182050            0    0.1250        2.81       0.37500
## PriorDefault       0.000000            0    0.0000        0.00       0.00000
## Employed           0.125000            0    0.3000        0.30       0.15000
## CreditStore        2.810000            0    0.3000        8.30       0.65000
## DriverLicense      0.375000            0    0.1500        0.65       0.20000
## ZipCode          -73.207500            0    1.0000     -207.00     -12.25000
## Income           -42.775000            0 -137.9500       11.55     -68.60000
## Approved           0.000000            0    0.0000        0.00       0.00000
##                  ZipCode      Income Approved
## Gender           -6.2500   -207.3000        0
## Age            -831.0325   2046.9725        0
## Dept           -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          1.0000   -137.9500        0
## CreditStore    -207.0000     11.5500        0
## DriverLicense   -12.2500    -68.6000        0
## ZipCode        8612.0000  12109.2500        0
## Income        12109.2500 151957.8000        0
## Approved          0.0000      0.0000        0
#Eigen Value dan Eigen Vector
eigen_result <- eigen(cov_matrix)
eigen_values <- eigen_result$values
eigen_vectors <- eigen_result$vectors

print("Eigen Values:")
## [1] "Eigen Values:"
print(eigen_values)
##  [1]  1.529995e+05  7.738299e+03  7.501731e+01  4.805864e+00  4.037435e-17
##  [6]  7.944076e-30  0.000000e+00 -2.688251e-16 -5.629193e-16 -1.843004e-15
## [11] -1.925470e-15 -1.215216e-13 -2.992215e-13
print("Eigen Vectors:")
## [1] "Eigen Vectors:"
print(eigen_vectors)
##                [,1]          [,2]          [,3]          [,4]          [,5]
##  [1,]  1.353862e-03  1.453043e-03  5.918653e-03  1.112572e-02  0.000000e+00
##  [2,] -1.289707e-02 -1.315593e-01 -9.789674e-01 -1.322619e-01 -2.387329e-04
##  [3,]  8.188055e-04 -1.960562e-02  1.279405e-01 -6.259008e-01 -2.839654e-03
##  [4,]  1.355253e-20 -6.938894e-18  1.110223e-16 -6.938894e-17 -3.130916e-02
##  [5,]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  4.904476e-01
##  [6,]  3.179442e-04 -9.024765e-03  1.843188e-02  3.260297e-01 -4.365799e-01
##  [7,]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00 -1.664282e-12
##  [8,]  8.979953e-04  1.599538e-03 -2.667001e-02  1.467268e-01 -3.626692e-01
##  [9,]  3.495043e-05 -2.713538e-02 -8.389858e-02  6.569034e-01  1.202893e-01
## [10,]  4.535470e-04 -8.272546e-04  1.330957e-02  1.766350e-01  6.495168e-01
## [11,] -8.349333e-02  9.873782e-01 -1.280608e-01 -8.934813e-03  3.429872e-04
## [12,] -9.964231e-01 -8.104951e-02  2.349989e-02  2.301082e-03 -1.942709e-04
## [13,]  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00  0.000000e+00
##                [,6] [,7]          [,8]          [,9]        [,10]         [,11]
##  [1,]  0.000000e+00    0  0.000000e+00  0.000000e+00  0.999918618  0.000000e+00
##  [2,]  3.826392e-16    0 -4.308543e-04 -9.377325e-04  0.007474909  5.897488e-04
##  [3,]  4.368016e-15    0 -1.320765e-02 -1.793913e-02  0.006234250  1.319211e-02
##  [4,]  5.305223e-14    0  1.898361e-01  4.871097e-01  0.000000000  8.518837e-01
##  [5,] -8.233721e-13    0  7.325549e-01 -4.574660e-01  0.000000000  1.163630e-01
##  [6,]  7.262236e-13    0  2.835177e-01 -3.256251e-02 -0.003724028 -6.104740e-02
##  [7,] -1.000000e+00    0 -1.059916e-15  1.238593e-14  0.000000000 -5.440093e-15
##  [8,]  5.924166e-13    0 -2.774154e-01 -7.152283e-01 -0.001478251  4.575999e-01
##  [9,] -1.974611e-13    0  4.770644e-02  1.818601e-01 -0.006773129 -1.098495e-01
## [10,] -1.082466e-12    0 -5.172239e-01 -8.609839e-02 -0.002043546  1.880781e-01
## [11,] -4.927008e-16    0  3.541792e-03  5.213148e-03 -0.000464348 -3.755040e-03
## [12,]  3.059082e-16    0 -6.953539e-04 -1.127208e-03  0.001302204  7.925272e-04
## [13,]  0.000000e+00    1  0.000000e+00  0.000000e+00  0.000000000  0.000000e+00
##               [,12]         [,13]
##  [1,]  0.0000000000  0.0000000000
##  [2,] -0.0017192150 -0.0812099920
##  [3,] -0.6022334674 -0.4775898218
##  [4,]  0.0004225671 -0.0003623297
##  [5,] -0.0028846332  0.0008601727
##  [6,]  0.2512599773 -0.7445579416
##  [7,]  0.0000000000  0.0000000000
##  [8,] -0.1967804235  0.0979511527
##  [9,] -0.7062277155 -0.0037057302
## [10,]  0.1893841249 -0.4478533205
## [11,] -0.0286664475 -0.0275303208
## [12,]  0.0018936819  0.0026122398
## [13,]  0.0000000000  0.0000000000
#Variance dan Covariance Matrix
variances <- apply(data_numeric, 2, var)
print("Variance:")
## [1] "Variance:"
print(variances)
##        Gender           Age          Dept       Married  BankCustomer 
##  3.000000e-01  2.313614e+02  6.187675e+00  0.000000e+00  0.000000e+00 
## YearsEmployed  PriorDefault      Employed   CreditStore DriverLicense 
##  1.182050e+00  0.000000e+00  3.000000e-01  8.300000e+00  2.000000e-01 
##       ZipCode        Income      Approved 
##  8.612000e+03  1.519578e+05  0.000000e+00
print("Covariance Matrix:")
## [1] "Covariance Matrix:"
print(cov_matrix)
##                  Gender         Age        Dept Married BankCustomer
## Gender           0.3000   -4.592500   -0.027500       0            0
## Age             -4.5925  231.361400    9.345663       0            0
## Dept            -0.0275    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   -0.0100    6.999375    0.605225       0            0
## PriorDefault     0.0000    0.000000    0.000000       0            0
## Employed         0.2000   -1.535000   -0.827500       0            0
## CreditStore     -0.3000   33.300000    1.340000       0            0
## DriverLicense    0.1000   -1.142500   -0.221250       0            0
## ZipCode         -6.2500 -831.032500 -161.461250       0            0
## Income        -207.3000 2046.972500 -112.313750       0            0
## Approved         0.0000    0.000000    0.000000       0            0
##               YearsEmployed PriorDefault  Employed CreditStore DriverLicense
## Gender            -0.010000            0    0.2000       -0.30       0.10000
## Age                6.999375            0   -1.5350       33.30      -1.14250
## Dept               0.605225            0   -0.8275        1.34      -0.22125
## Married            0.000000            0    0.0000        0.00       0.00000
## BankCustomer       0.000000            0    0.0000        0.00       0.00000
## YearsEmployed      1.182050            0    0.1250        2.81       0.37500
## PriorDefault       0.000000            0    0.0000        0.00       0.00000
## Employed           0.125000            0    0.3000        0.30       0.15000
## CreditStore        2.810000            0    0.3000        8.30       0.65000
## DriverLicense      0.375000            0    0.1500        0.65       0.20000
## ZipCode          -73.207500            0    1.0000     -207.00     -12.25000
## Income           -42.775000            0 -137.9500       11.55     -68.60000
## Approved           0.000000            0    0.0000        0.00       0.00000
##                  ZipCode      Income Approved
## Gender           -6.2500   -207.3000        0
## Age            -831.0325   2046.9725        0
## Dept           -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          1.0000   -137.9500        0
## CreditStore    -207.0000     11.5500        0
## DriverLicense   -12.2500    -68.6000        0
## ZipCode        8612.0000  12109.2500        0
## Income        12109.2500 151957.8000        0
## Approved          0.0000      0.0000        0
#Correlation Matrix
cor_matrix <- cor(data_numeric)
## Warning in cor(data_numeric): the standard deviation is zero
print("Correlation Matrix:")
## [1] "Correlation Matrix:"
print(cor_matrix)
##                    Gender        Age        Dept Married BankCustomer
## Gender         1.00000000 -0.5512430 -0.02018405      NA           NA
## Age           -0.55124300  1.0000000  0.24700224      NA           NA
## Dept          -0.02018405  0.2470022  1.00000000      NA           NA
## Married                NA         NA          NA       1           NA
## BankCustomer           NA         NA          NA      NA            1
## YearsEmployed -0.01679274  0.4232489  0.22378717      NA           NA
## PriorDefault           NA         NA          NA      NA           NA
## Employed       0.66666667 -0.1842478 -0.60735642      NA           NA
## CreditStore   -0.19011728  0.7599058  0.18698295      NA           NA
## DriverLicense  0.40824829 -0.1679561 -0.19888615      NA           NA
## ZipCode       -0.12296100 -0.5887359 -0.69944336      NA           NA
## Income        -0.97090598  0.3452272 -0.11582643      NA           NA
## Approved               NA         NA          NA      NA           NA
##               YearsEmployed PriorDefault    Employed CreditStore DriverLicense
## Gender          -0.01679274           NA  0.66666667 -0.19011728     0.4082483
## Age              0.42324895           NA -0.18424780  0.75990576    -0.1679561
## Dept             0.22378717           NA -0.60735642  0.18698295    -0.1988861
## Married                  NA           NA          NA          NA            NA
## BankCustomer             NA           NA          NA          NA            NA
## YearsEmployed    1.00000000           NA  0.20990919  0.89711754     0.7712556
## PriorDefault             NA            1          NA          NA            NA
## Employed         0.20990919           NA  1.00000000  0.19011728     0.6123724
## CreditStore      0.89711754           NA  0.19011728  1.00000000     0.5044978
## DriverLicense    0.77125563           NA  0.61237244  0.50449784     1.0000000
## ZipCode         -0.72558057           NA  0.01967376 -0.77424657    -0.2951679
## Income          -0.10092775           NA -0.64609976  0.01028446    -0.3935026
## Approved                 NA           NA          NA          NA            NA
##                   ZipCode      Income Approved
## Gender        -0.12296100 -0.97090598       NA
## Age           -0.58873594  0.34522724       NA
## Dept          -0.69944336 -0.11582643       NA
## Married                NA          NA       NA
## BankCustomer           NA          NA       NA
## YearsEmployed -0.72558057 -0.10092775       NA
## PriorDefault           NA          NA       NA
## Employed       0.01967376 -0.64609976       NA
## CreditStore   -0.77424657  0.01028446       NA
## DriverLicense -0.29516787 -0.39350261       NA
## ZipCode        1.00000000  0.33473701       NA
## Income         0.33473701  1.00000000       NA
## Approved               NA          NA        1