1 Memuat Data Numerik

data <- data.frame(
  Gender = c(0, 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),
  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),
  DriversLicense = c(0, 0, 0, 1, 0),
  ZipCode = c(202, 43, 280, 100, 120),
  Income = c(0, 560, 824, 3, 0),
  Approved = c(1, 1, 1, 1, 1)
)
knitr::kable(data, caption = "Tabel: Data Numerik (termasuk variabel biner)")
Tabel: Data Numerik (termasuk variabel biner)
Gender Age Debt Married BankCustomer YearsEmployed PriorDefault Employed CreditScore DriversLicense ZipCode Income Approved
0 30.83 0.000 1 1 1.25 1 1 1 0 202 0 1
0 58.67 4.460 1 1 3.04 1 1 6 0 43 560 1
0 24.50 0.500 1 1 1.50 1 0 0 0 280 824 1
1 27.83 1.540 1 1 3.75 1 1 5 1 100 3 1
1 20.17 5.625 1 1 1.71 1 0 0 0 120 0 1

1.1 Variance-Covariance Matrix

cov_matrix <- cov(data)
knitr::kable(round(cov_matrix, 2), caption = "Tabel: Variance-Covariance Matrix")
Tabel: Variance-Covariance Matrix
Gender Age Debt Married BankCustomer YearsEmployed PriorDefault Employed CreditScore DriversLicense ZipCode Income Approved
Gender 0.30 -4.20 0.58 0 0 0.24 0 -0.05 0.05 0.15 -19.50 -137.95 0
Age -4.20 231.36 9.35 0 0 7.00 0 5.03 33.30 -1.14 -831.03 2046.97 0
Debt 0.58 9.35 6.19 0 0 0.61 0 -0.32 1.34 -0.22 -161.46 -112.31 0
Married 0.00 0.00 0.00 0 0 0.00 0 0.00 0.00 0.00 0.00 0.00 0
BankCustomer 0.00 0.00 0.00 0 0 0.00 0 0.00 0.00 0.00 0.00 0.00 0
YearsEmployed 0.24 7.00 0.61 0 0 1.18 0 0.32 2.81 0.38 -73.21 -42.77 0
PriorDefault 0.00 0.00 0.00 0 0 0.00 0 0.00 0.00 0.00 0.00 0.00 0
Employed -0.05 5.03 -0.32 0 0 0.32 0 0.30 1.20 0.10 -25.50 -67.30 0
CreditScore 0.05 33.30 1.34 0 0 2.81 0 1.20 8.30 0.65 -207.00 11.55 0
DriversLicense 0.15 -1.14 -0.22 0 0 0.38 0 0.10 0.65 0.20 -12.25 -68.60 0
ZipCode -19.50 -831.03 -161.46 0 0 -73.21 0 -25.50 -207.00 -12.25 8612.00 12109.25 0
Income -137.95 2046.97 -112.31 0 0 -42.77 0 -67.30 11.55 -68.60 12109.25 151957.80 0
Approved 0.00 0.00 0.00 0 0 0.00 0 0.00 0.00 0.00 0.00 0.00 0

1.2 Eigenvalue dan Eigenvector

eigen_result <- eigen(cov_matrix)
print(round(eigen_result$values, 3))
##  [1] 152999.262   7738.325     75.272      4.772      0.000      0.000
##  [7]      0.000      0.000      0.000      0.000      0.000      0.000
## [13]      0.000
knitr::kable(round(eigen_result$vectors, 3), caption = "Tabel: Eigenvectors")
Tabel: Eigenvectors
0.001 -0.001 -0.046 -0.041 0.000 0.000 0.000 0.000 0 0 0.998 0.000 0.000
-0.013 -0.132 0.977 0.132 0.005 0.002 0.000 0.000 0 0 0.050 0.005 -0.086
0.001 -0.020 -0.128 0.628 -0.467 -0.015 -0.016 -0.001 0 0 0.020 -0.358 -0.492
0.000 0.000 0.000 0.000 0.616 0.013 -0.027 0.004 0 0 0.000 -0.787 -0.011
0.000 0.000 0.000 0.000 0.001 0.113 0.096 -0.989 0 0 0.000 -0.006 0.000
0.000 -0.009 -0.018 -0.327 0.170 0.145 0.590 0.073 0 0 -0.014 0.125 -0.688
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0 1 0.000 0.000 0.000
0.000 -0.003 0.045 -0.114 -0.336 0.789 0.255 0.116 0 0 -0.003 -0.263 0.319
0.000 -0.027 0.084 -0.659 -0.499 -0.349 -0.152 -0.052 0 0 -0.023 -0.390 -0.091
0.000 -0.001 -0.013 -0.177 0.109 0.470 -0.744 -0.019 0 0 -0.008 0.124 -0.407
-0.083 0.987 0.128 0.008 -0.022 -0.006 0.001 0.000 0 0 0.007 -0.017 -0.029
-0.996 -0.081 -0.024 -0.002 0.001 0.001 0.000 0.000 0 0 0.000 0.001 0.003
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1 0 0.000 0.000 0.000

1.3 Correlation Matrix

cor_matrix <- cor(data)
knitr::kable(round(cor_matrix, 2), caption = "Tabel: Correlation Matrix")
Tabel: Correlation Matrix
Gender Age Debt Married BankCustomer YearsEmployed PriorDefault Employed CreditScore DriversLicense ZipCode Income Approved
Gender 1.00 -0.50 0.42 NA NA 0.40 NA -0.17 0.03 0.61 -0.38 -0.65 NA
Age -0.50 1.00 0.25 NA NA 0.42 NA 0.60 0.76 -0.17 -0.59 0.35 NA
Debt 0.42 0.25 1.00 NA NA 0.22 NA -0.23 0.19 -0.20 -0.70 -0.12 NA
Married NA NA NA 1 NA NA NA NA NA NA NA NA NA
BankCustomer NA NA NA NA 1 NA NA NA NA NA NA NA NA
YearsEmployed 0.40 0.42 0.22 NA NA 1.00 NA 0.54 0.90 0.77 -0.73 -0.10 NA
PriorDefault NA NA NA NA NA NA 1 NA NA NA NA NA NA
Employed -0.17 0.60 -0.23 NA NA 0.54 NA 1.00 0.76 0.41 -0.50 -0.32 NA
CreditScore 0.03 0.76 0.19 NA NA 0.90 NA 0.76 1.00 0.50 -0.77 0.01 NA
DriversLicense 0.61 -0.17 -0.20 NA NA 0.77 NA 0.41 0.50 1.00 -0.30 -0.39 NA
ZipCode -0.38 -0.59 -0.70 NA NA -0.73 NA -0.50 -0.77 -0.30 1.00 0.33 NA
Income -0.65 0.35 -0.12 NA NA -0.10 NA -0.32 0.01 -0.39 0.33 1.00 NA
Approved NA NA NA NA NA NA NA NA NA NA NA NA 1

1.3.1 Visualisasi Korelasi (Heatmap)

library(corrplot)
corrplot(cor_matrix, method = "color", type = "upper",
         tl.col = "black", tl.srt = 45,
         col = colorRampPalette(c("red", "white", "blue"))(200),
         addCoef.col = "black")

1.4 Kesimpulan

  1. Eigenvalues: Menentukan dimensi paling signifikan untuk representasi data.
  2. Eigenvectors: Menunjukkan arah variansi maksimum.
  3. Variance-Covariance Matrix: Menunjukkan hubungan linear antar variabel dan tingkat varians masing-masing.
  4. Correlation Matrix: Memberikan kekuatan dan arah hubungan antar variabel.

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