Dataframe berdasarkan Data Numerik
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, 1, 0, 1, 0),
CreditScore = 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)
)
print(data)
## Age Debt YearsEmployed PriorDefault Employed CreditScore ZipCode Income
## 1 30.83 0.000 1.25 1 1 1 202 0
## 2 58.67 4.460 3.04 1 1 6 43 560
## 3 24.50 0.500 1.50 1 0 0 280 824
## 4 27.83 1.540 3.75 1 1 5 100 3
## 5 20.17 5.625 1.71 1 0 0 120 0
## Approved
## 1 1
## 2 1
## 3 1
## 4 1
## 5 1
a) Variance-Covariance Matrix
cov_matrix <- cov(data)
print(cov_matrix)
## Age Debt YearsEmployed PriorDefault Employed
## Age 231.361400 9.345663 6.999375 0 5.03250
## Debt 9.345663 6.187675 0.605225 0 -0.31875
## YearsEmployed 6.999375 0.605225 1.182050 0 0.32250
## PriorDefault 0.000000 0.000000 0.000000 0 0.00000
## Employed 5.032500 -0.318750 0.322500 0 0.30000
## CreditScore 33.300000 1.340000 2.810000 0 1.20000
## ZipCode -831.032500 -161.461250 -73.207500 0 -25.50000
## Income 2046.972500 -112.313750 -42.775000 0 -67.30000
## Approved 0.000000 0.000000 0.000000 0 0.00000
## CreditScore ZipCode Income Approved
## Age 33.30 -831.0325 2046.9725 0
## Debt 1.34 -161.4613 -112.3137 0
## YearsEmployed 2.81 -73.2075 -42.7750 0
## PriorDefault 0.00 0.0000 0.0000 0
## Employed 1.20 -25.5000 -67.3000 0
## CreditScore 8.30 -207.0000 11.5500 0
## ZipCode -207.00 8612.0000 12109.2500 0
## Income 11.55 12109.2500 151957.8000 0
## Approved 0.00 0.0000 0.0000 0
b) Eigen Value dan Eigen Vector
eig <- eigen(cov_matrix)
# menampilkan hasil Eigen Value dan eigen vector
print(eig$values)
## [1] 1.529991e+05 7.738312e+03 7.510055e+01 4.614250e+00 1.746734e-11
## [6] 9.587267e-12 4.312483e-16 0.000000e+00 -2.185975e-13
print(eig$vectors)
## [,1] [,2] [,3] [,4] [,5]
## [1,] -1.289706e-02 -1.315608e-01 0.97836973 1.389102e-01 0.0000000000
## [2,] 8.188138e-04 -1.960524e-02 -0.12802815 6.382658e-01 -0.6193192401
## [3,] 3.179447e-04 -9.024809e-03 -0.01834222 -3.327994e-01 0.2363524236
## [4,] 5.421011e-20 1.734723e-18 0.00000000 1.110223e-16 -0.0000247429
## [5,] 4.517906e-04 -2.638208e-03 0.04508399 -1.161630e-01 -0.3862406868
## [6,] 3.495339e-05 -2.713566e-02 0.08401060 -6.700607e-01 -0.6407623109
## [7,] -8.349366e-02 9.873768e-01 0.12815197 9.231879e-03 -0.0286334831
## [8,] -9.964244e-01 -8.105384e-02 -0.02348931 -2.229401e-03 0.0017681799
## [9,] 0.000000e+00 0.000000e+00 0.00000000 0.000000e+00 0.0000000000
## [,6] [,7] [,8] [,9]
## [1,] 7.760180e-02 0.000000e+00 0 0.0000000000
## [2,] 4.385016e-01 1.446780e-05 0 -0.0007738974
## [3,] 8.117272e-01 -4.672998e-04 0 -0.4172083384
## [4,] -3.330669e-16 -9.999994e-01 0 0.0011060457
## [5,] -3.648606e-01 -9.172550e-04 0 -0.8379501476
## [6,] 9.426717e-02 4.049592e-04 0 0.3517979487
## [7,] 2.784542e-02 4.618528e-06 0 0.0035351609
## [8,] -2.880460e-03 -9.259101e-07 0 -0.0007975797
## [9,] 0.000000e+00 0.000000e+00 1 0.0000000000
c) Correlation Matrix
cor_matrix <- cor(data)
## Warning in cor(data): the standard deviation is zero
print(cor_matrix)
## Age Debt YearsEmployed PriorDefault Employed
## Age 1.0000000 0.2470022 0.4232489 NA 0.6040567
## Debt 0.2470022 1.0000000 0.2237872 NA -0.2339515
## YearsEmployed 0.4232489 0.2237872 1.0000000 NA 0.5415657
## PriorDefault NA NA NA 1 NA
## Employed 0.6040567 -0.2339515 0.5415657 NA 1.0000000
## CreditScore 0.7599058 0.1869829 0.8971175 NA 0.7604691
## ZipCode -0.5887359 -0.6994434 -0.7255806 NA -0.5016809
## Income 0.3452272 -0.1158264 -0.1009278 NA -0.3152049
## Approved NA NA NA NA NA
## CreditScore ZipCode Income Approved
## Age 0.75990576 -0.5887359 0.34522724 NA
## Debt 0.18698295 -0.6994434 -0.11582643 NA
## YearsEmployed 0.89711754 -0.7255806 -0.10092775 NA
## PriorDefault NA NA NA NA
## Employed 0.76046910 -0.5016809 -0.31520488 NA
## CreditScore 1.00000000 -0.7742466 0.01028446 NA
## ZipCode -0.77424657 1.0000000 0.33473701 NA
## Income 0.01028446 0.3347370 1.00000000 NA
## Approved NA NA NA 1