Import data

data <- read.csv("Maternal Health Risk Data Set.csv")
head(data)
##   Age SystolicBP DiastolicBP    BS BodyTemp HeartRate RiskLevel
## 1  25        130          80 15.00       98        86 high risk
## 2  35        140          90 13.00       98        70 high risk
## 3  29         90          70  8.00      100        80 high risk
## 4  30        140          85  7.00       98        70 high risk
## 5  35        120          60  6.10       98        76  low risk
## 6  23        140          80  7.01       98        70 high risk

A. Correlation Matrix

data_numeric <- data[, sapply(data, is.numeric)]
cor_matrix <- cor(data_numeric)
cor_matrix
##                     Age  SystolicBP DiastolicBP         BS    BodyTemp
## Age          1.00000000  0.41604545  0.39802629  0.4732843 -0.25532314
## SystolicBP   0.41604545  1.00000000  0.78700648  0.4251717 -0.28661552
## DiastolicBP  0.39802629  0.78700648  1.00000000  0.4238241 -0.25753832
## BS           0.47328434  0.42517166  0.42382407  1.0000000 -0.10349336
## BodyTemp    -0.25532314 -0.28661552 -0.25753832 -0.1034934  1.00000000
## HeartRate    0.07979763 -0.02310796 -0.04615057  0.1428672  0.09877104
##               HeartRate
## Age          0.07979763
## SystolicBP  -0.02310796
## DiastolicBP -0.04615057
## BS           0.14286723
## BodyTemp     0.09877104
## HeartRate    1.00000000

Visualisasi corelation plot

if (!require(corrplot)) {
  install.packages("corrplot")
}
## Loading required package: corrplot
## corrplot 0.95 loaded
library(corrplot)
corrplot(cor_matrix, 
         method = "color",
         type = "upper",
         tl.col = "black",
         tl.srt = 45)

B. Variance-Covariance Matrix

cov_matrix <- cov(data_numeric)
cov_matrix
##                    Age SystolicBP DiastolicBP         BS   BodyTemp HeartRate
## Age         181.559065 103.171539   74.471739 21.0035619 -4.7180044  8.697168
## SystolicBP  103.171539 338.704005  201.121845 25.7712999 -7.2338429 -3.439938
## DiastolicBP  74.471739 201.121845  192.815323 19.3828770 -4.9042413 -5.183543
## BS           21.003562  25.771300   19.382877 10.8473512 -0.4674483  3.806040
## BodyTemp     -4.718004  -7.233843   -4.904241 -0.4674483  1.8806951  1.095640
## HeartRate     8.697168  -3.439938   -5.183543  3.8060397  1.0956395 65.427104
corrplot(cov_matrix,
         method = "color",
         addCoef.col = "black",
         tl.col = "black",
         tl.srt = 45,
         is.corr = FALSE,
         mar = c(0, 0, 1, 0))

C. Eigen value dan eigen vector

eigen <- eigen(cov_matrix)
eigen_values <- eigen$values
eigen_values
## [1] 529.521825 136.772898  64.572037  51.358769   7.360073   1.647943
eigen_vectors <- eigen$vectors
eigen_vectors
##              [,1]         [,2]        [,3]         [,4]        [,5]
## [1,] -0.346411189  0.923900546 -0.13192259  0.042731491 -0.08198705
## [2,] -0.764857940 -0.293487053  0.14910706  0.553048994 -0.02349903
## [3,] -0.537978589 -0.186074547 -0.12389090 -0.811464330 -0.04575582
## [4,] -0.072118241  0.069777475  0.04387199 -0.031191932  0.99247862
## [5,]  0.018657383 -0.008883756  0.01905652 -0.008215683  0.04608110
## [6,]  0.004638836  0.143880423  0.97094112 -0.181096759 -0.05911889
##              [,6]
## [1,]  0.021345781
## [2,]  0.014469639
## [3,]  0.006196148
## [4,] -0.044928412
## [5,]  0.998508320
## [6,] -0.016098692

D. Jelaskan hasil dari setiap output

  1. Covariance matrix menunjukkan besarnya variasi masing-masing variabel pada diagonal utama serta hubungan perubahan bersama antar variabel di luar diagonal. Nilai kovarians yang besar menandakan adanya keterkaitan perubahan antar variabel, namun nilainya dipengaruhi oleh perbedaan satuan pengukuran.
  2. Eigen value menunjukkan seberapa besar variasi data yang dijelaskan oleh setiap komponen utama. Komponen dengan eigen value terbesar merupakan komponen paling dominan dan menjelaskan variasi data paling besar.
  3. Eigen vector menunjukkan kontribusi masing-masing variabel terhadap setiap komponen utama. Nilai absolut yang lebih besar menandakan variabel tersebut memiliki peran yang lebih penting dalam membentuk komponen tersebut.```