data <- read.csv("https://archive.ics.uci.edu/static/public/863/data.csv")
# untuk cek data sudah masuk atau belum
data_angka <- data[, 1:6]

# 3a. correlation matrix
cor(data_angka)
##                     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
# 3b. matriks kovarians
cov(data_angka)
##                    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
# 3c. eigen value & vector
eigen(cor(data_angka))
## eigen() decomposition
## $values
## [1] 2.6078934 1.1443812 0.8370499 0.7063345 0.4925435 0.2117975
## 
## $vectors
##            [,1]       [,2]       [,3]       [,4]        [,5]        [,6]
## [1,] -0.4360752  0.1729019  0.2404386 -0.5550931 -0.64321080  0.01685752
## [2,] -0.5296016 -0.1128996 -0.2415842  0.3633726 -0.09386670 -0.71243407
## [3,] -0.5225675 -0.1230416 -0.2990961  0.3544156 -0.07810122  0.70043934
## [4,] -0.4255290  0.3528904 -0.1153507 -0.4254237  0.70709921 -0.01063092
## [5,]  0.2735090  0.4293197 -0.8093439 -0.1305413 -0.26067118 -0.02914362
## [6,] -0.0200401  0.7958469  0.3549994  0.4859993 -0.05856920  0.02399757

3d. Penjelasan output:

1. correlation matrix:

Hubungan terkuat ada pada SystolicBP dan DiastolicBP (0.78), artinya jika tekanan darah sistolik naik, diastolik cenderung ikut naik.

2. matriks kovarians:

Variabel SystolicBP memiliki variasi data paling tinggi (338.70) dibanding variabel lainnya.

3. eigen value & vector:

Nilai pertama (2.60) adalah yang terbesar, menunjukkan bahwa sebagian besar informasi data terwakili di komponen pertama.