1. import Dataset

Titanic_Dataset <- read.csv("C:/Users/ASUS/Downloads/Titanic-Dataset.csv")
head(Titanic_Dataset)
##   PassengerId Survived Pclass
## 1           1        0      3
## 2           2        1      1
## 3           3        1      3
## 4           4        1      1
## 5           5        0      3
## 6           6        0      3
##                                                  Name    Sex Age SibSp Parch
## 1                             Braund, Mr. Owen Harris   male  22     1     0
## 2 Cumings, Mrs. John Bradley (Florence Briggs Thayer) female  38     1     0
## 3                              Heikkinen, Miss. Laina female  26     0     0
## 4        Futrelle, Mrs. Jacques Heath (Lily May Peel) female  35     1     0
## 5                            Allen, Mr. William Henry   male  35     0     0
## 6                                    Moran, Mr. James   male  NA     0     0
##             Ticket    Fare Cabin Embarked
## 1        A/5 21171  7.2500              S
## 2         PC 17599 71.2833   C85        C
## 3 STON/O2. 3101282  7.9250              S
## 4           113803 53.1000  C123        S
## 5           373450  8.0500              S
## 6           330877  8.4583              Q

2.kolom Age, Sibsp, Parch, Fare dan menghapus row dengan missing value

datatitanic <- Titanic_Dataset[, c("Age", "SibSp", "Parch", "Fare")]
datatitanic <- na.omit(datatitanic)
head(datatitanic)
##   Age SibSp Parch    Fare
## 1  22     1     0  7.2500
## 2  38     1     0 71.2833
## 3  26     0     0  7.9250
## 4  35     1     0 53.1000
## 5  35     0     0  8.0500
## 7  54     0     0 51.8625

3a. Correlation matrix

cor_matrix <- cor(datatitanic)
cor_matrix
##               Age      SibSp      Parch       Fare
## Age    1.00000000 -0.3082468 -0.1891193 0.09606669
## SibSp -0.30824676  1.0000000  0.3838199 0.13832879
## Parch -0.18911926  0.3838199  1.0000000 0.20511888
## Fare   0.09606669  0.1383288  0.2051189 1.00000000

Correlation matrix menunjukkan hubungan antar variabel. Nilai mendekati 1 menunjukkan hubungan positif kuat, mendekati -1 hubungan negatif kuat, dan mendekati 0 menunjukkan hubungan lemah.

3b. Variance-Covariance Matrix

cov_matrix <- cov(datatitanic)
cov_matrix
##              Age      SibSp      Parch        Fare
## Age   211.019125 -4.1633339 -2.3441911   73.849030
## SibSp  -4.163334  0.8644973  0.3045128    6.806212
## Parch  -2.344191  0.3045128  0.7281027    9.262176
## Fare   73.849030  6.8062117  9.2621760 2800.413100

Covariance matrix menunjukkan bagaimana dua variabel berubah bersama.

3c. Eigen value dan eigen vector

eigen_result <- eigen(cov_matrix)
eigen_result$values
## [1] 2802.5636587  209.0385659    0.9438783    0.4787214
eigen_result$vectors
##             [,1]        [,2]         [,3]          [,4]
## [1,] 0.028477552  0.99929943 -0.024018111  0.0035788596
## [2,] 0.002386349 -0.02093144 -0.773693322  0.6332099362
## [3,] 0.003280818 -0.01253786 -0.633088089 -0.7739712590
## [4,] 0.999586200 -0.02837826  0.004609234  0.0009266652

Eigenvalue menunjukkan besarnya variasi pada setiap komponen utama, sedangkan eigenvector menunjukkan arah kontribusi masing-masing variabel.