Luthfiana Syakira Eka
Ramadani
NIM: 24031554071
Kelas: 2024 E
getwd()## [1] "D:/fiaa folder/UNESA/Semester 4/Analisis Multivariat"list.files()## [1] "__MACOSX"
## [2] "ajwa+or+medjool"
## [3] "AjwaOrMejdool.csv"
## [4] "Anmul - Materi 01 - Introduction.pdf"
## [5] "Anmul - Materi 02- Review Matrix Algebra.pdf"
## [6] "rsconnect"
## [7] "tugas_anmul.html"
## [8] "tugas_anmul.R"
## [9] "tugas_anmul.Rmd"## import data
data <- read.csv2("AjwaOrMejdool.csv")
str(data)## 'data.frame': 20 obs. of 7 variables:
## $ Date.Length..cm. : chr "3.2" "3.5" "3" "3.1" ...
## $ Date.Diameter..cm. : chr "2" "1.8" "1.7" "2" ...
## $ Date.Weight..g. : int 12 11 9 10 9 12 13 12 9 10 ...
## $ Pit.Length..cm. : chr "2.2" "1.9" "2" "1.9" ...
## $ Calories..Kcal. : chr "41.28" "37.84" "30.96" "34.4" ...
## $ Color : chr "Black" "Black" "Black" "Black" ...
## $ Class..Ajwa.or.Medjool.: chr "Ajwa" "Ajwa" "Ajwa" "Ajwa" ...head(data)## Date.Length..cm. Date.Diameter..cm. Date.Weight..g. Pit.Length..cm.
## 1 3.2 2 12 2.2
## 2 3.5 1.8 11 1.9
## 3 3 1.7 9 2
## 4 3.1 2 10 1.9
## 5 2.8 1.8 9 1.9
## 6 3.1 1.9 12 2.2
## Calories..Kcal. Color Class..Ajwa.or.Medjool.
## 1 41.28 Black Ajwa
## 2 37.84 Black Ajwa
## 3 30.96 Black Ajwa
## 4 34.4 Black Ajwa
## 5 30.96 Black Ajwa
## 6 41.28 Black Ajwa## ubah variabel numerik
data_num <- data
data_num[, 1:5] <- lapply(data_num[, 1:5], as.numeric)
str(data_num)## 'data.frame': 20 obs. of 7 variables:
## $ Date.Length..cm. : num 3.2 3.5 3 3.1 2.8 3.1 3.2 3.1 3.6 3.8 ...
## $ Date.Diameter..cm. : num 2 1.8 1.7 2 1.8 1.9 2.2 1.7 2.5 1.8 ...
## $ Date.Weight..g. : num 12 11 9 10 9 12 13 12 9 10 ...
## $ Pit.Length..cm. : num 2.2 1.9 2 1.9 1.9 2.2 1.9 2.1 2.7 1.9 ...
## $ Calories..Kcal. : num 41.3 37.8 31 34.4 31 ...
## $ Color : chr "Black" "Black" "Black" "Black" ...
## $ Class..Ajwa.or.Medjool.: chr "Ajwa" "Ajwa" "Ajwa" "Ajwa" ...## hanya ambil variabel numerik
data_feature <- data_num[, 1:5]
summary(data_feature)## Date.Length..cm. Date.Diameter..cm. Date.Weight..g. Pit.Length..cm.
## Min. :2.800 Min. :1.400 Min. : 9.00 Min. :1.900
## 1st Qu.:3.175 1st Qu.:1.700 1st Qu.:10.75 1st Qu.:1.975
## Median :4.000 Median :1.800 Median :13.00 Median :2.200
## Mean :4.005 Mean :1.875 Mean :13.15 Mean :2.280
## 3rd Qu.:5.000 3rd Qu.:2.000 3rd Qu.:15.25 3rd Qu.:2.625
## Max. :5.200 Max. :2.500 Max. :19.00 Max. :2.900
## Calories..Kcal.
## Min. :30.96
## 1st Qu.:36.98
## Median :42.76
## Mean :43.05
## 3rd Qu.:48.19
## Max. :60.04## 1.Correlation Matrix
cor_matrix <- cor(data_feature)
cor_matrix## Date.Length..cm. Date.Diameter..cm. Date.Weight..g.
## Date.Length..cm. 1.0000000 -0.154486605 0.84000936
## Date.Diameter..cm. -0.1544866 1.000000000 -0.04474655
## Date.Weight..g. 0.8400094 -0.044746555 1.00000000
## Pit.Length..cm. 0.6055983 0.185245092 0.49147954
## Calories..Kcal. 0.7842460 -0.007508119 0.99259322
## Pit.Length..cm. Calories..Kcal.
## Date.Length..cm. 0.6055983 0.784246036
## Date.Diameter..cm. 0.1852451 -0.007508119
## Date.Weight..g. 0.4914795 0.992593220
## Pit.Length..cm. 1.0000000 0.441245734
## Calories..Kcal. 0.4412457 1.000000000Nilai korelasi berada pada rentang antara -1 sampai 1. Semakin mendekati angka 1 atau -1, hubungan antar variabel tersebut semakin kuat, sedangkan jika mendekati 0, hubungannya semakin lemah
## 2.Variance-Covariance Matrix
cov_matrix <- cov(data_feature)
cov_matrix## Date.Length..cm. Date.Diameter..cm. Date.Weight..g.
## Date.Length..cm. 0.72892105 -0.03776316 2.13605263
## Date.Diameter..cm. -0.03776316 0.08197368 -0.03815789
## Date.Weight..g. 2.13605263 -0.03815789 8.87105263
## Pit.Length..cm. 0.17957895 0.01842105 0.50842105
## Calories..Kcal. 5.54098947 -0.01778947 24.46547368
## Pit.Length..cm. Calories..Kcal.
## Date.Length..cm. 0.17957895 5.54098947
## Date.Diameter..cm. 0.01842105 -0.01778947
## Date.Weight..g. 0.50842105 24.46547368
## Pit.Length..cm. 0.12063158 1.26825263
## Calories..Kcal. 1.26825263 68.48405895Diagonal matriks ini menunjukkan variasi tiap variabel, sedangkan nilai lainnya menunjukkan hubungan (kovarians). Semakin besar nilai kovariansnya, semakin kuat variabel- variabel tersebut berubah secara bersamaan.
## 3.Eigen Value dan Eigen Vector
eigen_cov <- eigen(cov_matrix)
#eigen values
eigen_cov$values## [1] 77.72132186 0.38961316 0.10460410 0.04614707 0.02495171#eigen vector
eigen_cov$vectors## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.0769089737 0.8098925 -0.07134208 0.47587185 -0.3265201
## [2,] -0.0004133983 -0.1240036 0.75061959 0.55474971 0.3368174
## [3,] 0.3360215174 0.4422197 -0.06769810 -0.28240806 0.7792265
## [4,] 0.0177182954 0.2831890 0.65312362 -0.61690177 -0.3351892
## [5,] 0.9385416564 -0.2300934 0.01808437 0.07400433 -0.2457497Eigen value dan eigen vector diperoleh dari matriks varians-kovarians karena matriks data asli tidak berbentuk persegi. Eigen value mengukur seberapa besar variasi yang ditangkap suatu komponen (semakin besar nilainya, semakin penting), sedangkan eigenvector menentukan arah atau komposisi variabel dalam membentuk komponen tersebut