TUGAS PENGANTAR ANALISIS MULTIVARIAT
Moh. Rasya Al Khalifi
2026-02-06
24031554132_MOH. RASYA AL KHALIFI_2024B
Pada tugas pengantar mata kuliah analisis multivariat ini yang akan dilakukan adalah mencari correlation matrix, variance covariance matrix, eigen values, dan eigen vector. Dataset yang digunakan adalah dataset Maternal Health Risk dari uci machine learning dengan 6 feature antara lain:
- Age : Usia wanita selama masa kehamilan
- SystolicBP : Nilai tekanan darah maksimum dalam mmHg
- DiastolicBP: Nilai tekanan darah yang lebih rendah dalam mmHg
- BS : Kadar glukosa darah dinyatakan dalam konsentrasi molar
- BodyTemp : Suhu tubuh
- HeartRate : Detak jantung istirahat normal
link dataset : https://archive.ics.uci.edu/dataset/863/maternal+health+risk
READ DATASET
data <- read.csv("Maternal Health Risk Data Set.csv")SELECT FEATURES WITHOUT TARGET
Data yang digunakan dalam analisis adalah dataset tanpa target/label, dalam hal ini target dihapus atau hanya dipilih feature yang memiliki nilai numerik yaitu age, systoliCB, DiastoliCB, BS, BodyTemp, dan HeartRate.
data_numeric <- data[, sapply(data, is.numeric)]
data_numeric## Age SystolicBP DiastolicBP BS BodyTemp HeartRate
## 1 25 130 80 15.00 98.0 86
## 2 35 140 90 13.00 98.0 70
## 3 29 90 70 8.00 100.0 80
## 4 30 140 85 7.00 98.0 70
## 5 35 120 60 6.10 98.0 76
## 6 23 140 80 7.01 98.0 70
## 7 23 130 70 7.01 98.0 78
## 8 35 85 60 11.00 102.0 86
## 9 32 120 90 6.90 98.0 70
## 10 42 130 80 18.00 98.0 70
## 11 23 90 60 7.01 98.0 76
## 12 19 120 80 7.00 98.0 70
## 13 25 110 89 7.01 98.0 77
## 14 20 120 75 7.01 100.0 70
## 15 48 120 80 11.00 98.0 88
## 16 15 120 80 7.01 98.0 70
## 17 50 140 90 15.00 98.0 90
## 18 25 140 100 7.01 98.0 80
## 19 30 120 80 6.90 101.0 76
## 20 10 70 50 6.90 98.0 70
## 21 40 140 100 18.00 98.0 90
## 22 50 140 80 6.70 98.0 70
## 23 21 90 65 7.50 98.0 76
## 24 18 90 60 7.50 98.0 70
## 25 21 120 80 7.50 98.0 76
## 26 16 100 70 7.20 98.0 80
## 27 19 120 75 7.20 98.0 66
## 28 22 100 65 7.20 98.0 70
## 29 49 120 90 7.20 98.0 77
## 30 28 90 60 7.20 98.0 82
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## 32 23 100 85 7.10 98.0 66
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## 67 17 85 60 9.00 102.0 86
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## 999 54 140 100 15.00 98.0 66
## 1000 40 120 95 11.00 98.0 80
## 1001 12 90 60 11.00 102.0 60
## 1002 60 120 85 15.00 98.0 60
## 1003 55 140 95 19.00 98.0 77
## 1004 50 130 100 16.00 98.0 76
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## 1008 40 120 75 7.70 98.0 70
## 1009 48 120 80 11.00 98.0 88
## 1010 22 120 60 15.00 98.0 80
## 1011 55 120 90 18.00 98.0 60
## 1012 35 85 60 19.00 98.0 86
## 1013 43 120 90 18.00 98.0 70
## 1014 32 120 65 6.00 101.0 76CORRELATION MATRIX
Correlation matrix adalah tabel yang menunjukkan hubungan atau korelasi antar variabel dari sebuah dataset. Correlation matrix juga digunakan untuk melihat seberapa kuat hubungan antar variabel dan arah hubungan linier antar variabel. Nilai dalam correlation matrix berada pada rentang -1 sampai 1, dimana nilai mendekati -1 menunjukkan hubungan hubungan linier negatif yang kuat, nilai mendekati 0 menunjukkan tidak adanya hubungan linier, dan nilai mendekati 1 menunjukkan hubungan linier positif yang kuat.
correlation_matrix <- cor(data_numeric)
correlation_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 1.00000000correlation_matrix_plot <- corrplot(correlation_matrix,
method = "color",
type = "upper",
addCoef.col = "black",
tl.col = "black",
tl.srt = 45)
Berdasarkan output correlation matrix diatas dapat dilihat bahwa nilai korelasi terbesar adalah antara DiastolicBP dan SystolicBP yaitu 0.78700648, hal ini menunjukkan Tekanan darah sistolik dan diastolik meningkat bersama secara signifikan. variabel age memiliki nilai korelasi yang sedang dengan variabel SystolicBP (0.41604545), DiastolicBP (0.39802629), dan BS (0.4732843), hal ini menunjukkan bahwa kenaikan usia wanita hamil juga diikuti oleh kenaikan tekanan darah dan kenaikan gula darah.Sementara itu variabel HeartRate memiliki korelasi yang kecil dengan variabel yang lainnya.
VARIANCE COVARIANCE MATRIX
Matriks kovarians (covariance matrix) merupakan matriks simetris yang berisi varians dan kovarians dari beberapa variabel, di mana diagonal utama mewakili varians dan elemen di luar diagonal mewakili kovarians antara variabel yang berbeda.
covariance_matrix <- cov(data_numeric)
covariance_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 65.427104covariance_matrix_plot <- corrplot(covariance_matrix,
method = "color",
type = "upper",
is.corr = FALSE,
tl.col = "black",
tl.srt = 45,
addCoef.col = "black",
number.cex = 0.7)
Berdasarkan output variance covariance matrix dapat dilihat bahwa variabel systolicBP memiliki nilai variance yang paling tinggi yaitu sebesar 338.704005, hal ini menunjukkan penyebaran nilai tekanan darah yang cukup tinggi, begitu juga dengan nilai variance dari variabel diastolicBP yang juga cukup besar yaitu 192.815323. Nilai covariance positif antara variabel systolicBP dan BS menunjukkan bahwa kadar gula darah mengalami peningkatan seiring dengan peningkatan tekanan darah. Nilai covariance negatif antara variabel diastolicBP dan bodytemp menunjukkan bahwa ketika tekanan darah diastolik meningkat, suhu tubuh cenderung sedikit menurun, dan sebaliknya.
EIGEN VALUES AND EIGEN VECTOR
Eigen values (nilai eigen) merepresentasikan besar variasi data yang dapat dijelaskan oleh setiap komponen, sedangkan eigen vector merepresentasikan arah kombinasi variabel yang membentuk komponen. Tanda minus pada eigen vector menunjukkan arah variabel yang berlawanan dengan arah komponen.
eigen <- eigen(covariance_matrix)
eigen_values <- eigen$values
eigen_values## [1] 529.521825 136.772898 64.572037 51.358769 7.360073 1.647943Berdasarkan output eigen values diatas dapat dilihat bahwa eigen value terbesar adalah komponen pertama yaitu sebesar 529.521825, hal ini menunjukkan bahwa komponen pertama menjelaskan variasi data yang paling besar. Sedangkan komponen keenam memiliki eigen value paling kecil sebesar 1.647943, hal ini menunjukkan bahwa komponen keenam menjelaskan variasi data yang sangat kecil.
eigen_vectors <- eigen$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,] -0.016098692Berdasarkan output eigen vector diatas dapat dilihat bahwa setiap komponen eigen vector didominasi oleh variabel yang berbeda beda, pada komponen pertama variabel yang memiliki kontribusi paling besar adalah systolicBP (-0.764857940) hal ini menunjukkan bahwa variasi yang dijelaskan oleh komponen pertama lebih dipengaruhi oleh variabel systolicBP. Lalu untuk komponen kedua lebih dipengaruhi oleh variabel age, komponen ketiga lebih dipengaruhi oleh variabel heartrate, komponen keempat lebih dipengaruhi oleh variabel diastolicBP, komponen kelima lebih dipengaruhi oleh variabel BS, dan komponen keenam lebih dipengaruhi oleh variabel bodytemp.