getwd()
## [1] "D:/fiaa folder/UNESA/Semester 4/Analisis Multivariat"
list.files()
## [1] "Anmul-Tugas1.Rmd"                            
## [2] "Anmul - Materi 01 - Introduction.pdf"        
## [3] "Anmul - Materi 02- Review Matrix Algebra.pdf"
## [4] "hcvdat0.csv"
## import data
data <- read.csv("hcvdat0.csv", header = TRUE)
str(data)
## 'data.frame':    615 obs. of  14 variables:
##  $ X       : int  1 2 3 4 5 6 7 8 9 10 ...
##  $ Category: chr  "0=Blood Donor" "0=Blood Donor" "0=Blood Donor" "0=Blood Donor" ...
##  $ Age     : int  32 32 32 32 32 32 32 32 32 32 ...
##  $ Sex     : chr  "m" "m" "m" "m" ...
##  $ ALB     : num  38.5 38.5 46.9 43.2 39.2 41.6 46.3 42.2 50.9 42.4 ...
##  $ ALP     : num  52.5 70.3 74.7 52 74.1 43.3 41.3 41.9 65.5 86.3 ...
##  $ ALT     : num  7.7 18 36.2 30.6 32.6 18.5 17.5 35.8 23.2 20.3 ...
##  $ AST     : num  22.1 24.7 52.6 22.6 24.8 19.7 17.8 31.1 21.2 20 ...
##  $ BIL     : num  7.5 3.9 6.1 18.9 9.6 12.3 8.5 16.1 6.9 35.2 ...
##  $ CHE     : num  6.93 11.17 8.84 7.33 9.15 ...
##  $ CHOL    : num  3.23 4.8 5.2 4.74 4.32 6.05 4.79 4.6 4.1 4.45 ...
##  $ CREA    : num  106 74 86 80 76 111 70 109 83 81 ...
##  $ GGT     : num  12.1 15.6 33.2 33.8 29.9 91 16.9 21.5 13.7 15.9 ...
##  $ PROT    : num  69 76.5 79.3 75.7 68.7 74 74.5 67.1 71.3 69.9 ...
head(data)
##   X      Category Age Sex  ALB  ALP  ALT  AST  BIL   CHE CHOL CREA  GGT PROT
## 1 1 0=Blood Donor  32   m 38.5 52.5  7.7 22.1  7.5  6.93 3.23  106 12.1 69.0
## 2 2 0=Blood Donor  32   m 38.5 70.3 18.0 24.7  3.9 11.17 4.80   74 15.6 76.5
## 3 3 0=Blood Donor  32   m 46.9 74.7 36.2 52.6  6.1  8.84 5.20   86 33.2 79.3
## 4 4 0=Blood Donor  32   m 43.2 52.0 30.6 22.6 18.9  7.33 4.74   80 33.8 75.7
## 5 5 0=Blood Donor  32   m 39.2 74.1 32.6 24.8  9.6  9.15 4.32   76 29.9 68.7
## 6 6 0=Blood Donor  32   m 41.6 43.3 18.5 19.7 12.3  9.92 6.05  111 91.0 74.0
## hanya ambil variabel numerik
data_feature <- data[, sapply(data, is.numeric)]
## 1.Correlation Matrix
cor_matrix <- cor(data_feature, use = "complete.obs")
cor_matrix
##                X         Age          ALB         ALP         ALT         AST
## X     1.00000000  0.44305790 -0.315204550  0.01794376 -0.20023304  0.30360292
## Age   0.44305790  1.00000000 -0.191093637  0.17771977 -0.04057647  0.07273886
## ALB  -0.31520455 -0.19109364  1.000000000 -0.14611991  0.03949714 -0.17760895
## ALP   0.01794376  0.17771977 -0.146119911  1.00000000  0.22160301  0.06702428
## ALT  -0.20023304 -0.04057647  0.039497139  0.22160301  1.00000000  0.19865775
## AST   0.30360292  0.07273886 -0.177608947  0.06702428  0.19865775  1.00000000
## BIL   0.17651109  0.03965486 -0.169597498  0.05837241 -0.10679662  0.30957974
## CHE  -0.27853454 -0.07586328  0.360919403  0.02948169  0.22434447 -0.19727042
## CHOL -0.05794709  0.12474161  0.210419878  0.12590008  0.14999727 -0.20121300
## CREA -0.02016270 -0.02514225  0.001433247  0.15390895 -0.03610554 -0.01794810
## GGT   0.22146275  0.14337927 -0.147598318  0.46130000  0.21970686  0.47777362
## PROT -0.16648242 -0.15975998  0.570725680 -0.06308514  0.01678633  0.01740394
##              BIL         CHE         CHOL         CREA          GGT        PROT
## X     0.17651109 -0.27853454 -0.057947087 -0.020162704  0.221462754 -0.16648242
## Age   0.03965486 -0.07586328  0.124741615 -0.025142253  0.143379268 -0.15975998
## ALB  -0.16959750  0.36091940  0.210419878  0.001433247 -0.147598318  0.57072568
## ALP   0.05837241  0.02948169  0.125900079  0.153908950  0.461299996 -0.06308514
## ALT  -0.10679662  0.22434447  0.149997271 -0.036105541  0.219706857  0.01678633
## AST   0.30957974 -0.19727042 -0.201213004 -0.017948098  0.477773617  0.01740394
## BIL   1.00000000 -0.32071323 -0.181569556  0.019909617  0.210566559 -0.05257491
## CHE  -0.32071323  1.00000000  0.428018276 -0.012119999 -0.095716131  0.30628754
## CHOL -0.18156956  0.42801828  1.000000000 -0.051464078  0.008822692  0.24504950
## CREA  0.01990962 -0.01212000 -0.051464078  1.000000000  0.125353469 -0.03011070
## GGT   0.21056656 -0.09571613  0.008822692  0.125353469  1.000000000 -0.03712701
## PROT -0.05257491  0.30628754  0.245049503 -0.030110695 -0.037127008  1.00000000

Nilai 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, use = "complete.obs")
cov_matrix
##                X        Age          ALB        ALP         ALT         AST
## X    30325.61267 766.254175 -316.2678135  80.997414 -727.477884 1737.677172
## Age    766.25418  98.631388  -10.9348172  45.750544   -8.407388   23.742827
## ALB   -316.26781 -10.934817   33.1982701 -21.823283    4.747912  -33.634186
## ALP     80.99741  45.750544  -21.8232826 671.901949  119.841675   57.100968
## ALT   -727.47788  -8.407388    4.7479116 119.841675  435.269784  136.220708
## AST   1737.67717  23.742827  -33.6341863  57.100968  136.220708 1080.231200
## BIL    535.04466   6.855155  -17.0094554  26.337454  -38.783770  177.110426
## CHE   -106.27733  -1.650806    4.5564303   1.674411   10.255372  -14.206173
## CHOL   -11.39233   1.398606    1.3687395   3.684302    3.532962   -7.466047
## CREA  -178.00646 -12.658841    0.4186596 202.254881  -38.188738  -29.906045
## GGT   2094.23092  77.323769  -46.1804560 649.315069  248.909775  852.706557
## PROT  -155.07302  -8.486697   17.5892871  -8.746677    1.873261    3.059630
##             BIL         CHE        CHOL         CREA          GGT        PROT
## X    535.044661 -106.277326 -11.3923339 -178.0064562 2094.2309247 -155.073024
## Age    6.855155   -1.650806   1.3986055  -12.6588412   77.3237685   -8.486697
## ALB  -17.009455    4.556430   1.3687395    0.4186596  -46.1804560   17.589287
## ALP   26.337454    1.674411   3.6843023  202.2548814  649.3150694   -8.746677
## ALT  -38.783770   10.255372   3.5329616  -38.1887382  248.9097752    1.873261
## AST  177.110426  -14.206173  -7.4660468  -29.9060449  852.7065571    3.059630
## BIL  302.988734  -12.231702  -3.5680635   17.5694569  199.0314564   -4.895025
## CHE  -12.231702    4.800799   1.0587548   -1.3462991  -11.3883550    3.589626
## CHOL  -3.568064    1.058755   1.2745375   -2.9455248    0.5408745    1.479767
## CREA  17.569457   -1.346299  -2.9455248 2570.1849279  345.0941704   -8.165186
## GGT  199.031456  -11.388355   0.5408745  345.0941704 2948.7514092  -10.783808
## PROT  -4.895025    3.589626   1.4797666   -8.1651857  -10.7838076   28.610549

Diagonal 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$values
##  [1] 3.064615e+04 3.411952e+03 2.431355e+03 8.106778e+02 4.759857e+02
##  [6] 3.597636e+02 2.295242e+02 7.550312e+01 4.386454e+01 1.225674e+01
## [11] 3.543169e+00 8.832592e-01
#eigen vector
eigen_cov$vectors
##                [,1]          [,2]          [,3]          [,4]         [,5]
##  [1,]  0.9943168408  0.0781794505 -0.0428895929 -0.0328121735  0.020212889
##  [2,]  0.0252084504 -0.0048342063  0.0049027524 -0.0592379614  0.060040370
##  [3,] -0.0104849795  0.0082864828 -0.0043684634 -0.0004021013 -0.025903024
##  [4,]  0.0044080667 -0.2356681437  0.0356393108 -0.4374522941  0.710618877
##  [5,] -0.0230437543 -0.1041992516  0.0916985555  0.0673718565  0.547112440
##  [6,]  0.0607143554 -0.2580042619  0.1999667225  0.8489173365  0.256978864
##  [7,]  0.0184370838 -0.0576707031  0.0297876343  0.1542686413 -0.079875667
##  [8,] -0.0035236442  0.0013755262 -0.0001678846 -0.0100541902  0.011976556
##  [9,] -0.0003865148  0.0002186455  0.0009124350 -0.0103444081  0.005339638
## [10,] -0.0053562951 -0.4023281847 -0.9087666493  0.1021482314  0.004426586
## [11,]  0.0771038647 -0.8340483849  0.3488376959 -0.2101014484 -0.343945278
## [12,] -0.0050747796  0.0005044839  0.0043774244  0.0163142811 -0.009811142
##               [,6]          [,7]         [,8]          [,9]        [,10]
##  [1,] -0.029899000  0.0117861445  0.028276257 -0.0075378056  0.002522380
##  [2,]  0.013200918 -0.0142637105 -0.987882489 -0.1224848387 -0.020137828
##  [3,] -0.041230519 -0.0196324002  0.073071176 -0.7117277819  0.693190933
##  [4,]  0.462008490 -0.1601735463  0.082208949 -0.0250189827  0.017575507
##  [5,] -0.680285668  0.4612712030  0.014509161 -0.0004604439 -0.009521025
##  [6,]  0.171499060 -0.2691408215 -0.025811818 -0.0013787705  0.020143047
##  [7,]  0.524197933  0.8290819581 -0.013118146 -0.0459489418  0.009776830
##  [8,] -0.030163171 -0.0150483056  0.002265340 -0.1084487331 -0.017859713
##  [9,] -0.009869622 -0.0007455209 -0.011252758 -0.0491322591 -0.030609508
## [10,] -0.039663866  0.0110805318 -0.008986684 -0.0015590011 -0.003436025
## [11,] -0.119064616  0.0091672413 -0.002651554  0.0038121325 -0.002258407
## [12,] -0.006258120 -0.0244543592  0.099611920 -0.6793031525 -0.718958094
##               [,11]         [,12]
##  [1,]  1.166495e-03 -0.0005701834
##  [2,] -1.638485e-02 -0.0153975609
##  [3,] -6.807153e-02  0.0016019737
##  [4,] -4.373501e-03 -0.0027458982
##  [5,] -2.126558e-02 -0.0043095508
##  [6,]  9.352837e-03  0.0072123962
##  [7,]  2.699176e-02 -0.0001634271
##  [8,]  9.680597e-01 -0.2222163944
##  [9,]  2.170998e-01  0.9742461763
## [10,]  4.016040e-04  0.0012264068
## [11,]  6.161861e-05 -0.0015769054
## [12,] -9.765782e-02 -0.0337955255

Eigen value dan eigen vector dihitung dari matriks varians-kovarians yang berbentuk persegi. Eigen value menunjukkan besarnya variasi yang dijelaskan setiap komponen, sedangkan eigen vector menunjukkan arah kombinasi variabel dalam membentuk komponen tersebut.