library(readxl)
ChemicalShipment <- read_excel("C:/Users/anggi/Documents/KULIAH/SEMESTER 5/APG/PRAKTIKUM 1/ChemicalShipment.xlsx")
Membuat Matriks
A <- as.matrix(ChemicalShipment)
A
## Y X1 X2
## [1,] 58 7 5.11
## [2,] 152 18 16.72
## [3,] 41 5 3.20
## [4,] 93 14 7.03
## [5,] 101 11 10.98
## [6,] 38 5 4.04
## [7,] 203 23 22.07
## [8,] 78 9 7.03
## [9,] 117 16 10.62
## [10,] 44 5 4.76
## [11,] 121 17 11.02
## [12,] 112 12 9.51
## [13,] 50 6 3.79
## [14,] 82 12 6.45
## [15,] 48 8 4.60
## [16,] 127 15 13.86
## [17,] 140 17 13.03
## [18,] 155 21 15.21
## [19,] 39 6 3.64
## [20,] 90 11 9.57
Vektor Rata-Rata
matrix(colMeans(A))
## [,1]
## [1,] 94.450
## [2,] 11.900
## [3,] 9.112
Matriks Kovarians
AC <- cov(A)
AC
## Y X1 X2
## Y 2159.6289 250.88947 233.48642
## X1 250.8895 30.93684 26.44232
## X2 233.4864 26.44232 26.35034
Matriks Korelasi
AR <- cor(A)
AR
## Y X1 X2
## Y 1.0000000 0.9706326 0.9787661
## X1 0.9706326 1.0000000 0.9261223
## X2 0.9787661 0.9261223 1.0000000
Eigen Value dan Vektor
EC <- eigen(AC)
EC
## eigen() decomposition
## $values
## [1] 2214.0380666 2.2081154 0.6699507
##
## $vectors
## [,1] [,2] [,3]
## [1,] 0.9876319 0.04064564 0.1514303
## [2,] 0.1147956 -0.84530210 -0.5218106
## [3,] 0.1067950 0.53274036 -0.8395133
ER <- eigen (AR)
ER
## eigen() decomposition
## $values
## [1] 2.917198321 0.074207721 0.008593958
##
## $vectors
## [,1] [,2] [,3]
## [1,] -0.5837627 0.05724282 0.8099039
## [2,] -0.5732816 -0.73543217 -0.3612308
## [3,] -0.5749515 0.67517611 -0.4621341
Matriks Ortonormal
ortonormal_cov <- t(EC$vectors[,1])%*%EC$vectors[,2]
round(ortonormal_cov,2)
## [,1]
## [1,] 0
norm_vector_EC <- sqrt(sum(EC$vectors[, 1]^2))
round(norm_vector_EC,2)
## [1] 1
ortonormal_cor <- t(ER$vectors[,1])%*%ER$vectors[,2]
round(ortonormal_cor,2)
## [,1]
## [1,] 0
norm_vector_ER <- sqrt(sum(ER$vectors[, 1]^2))
round(norm_vector_ER,2)
## [1] 1
Matriks Orthogonal
orthogonal_cov <- t(EC$vectors)%*%EC$vectors
round(orthogonal_cov,2)
## [,1] [,2] [,3]
## [1,] 1 0 0
## [2,] 0 1 0
## [3,] 0 0 1
orthogonal_cor <- t(ER$vectors)%*%ER$vectors
round(orthogonal_cor,2)
## [,1] [,2] [,3]
## [1,] 1 0 0
## [2,] 0 1 0
## [3,] 0 0 1
Matriks Rata-Rata
n <- 20
v1 <- matrix(rep(1, n), nrow=n)
xbar <- 1/n*t(A)%*%v1
xbar
## [,1]
## Y 94.450
## X1 11.900
## X2 9.112
Xbar <- v1%*%t(xbar)
Xbar
## Y X1 X2
## [1,] 94.45 11.9 9.112
## [2,] 94.45 11.9 9.112
## [3,] 94.45 11.9 9.112
## [4,] 94.45 11.9 9.112
## [5,] 94.45 11.9 9.112
## [6,] 94.45 11.9 9.112
## [7,] 94.45 11.9 9.112
## [8,] 94.45 11.9 9.112
## [9,] 94.45 11.9 9.112
## [10,] 94.45 11.9 9.112
## [11,] 94.45 11.9 9.112
## [12,] 94.45 11.9 9.112
## [13,] 94.45 11.9 9.112
## [14,] 94.45 11.9 9.112
## [15,] 94.45 11.9 9.112
## [16,] 94.45 11.9 9.112
## [17,] 94.45 11.9 9.112
## [18,] 94.45 11.9 9.112
## [19,] 94.45 11.9 9.112
## [20,] 94.45 11.9 9.112
Matriks Varians-Covarians
D <- A - Xbar
D
## Y X1 X2
## [1,] -36.45 -4.9 -4.002
## [2,] 57.55 6.1 7.608
## [3,] -53.45 -6.9 -5.912
## [4,] -1.45 2.1 -2.082
## [5,] 6.55 -0.9 1.868
## [6,] -56.45 -6.9 -5.072
## [7,] 108.55 11.1 12.958
## [8,] -16.45 -2.9 -2.082
## [9,] 22.55 4.1 1.508
## [10,] -50.45 -6.9 -4.352
## [11,] 26.55 5.1 1.908
## [12,] 17.55 0.1 0.398
## [13,] -44.45 -5.9 -5.322
## [14,] -12.45 0.1 -2.662
## [15,] -46.45 -3.9 -4.512
## [16,] 32.55 3.1 4.748
## [17,] 45.55 5.1 3.918
## [18,] 60.55 9.1 6.098
## [19,] -55.45 -5.9 -5.472
## [20,] -4.45 -0.9 0.458
S <- 1/(n-1)*t(D)%*%D
S
## Y X1 X2
## Y 2159.6289 250.88947 233.48642
## X1 250.8895 30.93684 26.44232
## X2 233.4864 26.44232 26.35034
Matriks Korelasii
Du<-diag(c(sqrt(S[1,1]),sqrt(S[2,2]),sqrt(S[3,3])))
R <- solve(Du)%*%S%*%solve(Du)
R
## [,1] [,2] [,3]
## [1,] 1.0000000 0.9706326 0.9787661
## [2,] 0.9706326 1.0000000 0.9261223
## [3,] 0.9787661 0.9261223 1.0000000
Matriks Generalized Variance
GV <- det(S)
GV
## [1] 3275.289