Analisis Korelasi Kanonik
Firli Fiora
2025-03-18
library(readxl)
Data_Sosial_Ekonomi <- read_excel("C:/Users/62852/OneDrive/Data Sosial Ekonomi.xlsx")
Data_Sosial_EkonomiX1 <- Data_Sosial_Ekonomi$`Akses pada fasilitas kesehatan dasar`
X2 <- Data_Sosial_Ekonomi$`Angka Partisipasi Murni`
X3 <- Data_Sosial_Ekonomi$`Panjang Jalan Provinsi (km) (Km)`
Y1 <- Data_Sosial_Ekonomi$`Umur Harapan Hidup`
Y2 <- Data_Sosial_Ekonomi$`Harapan Lama Sekolah`
Y3 <- Data_Sosial_Ekonomi$`Rata-rata Pengeluaran Perkapita Sebulan (Rp)`
data_f <- data.frame(X1,X2,X3,Y1,Y2,Y3)
data_f#Statistika deskriptif
deskriptif <- summary(data_f)
deskriptif## X1 X2 X3 Y1
## Min. :36.97 Min. :44.41 Min. : 350.0 Min. :61.40
## 1st Qu.:75.14 1st Qu.:59.71 1st Qu.: 895.2 1st Qu.:70.96
## Median :80.06 Median :62.98 Median :1452.5 Median :72.89
## Mean :78.74 Mean :62.60 Mean :1603.6 Mean :72.53
## 3rd Qu.:85.41 3rd Qu.:65.92 3rd Qu.:1952.2 3rd Qu.:73.88
## Max. :91.30 Max. :74.82 Max. :6432.0 Max. :82.25
## Y2 Y3
## Min. :11.11 Min. : 842490
## 1st Qu.:12.82 1st Qu.:1148069
## Median :13.12 Median :1211058
## Mean :13.21 Mean :1315934
## 3rd Qu.:13.63 3rd Qu.:1418032
## Max. :15.64 Max. :2388129#Uji Normalitas
#Jumlah baris dan kolom
n <- nrow(data_f)
p <- ncol(data_f)
#Mengubah data menjadi matriks
data <- data.matrix(data_f)
#Mean
mean <- matrix(colMeans(data),p,1)
#Covarians
cov.matriks <- cov(data)
cov.invers <- solve(cov.matriks)
#Menghitung nilai di^2
Di <- mahalanobis(data, mean, cov.matriks)
#Peringkat untuk nilai di^2
rank <- rank(Di)
#Peluang nilai k
p <- (rank-0.5)/n
#Nilai Chi Square
chi.square <- qchisq(p, df=p)
#Membuat Kategori dalam tabel
data_f$di.kuadrat <- Di
data_f$k <- rank
data_f$p.k <- p
data_f$Chi.Square <- chi.square
m <- data.matrix(data_f)
m## X1 X2 X3 Y1 Y2 Y3 di.kuadrat k p.k
## [1,] 69.31 70.80 1782 73.48 14.36 1144396 6.0553736 25 0.72058824
## [2,] 68.22 67.99 3006 73.84 13.27 1165364 8.0979059 29 0.83823529
## [3,] 82.09 68.99 1525 74.56 14.09 1299399 1.5479661 3 0.07352941
## [4,] 74.93 64.00 2800 73.89 13.28 1370402 1.6099039 5 0.13235294
## [5,] 73.41 61.56 1033 72.62 13.04 1209140 2.2184745 8 0.22058824
## [6,] 75.28 60.53 1514 71.83 12.54 1085190 3.6503418 16 0.45588235
## [7,] 78.83 66.08 1563 73.16 13.67 1202285 0.7119273 1 0.01470588
## [8,] 80.69 60.31 1693 71.25 12.73 1033215 2.7521500 12 0.33823529
## [9,] 89.44 58.79 851 72.96 12.17 1588103 5.5645186 23 0.66176471
## [10,] 83.77 73.36 896 77.87 12.98 1954610 11.5995858 30 0.86764706
## [11,] 79.52 60.53 6432 82.25 13.07 2388129 25.9186952 34 0.98529412
## [12,] 79.49 58.58 2361 72.96 12.61 1387830 1.5728427 4 0.10294118
## [13,] 85.81 60.46 2501 72.17 12.77 1055560 5.9919924 24 0.69117647
## [14,] 87.54 71.42 760 80.22 15.64 1403151 15.7511673 32 0.92647059
## [15,] 81.88 62.63 1421 73.48 13.36 1107090 1.4581982 2 0.04411765
## [16,] 80.27 59.69 762 74.68 13.02 1526545 3.9890965 17 0.48529412
## [17,] 91.30 74.82 743 76.69 13.40 1466506 6.9353663 27 0.77941176
## [18,] 75.10 67.09 1484 70.86 13.90 1212976 2.7030307 10 0.27941176
## [19,] 56.33 54.29 2650 67.02 13.20 842490 8.0056291 28 0.80882353
## [20,] 74.94 51.77 1535 68.99 12.65 1247266 4.1014557 19 0.54411765
## [21,] 79.63 54.25 1272 72.81 12.74 1409465 4.3006602 21 0.60294118
## [22,] 87.16 58.37 756 73.45 12.81 1420887 3.1886251 14 0.39705882
## [23,] 78.03 69.29 895 76.60 13.81 1777179 6.5689348 26 0.75000000
## [24,] 87.73 65.37 852 71.57 12.94 1562306 4.8897530 22 0.63235294
## [25,] 84.58 63.33 927 74.03 12.94 1176962 2.7609690 13 0.36764706
## [26,] 82.23 65.44 1644 70.54 13.23 1119343 2.7222477 11 0.30882353
## [27,] 89.08 60.35 2009 73.38 13.52 1151968 4.1217920 20 0.57352941
## [28,] 85.69 63.70 1009 71.82 13.68 1171510 1.6786452 6 0.16176471
## [29,] 86.87 58.21 467 69.82 13.11 1187600 4.0191222 18 0.51470588
## [30,] 76.25 59.77 350 68.64 12.86 945109 2.5786326 9 0.25000000
## [31,] 79.84 64.71 1080 71.55 13.97 1190482 2.1036253 7 0.19117647
## [32,] 81.21 64.11 1277 69.56 13.68 1146769 3.2634377 15 0.42647059
## [33,] 73.71 63.51 2310 66.11 13.13 1472938 14.6950544 31 0.89705882
## [34,] 36.97 44.41 2362 61.40 11.11 1319601 20.8728792 33 0.95588235
## Chi.Square
## [1,] 7.585302e-01
## [2,] 1.649490e+00
## [3,] 1.702130e-31
## [4,] 6.333960e-14
## [5,] 1.368527e-06
## [6,] 4.313852e-02
## [7,] 6.788180e-250
## [8,] 2.103412e-03
## [9,] 4.868726e-01
## [10,] 1.996032e+00
## [11,] 5.908506e+00
## [12,] 7.661346e-20
## [13,] 6.120916e-01
## [14,] 3.030812e+00
## [15,] 4.110586e-62
## [16,] 7.020097e-02
## [17,] 1.129915e+00
## [18,] 1.359713e-04
## [19,] 1.366418e+00
## [20,] 1.553330e-01
## [21,] 2.906201e-01
## [22,] 1.249917e-02
## [23,] 9.295665e-01
## [24,] 3.803627e-01
## [25,] 5.594225e-03
## [26,] 6.267963e-04
## [27,] 2.160663e-01
## [28,] 1.981919e-10
## [29,] 1.071409e-01
## [30,] 1.888043e-05
## [31,] 3.678716e-08
## [32,] 2.444872e-02
## [33,] 2.436058e+00
## [34,] 3.939638e+00#Korelasi
cor.test(data_f$di.kuadrat, data_f$Chi.Square,
alternative = c("two.sided"),
method = c("pearson"),
conf.level = 0.95)##
## Pearson's product-moment correlation
##
## data: data_f$di.kuadrat and data_f$Chi.Square
## t = 34.935, df = 32, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.9741726 0.9936201
## sample estimates:
## cor
## 0.9871423#Plot Normalitas
plot(data_f$di.kuadrat, data_f$Chi.Square,
main = "Plot Normalitas",
xlab = "Di^2",
ylab = "X^2",
col = "blue")
abline(lm(data_f$Chi.Square~data_f$di.kuadrat), col="red")
Interpretasi: Plot normalitas di atas menunjukkan hubungan antara Di^2 pada sumbu X dan𝜒2 pada sumbu Y. Titik -titik data tersebar disekitar garis regresi merah, menunjukkan tren positif dengan pola yang mendekati linear. Analisis korelasi Pearson menghasilkan nilai korelasi sebesar 0.987, yang menunjukkan hubungan yang sangat kuat antara variabel tersebut. Dengan demikian, dapat disimpulkan bahwa terdapat korelasi positif yang sangat kuat antara Di^2 dan𝜒2.
#Uji Linearitas
pairs(data_f[, c("X1", "X2", "X3", "Y1", "Y2", "Y3")], main = "Scatterplot Matrix")
Interpretasi: Scatterplot matrix menunjukkan bahwa hubungan antara variabel dalam analisis korelasi kanonik cenderung linear, ditandai dengan pola sebaran titik yang mengikuti arah tertentu. Hal ini mengindikasikan bahwa asumsi linearitas dalam korelasi kanonik terpenuhi, sehingga analisis dapat dilakukan dengan hasil yang optimal.
#Uji Multikolinieritas
cor <- cor(data_f)
cor## X1 X2 X3 Y1 Y2 Y3
## X1 1.0000000 0.49086857 -0.3277968 0.59025170 0.36033401 0.19556484
## X2 0.4908686 1.00000000 -0.1842522 0.61410768 0.71574876 0.19617225
## X3 -0.3277968 -0.18425219 1.0000000 0.15711743 -0.13612654 0.34586046
## Y1 0.5902517 0.61410768 0.1571174 1.00000000 0.49574551 0.58791613
## Y2 0.3603340 0.71574876 -0.1361265 0.49574551 1.00000000 -0.04719024
## Y3 0.1955648 0.19617225 0.3458605 0.58791613 -0.04719024 1.00000000
## di.kuadrat -0.3675103 -0.11594729 0.5763574 0.13195614 -0.10964589 0.58969923
## k -0.2376672 -0.02433623 0.2956801 0.08987436 -0.09617730 0.43662278
## p.k -0.2376672 -0.02433623 0.2956801 0.08987436 -0.09617730 0.43662278
## Chi.Square -0.3589754 -0.06301309 0.6440249 0.20654626 -0.05681824 0.60490444
## di.kuadrat k p.k Chi.Square
## X1 -0.3675103 -0.23766724 -0.23766724 -0.35897545
## X2 -0.1159473 -0.02433623 -0.02433623 -0.06301309
## X3 0.5763574 0.29568012 0.29568012 0.64402494
## Y1 0.1319561 0.08987436 0.08987436 0.20654626
## Y2 -0.1096459 -0.09617730 -0.09617730 -0.05681824
## Y3 0.5896992 0.43662278 0.43662278 0.60490444
## di.kuadrat 1.0000000 0.80768184 0.80768184 0.98714228
## k 0.8076818 1.00000000 1.00000000 0.74909162
## p.k 0.8076818 1.00000000 1.00000000 0.74909162
## Chi.Square 0.9871423 0.74909162 0.74909162 1.00000000library(car)## Loading required package: carDatamodel <- lm(X1+X2+X3~Y1+Y2+Y3, data = data_f)
vif(model)## Y1 Y2 Y3
## 2.633645 1.727184 1.990825Interpretasi: Berdasarkan matriks korelasi dan uji VIF, tidak terdapat masalah multikolinearitas dalam data karena semua nilai korelasi antar variabel independen berada di bawah 0.8, dan nilai VIF untuk X1, X2, dan X3 masing-masing 2.63, 1.73, dan 1.99, yang masih jauh di bawah batas kritis 5. Dengan demikian, model memenuhi asumsi multikolinearitas dan dapat digunakan untuk analisis lebih lanjut.
#standarisasi data
data.scale <- scale(data_f)
data.scale## X1 X2 X3 Y1 Y2 Y3
## [1,] -0.923267467 1.316193398 0.16197388 0.24738013 1.54838584 -0.57895277
## [2,] -1.029996599 0.864978366 1.27320124 0.34124042 0.07551163 -0.50818442
## [3,] 0.328107123 1.025553110 -0.07134755 0.52896099 1.18354544 -0.05580768
## [4,] -0.372975981 0.224285136 1.08618095 0.35427657 0.08902424 0.18383201
## [5,] -0.521809265 -0.167517241 -0.51801737 0.02315834 -0.23527834 -0.36043761
## [6,] -0.338705159 -0.332909227 -0.08133407 -0.18281284 -0.91090871 -0.77877682
## [7,] 0.008898894 0.558280604 -0.03684866 0.16394877 0.61601593 -0.38357367
## [8,] 0.191023835 -0.368235671 0.08117386 -0.33403219 -0.65416917 -0.95419579
## [9,] 1.047794387 -0.612309283 -0.68324889 0.11180416 -1.41087519 0.91858687
## [10,] 0.492607069 1.727264743 -0.64239494 1.39195417 -0.31635399 2.15557155
## [11,] 0.076461372 -0.332909227 4.38354841 2.53392098 -0.19474052 3.61872604
## [12,] 0.073523873 -0.646029979 0.68762800 0.11180416 -0.81632046 0.24265263
## [13,] 0.692357004 -0.344149460 0.81472917 -0.09416702 -0.60011874 -0.87877998
## [14,] 0.861752782 1.415749739 -0.76586465 2.00465326 3.27799959 0.29436199
## [15,] 0.307544630 0.004297736 -0.16576556 0.24738013 0.19712510 -0.70486291
## [16,] 0.149898848 -0.467792013 -0.76404892 0.56024775 -0.26230356 0.71082467
## [17,] 1.229919328 1.961703870 -0.78129836 1.08430101 0.25117553 0.50818918
## [18,] -0.356330153 0.720461096 -0.10857003 -0.43571417 0.92680590 -0.34749086
## [19,] -2.194225385 -1.334895633 0.95000113 -1.43689055 -0.01907662 -1.59790492
## [20,] -0.371996815 -1.739543989 -0.06226889 -0.92326621 -0.76227003 -0.23175991
## [21,] 0.087232202 -1.341318622 -0.30103752 0.07269571 -0.64065656 0.31567214
## [22,] 0.824544461 -0.679750675 -0.76949611 0.23955844 -0.54606831 0.35422213
## [23,] -0.069434414 1.073725534 -0.64330281 1.06083594 0.80519243 1.55673053
## [24,] 0.880356942 0.444272536 -0.68234102 -0.25060083 -0.37040442 0.83152034
## [25,] 0.571919543 0.116700057 -0.61425111 0.39077779 -0.37040442 -0.46904042
## [26,] 0.341815452 0.455512768 0.03668845 -0.51914553 0.02146120 -0.66350825
## [27,] 1.012544399 -0.361812681 0.36805935 0.22130783 0.41332682 -0.55339678
## [28,] 0.680607008 0.176112712 -0.53980614 -0.18542007 0.62952853 -0.48744127
## [29,] 0.796148636 -0.705442635 -1.03186923 -0.70686611 -0.14069009 -0.43313649
## [30,] -0.243726023 -0.454946033 -1.13808950 -1.01451926 -0.47850528 -1.25155920
## [31,] 0.107794695 0.338293204 -0.47534769 -0.25581529 1.02139415 -0.42340956
## [32,] 0.241940485 0.241948358 -0.29649819 -0.77465409 0.62952853 -0.57094374
## [33,] -0.492434275 0.145603511 0.64132686 -1.67414849 -0.11366487 0.52989760
## [34,] -4.089891431 -2.921374107 0.68853587 -2.90215390 -2.84321158 0.01237537
## di.kuadrat k p.k Chi.Square
## [1,] 0.04055128 0.75314467 0.75314467 0.005250145
## [2,] 0.39780542 1.15482182 1.15482182 0.674039137
## [3,] -0.74782794 -1.45607969 -1.45607969 -0.564131729
## [4,] -0.73699454 -1.25524111 -1.25524111 -0.564131729
## [5,] -0.63055100 -0.95398325 -0.95398325 -0.564130702
## [6,] -0.38010673 -0.15062893 -0.15062893 -0.531750295
## [7,] -0.89405736 -1.65691827 -1.65691827 -0.564131729
## [8,] -0.53720719 -0.55230609 -0.55230609 -0.562552827
## [9,] -0.04530292 0.55230609 0.55230609 -0.198666453
## [10,] 1.01027536 1.25524111 1.25524111 0.934166824
## [11,] 3.51479448 1.65691827 1.65691827 3.871020167
## [12,] -0.74347682 -1.35566040 -1.35566040 -0.564131729
## [13,] 0.02946543 0.65272538 0.65272538 -0.104672270
## [14,] 1.73641795 1.45607969 1.45607969 1.710912133
## [15,] -0.76352901 -1.55649898 -1.55649898 -0.564131729
## [16,] -0.32085601 -0.05020964 -0.05020964 -0.511436183
## [17,] 0.19446858 0.95398325 0.95398325 0.284026004
## [18,] -0.54579852 -0.75314467 -0.75314467 -0.564029664
## [19,] 0.38166551 1.05440254 1.05440254 0.461553992
## [20,] -0.30120355 0.15062893 0.15062893 -0.447532825
## [21,] -0.26636120 0.35146751 0.35146751 -0.345981121
## [22,] -0.46086443 -0.35146751 -0.35146751 -0.554749375
## [23,] 0.13037697 0.85356396 0.85356396 0.133636623
## [24,] -0.16332446 0.45188680 0.45188680 -0.278616898
## [25,] -0.53566467 -0.45188680 -0.45188680 -0.559932489
## [26,] -0.54243732 -0.65272538 -0.65272538 -0.563661232
## [27,] -0.29764657 0.25104822 0.25104822 -0.401944063
## [28,] -0.72497118 -1.15482182 -1.15482182 -0.564131729
## [29,] -0.31560430 0.05020964 0.05020964 -0.483707671
## [30,] -0.56755666 -0.85356396 -0.85356396 -0.564117557
## [31,] -0.65063900 -1.05440254 -1.05440254 -0.564131701
## [32,] -0.44777914 -0.25104822 -0.25104822 -0.545779577
## [33,] 1.55169593 1.35566040 1.35566040 1.264466737
## [34,] 2.63224360 1.55649898 1.55649898 2.393111517
## attr(,"scaled:center")
## X1 X2 X3 Y1 Y2 Y3
## 7.873912e+01 6.260324e+01 1.603588e+03 7.253118e+01 1.321412e+01 1.315934e+06
## di.kuadrat k p.k Chi.Square
## 5.823529e+00 1.750000e+01 5.000000e-01 7.515359e-01
## attr(,"scaled:scale")
## X1 X2 X3 Y1 Y2 Y3
## 1.021277e+01 6.227629e+00 1.101485e+03 3.835488e+00 7.400496e-01 2.962907e+05
## di.kuadrat k p.k Chi.Square
## 5.717309e+00 9.958246e+00 2.928896e-01 1.332199e+00Penjelasan: Standarisasi data digunakan karena satuan tiap variabelnya berbeda.
#Matriks data standarisasi
data.matriks <- as.matrix(data.scale)
data.matriks## X1 X2 X3 Y1 Y2 Y3
## [1,] -0.923267467 1.316193398 0.16197388 0.24738013 1.54838584 -0.57895277
## [2,] -1.029996599 0.864978366 1.27320124 0.34124042 0.07551163 -0.50818442
## [3,] 0.328107123 1.025553110 -0.07134755 0.52896099 1.18354544 -0.05580768
## [4,] -0.372975981 0.224285136 1.08618095 0.35427657 0.08902424 0.18383201
## [5,] -0.521809265 -0.167517241 -0.51801737 0.02315834 -0.23527834 -0.36043761
## [6,] -0.338705159 -0.332909227 -0.08133407 -0.18281284 -0.91090871 -0.77877682
## [7,] 0.008898894 0.558280604 -0.03684866 0.16394877 0.61601593 -0.38357367
## [8,] 0.191023835 -0.368235671 0.08117386 -0.33403219 -0.65416917 -0.95419579
## [9,] 1.047794387 -0.612309283 -0.68324889 0.11180416 -1.41087519 0.91858687
## [10,] 0.492607069 1.727264743 -0.64239494 1.39195417 -0.31635399 2.15557155
## [11,] 0.076461372 -0.332909227 4.38354841 2.53392098 -0.19474052 3.61872604
## [12,] 0.073523873 -0.646029979 0.68762800 0.11180416 -0.81632046 0.24265263
## [13,] 0.692357004 -0.344149460 0.81472917 -0.09416702 -0.60011874 -0.87877998
## [14,] 0.861752782 1.415749739 -0.76586465 2.00465326 3.27799959 0.29436199
## [15,] 0.307544630 0.004297736 -0.16576556 0.24738013 0.19712510 -0.70486291
## [16,] 0.149898848 -0.467792013 -0.76404892 0.56024775 -0.26230356 0.71082467
## [17,] 1.229919328 1.961703870 -0.78129836 1.08430101 0.25117553 0.50818918
## [18,] -0.356330153 0.720461096 -0.10857003 -0.43571417 0.92680590 -0.34749086
## [19,] -2.194225385 -1.334895633 0.95000113 -1.43689055 -0.01907662 -1.59790492
## [20,] -0.371996815 -1.739543989 -0.06226889 -0.92326621 -0.76227003 -0.23175991
## [21,] 0.087232202 -1.341318622 -0.30103752 0.07269571 -0.64065656 0.31567214
## [22,] 0.824544461 -0.679750675 -0.76949611 0.23955844 -0.54606831 0.35422213
## [23,] -0.069434414 1.073725534 -0.64330281 1.06083594 0.80519243 1.55673053
## [24,] 0.880356942 0.444272536 -0.68234102 -0.25060083 -0.37040442 0.83152034
## [25,] 0.571919543 0.116700057 -0.61425111 0.39077779 -0.37040442 -0.46904042
## [26,] 0.341815452 0.455512768 0.03668845 -0.51914553 0.02146120 -0.66350825
## [27,] 1.012544399 -0.361812681 0.36805935 0.22130783 0.41332682 -0.55339678
## [28,] 0.680607008 0.176112712 -0.53980614 -0.18542007 0.62952853 -0.48744127
## [29,] 0.796148636 -0.705442635 -1.03186923 -0.70686611 -0.14069009 -0.43313649
## [30,] -0.243726023 -0.454946033 -1.13808950 -1.01451926 -0.47850528 -1.25155920
## [31,] 0.107794695 0.338293204 -0.47534769 -0.25581529 1.02139415 -0.42340956
## [32,] 0.241940485 0.241948358 -0.29649819 -0.77465409 0.62952853 -0.57094374
## [33,] -0.492434275 0.145603511 0.64132686 -1.67414849 -0.11366487 0.52989760
## [34,] -4.089891431 -2.921374107 0.68853587 -2.90215390 -2.84321158 0.01237537
## di.kuadrat k p.k Chi.Square
## [1,] 0.04055128 0.75314467 0.75314467 0.005250145
## [2,] 0.39780542 1.15482182 1.15482182 0.674039137
## [3,] -0.74782794 -1.45607969 -1.45607969 -0.564131729
## [4,] -0.73699454 -1.25524111 -1.25524111 -0.564131729
## [5,] -0.63055100 -0.95398325 -0.95398325 -0.564130702
## [6,] -0.38010673 -0.15062893 -0.15062893 -0.531750295
## [7,] -0.89405736 -1.65691827 -1.65691827 -0.564131729
## [8,] -0.53720719 -0.55230609 -0.55230609 -0.562552827
## [9,] -0.04530292 0.55230609 0.55230609 -0.198666453
## [10,] 1.01027536 1.25524111 1.25524111 0.934166824
## [11,] 3.51479448 1.65691827 1.65691827 3.871020167
## [12,] -0.74347682 -1.35566040 -1.35566040 -0.564131729
## [13,] 0.02946543 0.65272538 0.65272538 -0.104672270
## [14,] 1.73641795 1.45607969 1.45607969 1.710912133
## [15,] -0.76352901 -1.55649898 -1.55649898 -0.564131729
## [16,] -0.32085601 -0.05020964 -0.05020964 -0.511436183
## [17,] 0.19446858 0.95398325 0.95398325 0.284026004
## [18,] -0.54579852 -0.75314467 -0.75314467 -0.564029664
## [19,] 0.38166551 1.05440254 1.05440254 0.461553992
## [20,] -0.30120355 0.15062893 0.15062893 -0.447532825
## [21,] -0.26636120 0.35146751 0.35146751 -0.345981121
## [22,] -0.46086443 -0.35146751 -0.35146751 -0.554749375
## [23,] 0.13037697 0.85356396 0.85356396 0.133636623
## [24,] -0.16332446 0.45188680 0.45188680 -0.278616898
## [25,] -0.53566467 -0.45188680 -0.45188680 -0.559932489
## [26,] -0.54243732 -0.65272538 -0.65272538 -0.563661232
## [27,] -0.29764657 0.25104822 0.25104822 -0.401944063
## [28,] -0.72497118 -1.15482182 -1.15482182 -0.564131729
## [29,] -0.31560430 0.05020964 0.05020964 -0.483707671
## [30,] -0.56755666 -0.85356396 -0.85356396 -0.564117557
## [31,] -0.65063900 -1.05440254 -1.05440254 -0.564131701
## [32,] -0.44777914 -0.25104822 -0.25104822 -0.545779577
## [33,] 1.55169593 1.35566040 1.35566040 1.264466737
## [34,] 2.63224360 1.55649898 1.55649898 2.393111517
## attr(,"scaled:center")
## X1 X2 X3 Y1 Y2 Y3
## 7.873912e+01 6.260324e+01 1.603588e+03 7.253118e+01 1.321412e+01 1.315934e+06
## di.kuadrat k p.k Chi.Square
## 5.823529e+00 1.750000e+01 5.000000e-01 7.515359e-01
## attr(,"scaled:scale")
## X1 X2 X3 Y1 Y2 Y3
## 1.021277e+01 6.227629e+00 1.101485e+03 3.835488e+00 7.400496e-01 2.962907e+05
## di.kuadrat k p.k Chi.Square
## 5.717309e+00 9.958246e+00 2.928896e-01 1.332199e+00#Menghitung rata-rata
mean <- colMeans(data.matriks)
mean## X1 X2 X3 Y1 Y2
## 3.109237e-16 1.963554e-16 9.734860e-17 -1.707172e-16 -1.060426e-15
## Y3 di.kuadrat k p.k Chi.Square
## 2.279121e-16 1.571455e-17 0.000000e+00 -1.632681e-18 -1.352064e-17#Menghitung covarian matriks
cov.matriks <- cov(data.matriks)
cov.matriks## X1 X2 X3 Y1 Y2 Y3
## X1 1.0000000 0.49086857 -0.3277968 0.59025170 0.36033401 0.19556484
## X2 0.4908686 1.00000000 -0.1842522 0.61410768 0.71574876 0.19617225
## X3 -0.3277968 -0.18425219 1.0000000 0.15711743 -0.13612654 0.34586046
## Y1 0.5902517 0.61410768 0.1571174 1.00000000 0.49574551 0.58791613
## Y2 0.3603340 0.71574876 -0.1361265 0.49574551 1.00000000 -0.04719024
## Y3 0.1955648 0.19617225 0.3458605 0.58791613 -0.04719024 1.00000000
## di.kuadrat -0.3675103 -0.11594729 0.5763574 0.13195614 -0.10964589 0.58969923
## k -0.2376672 -0.02433623 0.2956801 0.08987436 -0.09617730 0.43662278
## p.k -0.2376672 -0.02433623 0.2956801 0.08987436 -0.09617730 0.43662278
## Chi.Square -0.3589754 -0.06301309 0.6440249 0.20654626 -0.05681824 0.60490444
## di.kuadrat k p.k Chi.Square
## X1 -0.3675103 -0.23766724 -0.23766724 -0.35897545
## X2 -0.1159473 -0.02433623 -0.02433623 -0.06301309
## X3 0.5763574 0.29568012 0.29568012 0.64402494
## Y1 0.1319561 0.08987436 0.08987436 0.20654626
## Y2 -0.1096459 -0.09617730 -0.09617730 -0.05681824
## Y3 0.5896992 0.43662278 0.43662278 0.60490444
## di.kuadrat 1.0000000 0.80768184 0.80768184 0.98714228
## k 0.8076818 1.00000000 1.00000000 0.74909162
## p.k 0.8076818 1.00000000 1.00000000 0.74909162
## Chi.Square 0.9871423 0.74909162 0.74909162 1.00000000#Membuat partisi antara 2 himpunan variabel dari covarian matriks
P11 <- cov.matriks[1:3, 1:3]
P11## X1 X2 X3
## X1 1.0000000 0.4908686 -0.3277968
## X2 0.4908686 1.0000000 -0.1842522
## X3 -0.3277968 -0.1842522 1.0000000P12 <- cov.matriks[1:3, 4:6]
P12## Y1 Y2 Y3
## X1 0.5902517 0.3603340 0.1955648
## X2 0.6141077 0.7157488 0.1961722
## X3 0.1571174 -0.1361265 0.3458605P21 <- cov.matriks[4:6, 1:3]
P21## X1 X2 X3
## Y1 0.5902517 0.6141077 0.1571174
## Y2 0.3603340 0.7157488 -0.1361265
## Y3 0.1955648 0.1961722 0.3458605P22 <- cov.matriks[4:6, 4:6]
P22## Y1 Y2 Y3
## Y1 1.0000000 0.49574551 0.58791613
## Y2 0.4957455 1.00000000 -0.04719024
## Y3 0.5879161 -0.04719024 1.00000000#Mencari nilai sigma 11^-1/2
eig.P11 <- eigen(P11)
nilai.eigen.P11 <- eig.P11$values
nilai.eigen.P11## [1] 1.6847911 0.8326684 0.4825405l1.11 <- nilai.eigen.P11[1]
l2.11 <- nilai.eigen.P11[2]
l3.11 <- nilai.eigen.P11[3]
vector.eigen.P11 <- eig.P11$vectors
vector.eigen.P11## [,1] [,2] [,3]
## [1,] -0.6516150 0.1412073 0.7452908
## [2,] -0.5940164 0.5160418 -0.6171267
## [3,] 0.4717440 0.8448440 0.2523811v1.11<-matrix(vector.eigen.P11[,1])
v1.11## [,1]
## [1,] -0.6516150
## [2,] -0.5940164
## [3,] 0.4717440v2.11<-matrix(vector.eigen.P11[,2])
v2.11## [,1]
## [1,] 0.1412073
## [2,] 0.5160418
## [3,] 0.8448440v3.11<-matrix(vector.eigen.P11[,3])
v3.11## [,1]
## [1,] 0.7452908
## [2,] -0.6171267
## [3,] 0.2523811sig11<-((v1.11%*%t(v1.11))/sqrt(l1.11))+((v2.11%*%t(v2.11))/sqrt(l2.11))+((v3.11%*%t(v3.11))/sqrt(l3.11))
sig11## [,1] [,2] [,3]
## [1,] 1.1485947 -0.28405291 0.16469291
## [2,] -0.2840529 1.11193309 0.03767269
## [3,] 0.1646929 0.03767269 1.04534468eig.P22<-eigen(P22)
nilai.eigen.P22<-eig.P22$values
nilai.eigen.P22## [1] 1.7461706 1.0465073 0.2073221l1.22<-nilai.eigen.P22[1]
l2.22<-nilai.eigen.P22[2]
l3.22<-nilai.eigen.P22[3]
vektor.eigen.P22<-eig.P22$vectors
vektor.eigen.P22## [,1] [,2] [,3]
## [1,] 0.7176710 -0.0104393 0.6963041
## [2,] 0.4428203 -0.7648545 -0.4678758
## [3,] 0.5374556 0.6441185 -0.5442911v1.22<-matrix(vektor.eigen.P22[,1])
v1.22## [,1]
## [1,] 0.7176710
## [2,] 0.4428203
## [3,] 0.5374556v2.22<-matrix(vektor.eigen.P22[,2])
v2.22## [,1]
## [1,] -0.0104393
## [2,] -0.7648545
## [3,] 0.6441185v3.22<-matrix(vektor.eigen.P22[,3])
v3.22## [,1]
## [1,] 0.6963041
## [2,] -0.4678758
## [3,] -0.5442911sig22<-((v1.22%*%t(v1.22))/sqrt(l1.22))+((v2.22%*%t(v2.22))/sqrt(l2.22))+((v3.22%*%t(v3.22))/sqrt(l3.22))
sig22## [,1] [,2] [,3]
## [1,] 1.4546930 -0.4671932 -0.5470322
## [2,] -0.4671932 1.2010194 0.2578125
## [3,] -0.5470322 0.2578125 1.2747993#mencari nilai eigen dan vektor eigen a untuk sigma 11 (matriks m)
M.sig.11<-sig11%*%P12%*%solve(P22)%*%P21%*%sig11
M.sig.11## [,1] [,2] [,3]
## [1,] 0.3156483 0.2187726 0.1357155
## [2,] 0.2187726 0.5244869 0.0539689
## [3,] 0.1357155 0.0539689 0.1745388#Nilai eigen matriks m
eigen11<-eigen(M.sig.11)
nilai.eigenM11<-eigen11$values
nilai.eigenM11## [1] 0.69028138 0.24724364 0.07714894l1.M11<-nilai.eigenM11[1]
l1.M11## [1] 0.6902814l2.M11<-nilai.eigenM11[2]
l2.M11## [1] 0.2472436l3.M11<-nilai.eigenM11[3]
l3.M11## [1] 0.07714894#Vektor eigen matriks m
vektor.eigen.M11<-eigen11$vectors
vektor.eigen.M11## [,1] [,2] [,3]
## [1,] -0.5514148 0.5532916 0.6243477
## [2,] -0.8021723 -0.5571452 -0.2147296
## [3,] -0.2290443 0.6192395 -0.7510533e1<-matrix(vektor.eigen.M11[,1])
e1## [,1]
## [1,] -0.5514148
## [2,] -0.8021723
## [3,] -0.2290443e2<-matrix(vektor.eigen.M11[,2])
e2## [,1]
## [1,] 0.5532916
## [2,] -0.5571452
## [3,] 0.6192395e3<-matrix(vektor.eigen.M11[,3])
e3## [,1]
## [1,] 0.6243477
## [2,] -0.2147296
## [3,] -0.7510533#mencari nilai eigen dan vektor eigen a untuk sigma 22 (matriks n)
N.sig.22<-sig22%*%P21%*%solve(P11)%*%P12%*%sig22
N.sig.22## [,1] [,2] [,3]
## [1,] 0.4766611 0.21318775 0.14106448
## [2,] 0.2131877 0.40583824 0.04178952
## [3,] 0.1410645 0.04178952 0.13217459#Nilai eigen matriks n
eigen22<-eigen(N.sig.22)
nilai.eigenM22<-eigen22$values
nilai.eigenM22## [1] 0.69028138 0.24724364 0.07714894l1.M22<-nilai.eigenM22[1]
l1.M22## [1] 0.6902814l2.M22<-nilai.eigenM22[2]
l2.M22## [1] 0.2472436l3.M22<-nilai.eigenM22[3]
l3.M22## [1] 0.07714894#Vektor eigen matriks n
vektor.eigen.M22<-eigen22$vectors
vektor.eigen.M22## [,1] [,2] [,3]
## [1,] -0.7602507 0.5151130 -0.3958250
## [2,] -0.6046847 -0.7838186 0.1413678
## [3,] -0.2374346 0.3468243 0.9073796v1.M22<-matrix(vektor.eigen.M22[,1])
v1.M22## [,1]
## [1,] -0.7602507
## [2,] -0.6046847
## [3,] -0.2374346v2.M22<-matrix(vektor.eigen.M22[,2])
v2.M22## [,1]
## [1,] 0.5151130
## [2,] -0.7838186
## [3,] 0.3468243v3.M22<-matrix(vektor.eigen.M22[,3])
v3.M22## [,1]
## [1,] -0.3958250
## [2,] 0.1413678
## [3,] 0.9073796#mencari nilai koefisien a
a1<-sig11%*%e1
a1## [,1]
## [1,] -0.4432147
## [2,] -0.7439597
## [3,] -0.3604643a2<-sig11%*%e2
a2## [,1]
## [1,] 0.8957509
## [2,] -0.7533438
## [3,] 0.7174528a3<-sig11%*%e3
a3## [,1]
## [1,] 0.6544239
## [2,] -0.4444069
## [3,] -0.6903734#mencari nilai koefisien b
b1<-sig22%*%v1.M22
b1## [,1]
## [1,] -0.69354246
## [2,] -0.43226770
## [3,] -0.04269513b2<-sig22%*%v2.M22
b2## [,1]
## [1,] 0.92580189
## [2,] -1.09262292
## [3,] -0.04173022b3<-sig22%*%v3.M22
b3## [,1]
## [1,] -1.138216
## [2,] 0.588646
## [3,] 1.409702#Korelasi U1V1
U1V1<-(t(a1)%*%P12%*%b1)/((sqrt(t(a1)%*%P11%*%a1))*(sqrt(t(b1)%*%P22%*%b1)))
U1V1## [,1]
## [1,] 0.8308317#Korelasi U2V2
U2V2<-(t(a2)%*%P12%*%b2)/((sqrt(t(a2)%*%P11%*%a2))*(sqrt(t(b2)%*%P22%*%b2)))
U2V2## [,1]
## [1,] 0.497236#Korelasi U3V3
U3V3<-(t(a3)%*%P12%*%b3)/((sqrt(t(a3)%*%P11%*%a3))*(sqrt(t(b3)%*%P22%*%b3)))
U3V3## [,1]
## [1,] -0.277757Interpretasi Korelasi Kanonik: Koefisien korelasi kanonik fungsi pertama sebesar 0,8308. Hal tersebut menunjukkan secara nyata adanya hubungan yang kuat antar variabel kanonik. Kanonik fungsi kedua menunjukkan adanya hubungan yang sedang antar variabel kanonik yaitu sebesar 0,4972 dan yang terakhir, fungsi kanonik ketiga, yang menunjukkan adanya hubungan yang lemah dan negatif antar variabel kanonik yaitu sebesar -0,2778.
an<-(t(a1)%*%P11%*%a1)
an## [,1]
## [1,] 1#Uji korelasi kanonik secara simultan
n <- 34
p <- 3
q <- 3
Lambda1 <- U1V1
Lambda2 <- U2V2
Lambda3 <- U3V3
lambda <- (1 - Lambda1^2) * (1 - Lambda2) * (1 - Lambda3)
# Perhitungan B
B <- - ( (n - 1) - (1/2) * (p + q + 1) ) * log(lambda)
B## [,1]
## [1,] 47.63127# Menghitung nilai chi-square kritis
alpha <- 0.05
df <- 9
chi_critical <- qchisq(1 - alpha, df)
print(paste("Nilai chi-square dengan taraf signifikan 5% dan df = 9 yaitu", chi_critical))## [1] "Nilai chi-square dengan taraf signifikan 5% dan df = 9 yaitu 16.9189776046204"Interpretasi: Karena, nilai B > nilai chi-square yaitu 47.6313 > 16.9189, maka belum cukup bukti untuk menerima H0, dengan kata lain kita terima H0. artinya, paling tidak ada satu korelasi kanonik yang tidak bernilai nol.
#Uji korelasi kanonik secara individu
lamda1 <- (1 - Lambda1^2) * (1 - Lambda2) * (1 - Lambda3)
lamda2 <- (1 - Lambda2) * (1 - Lambda3)
lamda3 <- (1 - Lambda3)
B1 <- - ( (n - 1) - (1/2) * (p + q + 1) ) * log(lamda1)
print(paste("Nilai B1 yaitu", B1))## [1] "Nilai B1 yaitu 47.6312691697728"# Menghitung nilai chi-square kritis B1
alpha <- 0.05
df <- 9
chi_critical.B1 <- qchisq(1 - alpha, df)
cat("Nilai chi-square B1 dengan taraf signifikan 5% dan df = 9 yaitu", chi_critical.B1,"\n\n")## Nilai chi-square B1 dengan taraf signifikan 5% dan df = 9 yaitu 16.91898B2 <- - ( (n - 1) - (1/2) * (p + q + 1) ) * log(lamda2)
print(paste("Nilai B2 yaitu", B2))## [1] "Nilai B2 yaitu 13.0545825875325"# Menghitung nilai chi-square kritis
alpha <- 0.05
df <- 4
chi_critical.B2 <- qchisq(1 - alpha, df)
cat("Nilai chi-square B2 dengan taraf signifikan 5% dan df = 4 yaitu", chi_critical.B2, "\n\n")## Nilai chi-square B2 dengan taraf signifikan 5% dan df = 4 yaitu 9.487729B3 <- - ( (n - 1) - (1/2) * (p + q + 1) ) * log(lamda3)
print(paste("Nilai B3 yaitu", B3))## [1] "Nilai B3 yaitu -7.23063226489732"# Menghitung nilai chi-square kritis
alpha <- 0.05
df <- 1
chi_critical.B3 <- qchisq(1 - alpha, df)
cat("Nilai chi-square B3 dengan taraf signifikan 5% dan df = 1 yaitu", chi_critical.B3, "\n\n")## Nilai chi-square B3 dengan taraf signifikan 5% dan df = 1 yaitu 3.841459Interpretasi korelasi kanonik secara individu: Berdasarkan hasil diatas dapat dilihat bahwa fungsi kanonik ke-1 dan ke-2 memiliki nilai hitung B > X^2, dari hasil pengujian individu tersebut, dapat disimpulkan bahwa fungsi korelasi kanonik pertama dan kedua yang signifikan dan dapat diinterpretasikan lebih lanjut.
#Muatan Kanonik untuk variabel X
xk1 <- sig11 %*% a1
xk1## [,1]
## [1,] -0.3571161
## [2,] -0.7149166
## [3,] -0.4778307xk2 <- sig11 %*% a2
xk2## [,1]
## [1,] 1.3610037
## [2,] -1.0650802
## [3,] 0.8691288Interpretasi: Pada fungsi kanonik pertama, variabel yang memiliki kontribusi terbesar adalah Angka Partisipasi Murni (X2) (-0.7149). Hal ini menunjukkan bahwa Angka Partisipasi Murni (X2) memiliki pengaruh terbesar dalam membentuk hubungan dengan variabel terikat pada fungsi pertama dibandingkan dengan variabel lainnya.
Pada fungsi kanonik kedua, variabel yang memiliki kontribusi terbesar adalah Akses pada Fasilitas Kesehatan Dasar (X1) (1.3610). Ini menunjukkan bahwa Akses pada Fasilitas Kesehatan Dasar (X1) lebih dominan dalam membentuk hubungan pada fungsi kanonik kedua dibandingkan variabel lainnya.
#Muatan Kanonik untuk variabel Y
yk1 <- sig22 %*% b1
yk1## [,1]
## [1,] -0.7835832
## [2,] -0.2061509
## [3,] 0.2135183yk2 <- sig22 %*% b2
yk2## [,1]
## [1,] 1.8800513
## [2,] -1.7555483
## [3,] -0.8413329Interpretasi: Pada fungsi kanonik pertama, variabel yang memiliki kontribusi terbesar adalah Umur Harapan Hidup (Y1) (-0.7836), diikuti oleh Rata-rata Pengeluaran Perkapita Sebulan (Y3) (0.2135), dan Harapan Lama Sekolah (Y2) (-0.2062). Hal ini mengindikasikan bahwa Umur Harapan Hidup (Y1) memiliki hubungan paling kuat dengan variabel bebas pada fungsi pertama, diikuti oleh Rata-rata Pengeluaran Perkapita Sebulan (Y3) dan Harapan Lama Sekolah (Y2).
Pada fungsi kanonik kedua, variabel yang memiliki kontribusi terbesar adalah Umur Harapan Hidup (Y1) (1.8801), diikuti oleh Harapan Lama Sekolah (Y2) (-1.7555), dan Rata-rata Pengeluaran Perkapita Sebulan (Y3) (-0.8413). Ini menunjukkan bahwa Umur Harapan Hidup (Y1) tetap menjadi variabel paling dominan dalam membentuk hubungan dengan variabel bebas pada fungsi kedua, sementara Harapan Lama Sekolah (Y2) memiliki korelasi negatif yang cukup besar.
#ANALISIS KORELASI KANONIK DENGAN CEPAT
X <- data.frame(X1,X2,X3)
Y <- data.frame(Y1,Y2,Y3)
#Menghitung Analisis Korelasi Kanonik
cor.XY <- cancor(X,Y)
cor.XY## $cor
## [1] 0.8308317 0.4972360 0.2777570
##
## $xcoef
## [,1] [,2] [,3]
## X1 -7.554638e-03 -0.0152681627 -0.011154720
## X2 -2.079552e-02 0.0210578252 0.012422273
## X3 -5.696745e-05 -0.0001133856 0.000109106
##
## $ycoef
## [,1] [,2] [,3]
## Y1 -3.147715e-02 -4.201849e-02 -5.165912e-02
## Y2 -1.016799e-01 2.570115e-01 1.384639e-01
## Y3 -2.508438e-08 2.451747e-08 8.282329e-07
##
## $xcenter
## X1 X2 X3
## 78.73912 62.60324 1603.58824
##
## $ycenter
## Y1 Y2 Y3
## 7.253118e+01 1.321412e+01 1.315934e+06