library(car)
## Loading required package: carData
library(CCA)
## Loading required package: fda
## Loading required package: splines
## Loading required package: fds
## Loading required package: rainbow
## Loading required package: MASS
## Loading required package: pcaPP
## Loading required package: RCurl
## Loading required package: deSolve
##
## Attaching package: 'fda'
## The following object is masked from 'package:graphics':
##
## matplot
## Loading required package: fields
## Loading required package: spam
## Spam version 2.11-0 (2024-10-03) is loaded.
## Type 'help( Spam)' or 'demo( spam)' for a short introduction
## and overview of this package.
## Help for individual functions is also obtained by adding the
## suffix '.spam' to the function name, e.g. 'help( chol.spam)'.
##
## Attaching package: 'spam'
## The following objects are masked from 'package:base':
##
## backsolve, forwardsolve
## Loading required package: viridisLite
##
## Try help(fields) to get started.
library(candisc)
## Loading required package: heplots
## Loading required package: broom
##
## Attaching package: 'candisc'
## The following object is masked from 'package:stats':
##
## cancor
library(readxl)
dataset <- read_excel("dataset.xlsx")
dataCCA <- dataset
dataCCA
## # A tibble: 34 × 6
## X1 X2 X3 Y1 Y2 Y3
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 15.3 14.6 14.4 9.38 9.45 9.55
## 2 9.01 8.42 8.15 9.59 9.72 9.82
## 3 6.63 5.92 5.95 9.07 9.18 9.28
## 4 7.12 6.78 6.68 9.21 9.25 9.34
## 5 8.09 7.62 7.58 8.59 8.68 8.81
## 6 12.8 11.9 11.8 8.30 8.39 8.5
## 7 15.2 14.6 14.0 8.89 8.92 9.02
## 8 12.6 11.6 11.1 8.07 8.17 8.28
## 9 4.9 4.45 4.52 8.12 8.15 8.28
## 10 6.12 6.24 5.69 10.2 10.4 10.4
## # ℹ 24 more rows
CCA <- as.matrix(dataCCA) #mengubah menjadi matriks
rata2<- colMeans(CCA) #rata rata masing masing varibael
rata2
## X1 X2 X3 Y1 Y2 Y3
## 10.762353 10.243235 10.089118 8.761618 8.882206 8.972059
n <- nrow(dataCCA) #menghitung jumlah baris pada data
n
## [1] 34
p <- ncol (dataCCA)
p
## [1] 6
kovarian <- cov(CCA) #covarian dari data CCA yaitu gabungan dari cov X dan Y
d<- mahalanobis(CCA,rata2,kovarian) #Sebelum melakukan KK kita perlu menghitung jarak mahalanobis untuk melihat normalitas data
d
## [1] 3.178702 1.859418 1.632642 3.223461 2.679754 1.818222 6.360051
## [8] 6.980799 6.829145 6.866996 14.695965 3.995753 3.892642 7.187205
## [15] 3.461068 2.553188 11.936217 8.585601 4.845631 4.173037 5.134871
## [22] 2.834425 3.151160 4.286571 3.026196 4.626417 6.149263 5.035178
## [29] 2.748290 8.815909 17.158253 3.964074 9.889131 14.424764
qchisq(ppoints(n), df=p) #q chisquare
## [1] 1.008342 1.553205 1.924941 2.233120 2.507324 2.760624 3.000186
## [8] 3.230487 3.454599 3.674787 3.892832 4.110211 4.328215 4.548029
## [15] 4.770788 4.997626 5.229717 5.468318 5.714817 5.970786 6.238051
## [22] 6.518782 6.815625 7.131875 7.471751 7.840804 8.246593 8.699829
## [29] 9.216475 9.821954 10.560668 11.521732 12.932673 15.828291
qqplot (qchisq(ppoints(n), df=p),d,xlim=c(0,30),pch=20,col="black",ylim=c(0,30),main="QQ Plot Data",
ylab="Jarak Mahalanobis") #Asumsi normalitasnya terpenuhi berdasarkan plot karena berada dalam garis berarti berdistribusi normal
abline(a=0,b=1,col="red")
qchisq(ppoints(n),df=p)
## [1] 1.008342 1.553205 1.924941 2.233120 2.507324 2.760624 3.000186
## [8] 3.230487 3.454599 3.674787 3.892832 4.110211 4.328215 4.548029
## [15] 4.770788 4.997626 5.229717 5.468318 5.714817 5.970786 6.238051
## [22] 6.518782 6.815625 7.131875 7.471751 7.840804 8.246593 8.699829
## [29] 9.216475 9.821954 10.560668 11.521732 12.932673 15.828291
#Untuk melihat asumsi multikolinearitas
dataCCA
## # A tibble: 34 × 6
## X1 X2 X3 Y1 Y2 Y3
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 15.3 14.6 14.4 9.38 9.45 9.55
## 2 9.01 8.42 8.15 9.59 9.72 9.82
## 3 6.63 5.92 5.95 9.07 9.18 9.28
## 4 7.12 6.78 6.68 9.21 9.25 9.34
## 5 8.09 7.62 7.58 8.59 8.68 8.81
## 6 12.8 11.9 11.8 8.30 8.39 8.5
## 7 15.2 14.6 14.0 8.89 8.92 9.02
## 8 12.6 11.6 11.1 8.07 8.17 8.28
## 9 4.9 4.45 4.52 8.12 8.15 8.28
## 10 6.12 6.24 5.69 10.2 10.4 10.4
## # ℹ 24 more rows
X <- dataCCA[, c("X1", "X2", "X3")]
X
## # A tibble: 34 × 3
## X1 X2 X3
## <dbl> <dbl> <dbl>
## 1 15.3 14.6 14.4
## 2 9.01 8.42 8.15
## 3 6.63 5.92 5.95
## 4 7.12 6.78 6.68
## 5 8.09 7.62 7.58
## 6 12.8 11.9 11.8
## 7 15.2 14.6 14.0
## 8 12.6 11.6 11.1
## 9 4.9 4.45 4.52
## 10 6.12 6.24 5.69
## # ℹ 24 more rows
Y <- dataCCA[, c("Y1", "Y2", "Y3")]
Y
## # A tibble: 34 × 3
## Y1 Y2 Y3
## <dbl> <dbl> <dbl>
## 1 9.38 9.45 9.55
## 2 9.59 9.72 9.82
## 3 9.07 9.18 9.28
## 4 9.21 9.25 9.34
## 5 8.59 8.68 8.81
## 6 8.30 8.39 8.5
## 7 8.89 8.92 9.02
## 8 8.07 8.17 8.28
## 9 8.12 8.15 8.28
## 10 10.2 10.4 10.4
## # ℹ 24 more rows
korelasi <- matcor(X,Y)
korelasi #mencari apakah ada yang diatas 0.8 hasil cor nya
## $Xcor
## X1 X2 X3
## X1 1.0000000 0.9968177 0.9972616
## X2 0.9968177 1.0000000 0.9987520
## X3 0.9972616 0.9987520 1.0000000
##
## $Ycor
## Y1 Y2 Y3
## Y1 1.0000000 0.9983514 0.998037
## Y2 0.9983514 1.0000000 0.999411
## Y3 0.9980370 0.9994110 1.000000
##
## $XYcor
## X1 X2 X3 Y1 Y2 Y3
## X1 1.0000000 0.9968177 0.9972616 -0.3951843 -0.3969859 -0.3986361
## X2 0.9968177 1.0000000 0.9987520 -0.4101743 -0.4113221 -0.4125987
## X3 0.9972616 0.9987520 1.0000000 -0.4142962 -0.4157257 -0.4171227
## Y1 -0.3951843 -0.4101743 -0.4142962 1.0000000 0.9983514 0.9980370
## Y2 -0.3969859 -0.4113221 -0.4157257 0.9983514 1.0000000 0.9994110
## Y3 -0.3986361 -0.4125987 -0.4171227 0.9980370 0.9994110 1.0000000
img.matcor(korelasi, type=2)
analisis <- candisc::cancor(X,Y)
summary (analisis)
##
## Canonical correlation analysis of:
## 3 X variables: X1, X2, X3
## with 3 Y variables: Y1, Y2, Y3
##
## CanR CanRSQ Eigen percent cum scree
## 1 0.48088 0.2312493 0.3008119 85.1922 85.19 ******************************
## 2 0.22200 0.0492836 0.0518384 14.6810 99.87 *****
## 3 0.02116 0.0004476 0.0004478 0.1268 100.00
##
## Test of H0: The canonical correlations in the
## current row and all that follow are zero
##
## CanR LR test stat approx F numDF denDF Pr(> F)
## 1 0.48088 0.73054 1.04493 9 68.295 0.4144
## 2 0.22200 0.95029 0.37441 4 58.000 0.8260
## 3 0.02116 0.99955 0.01343 1 30.000 0.9085
##
## Raw canonical coefficients
##
## X variables:
## Xcan1 Xcan2 Xcan3
## X1 1.26447 1.8909 -1.1826
## X2 0.12974 -2.8832 -2.6350
## X3 -1.61104 1.0128 3.8170
##
## Y variables:
## Ycan1 Ycan2 Ycan3
## Y1 1.39602 14.6894 12.289
## Y2 0.39315 9.0547 -33.870
## Y3 -0.70440 -23.9981 21.736
hasil <- cc(X,Y)
hasil
## $cor
## [1] 0.48088390 0.22199921 0.02115657
##
## $names
## $names$Xnames
## [1] "X1" "X2" "X3"
##
## $names$Ynames
## [1] "Y1" "Y2" "Y3"
##
## $names$ind.names
## [1] "1" "2" "3" "4" "5" "6" "7" "8" "9" "10" "11" "12" "13" "14" "15"
## [16] "16" "17" "18" "19" "20" "21" "22" "23" "24" "25" "26" "27" "28" "29" "30"
## [31] "31" "32" "33" "34"
##
##
## $xcoef
## [,1] [,2] [,3]
## X1 1.2644667 1.890923 -1.182560
## X2 0.1297381 -2.883217 -2.634965
## X3 -1.6110390 1.012772 3.816965
##
## $ycoef
## [,1] [,2] [,3]
## Y1 1.3960219 14.689415 12.28876
## Y2 0.3931482 9.054677 -33.87048
## Y3 -0.7044044 -23.998129 21.73638
##
## $scores
## $scores$xscores
## [,1] [,2] [,3]
## [1,] -0.6794862 0.37682535 -0.34150444
## [2,] 0.6716592 -0.02066714 -0.52511976
## [3,] 0.8821690 0.45887824 0.47946349
## [4,] 0.4372740 -0.35481185 0.42032348
## [5,] 0.3228516 -0.03102330 0.49513775
## [6,] 0.1179836 0.86433812 -0.36842147
## [7,] -0.1606463 -0.18874855 -1.72367907
## [8,] 0.8763834 0.72123899 -1.79608622
## [9,] 0.8077125 -0.02235471 0.94043162
## [10,] 0.6976774 -1.69144257 -0.75303025
## [11,] 0.7401287 -1.13571460 0.21554378
## [12,] 0.7074795 -0.67294157 -0.87816190
## [13,] 0.2915970 0.65268891 -0.42595161
## [14,] 1.1869204 1.65385084 -1.67009275
## [15,] 0.4037354 1.07563363 -0.11864763
## [16,] 0.5968116 0.04644390 0.65132739
## [17,] 0.7904089 -1.34143074 0.03120273
## [18,] -1.3421267 0.28685147 1.30512982
## [19,] -1.6975466 1.06162386 -0.25847995
## [20,] 0.4203899 -0.12354016 0.63110384
## [21,] 0.2936434 -1.32624872 0.69795439
## [22,] 1.0949283 -0.50298564 0.03991036
## [23,] 0.5611987 -0.67371567 0.16897204
## [24,] 1.1099876 -0.10509585 -0.71504330
## [25,] 0.1963191 0.14162050 1.00605216
## [26,] -0.6388690 0.56514933 0.71402185
## [27,] -0.4779946 -0.50403003 1.29285721
## [28,] -0.9049323 0.38332679 1.61458649
## [29,] -1.3519671 -0.63368441 -0.05601851
## [30,] -1.3941992 -1.92781393 0.75287220
## [31,] -0.4689360 3.34025330 0.66970951
## [32,] 0.4295193 0.57323503 1.30181075
## [33,] -1.3105358 -0.48483942 -2.61341990
## [34,] -3.2095389 -0.46086942 -1.18475411
##
## $scores$yscores
## [,1] [,2] [,3]
## [1,] 0.6863783 0.42880739 0.991485926
## [2,] 0.8780215 -0.78803232 0.281713341
## [3,] 0.3271486 -0.28361687 0.505415506
## [4,] 0.5148918 1.20682214 0.941726948
## [5,] -0.2068897 -0.50803660 1.386622270
## [6,] -0.5123980 0.01742308 0.676246890
## [7,] 0.1567913 0.95758597 1.448304161
## [8,] -0.7545684 -0.04667938 0.750903476
## [9,] -0.6960884 0.55324138 1.872625082
## [10,] 1.5255043 -1.08640381 -0.776377906
## [11,] 2.5726569 -2.19714999 1.566431347
## [12,] -0.1607226 0.13780976 -1.381366462
## [13,] -1.1089838 -0.56091041 -0.812725032
## [14,] 0.9684989 0.17026497 0.050935772
## [15,] -0.9461587 0.09307942 -0.645186846
## [16,] 0.1603198 -0.52506548 -1.189387361
## [17,] 0.2849290 -2.13096333 -2.441041498
## [18,] -1.5255099 -1.55412835 1.140054329
## [19,] -1.1304586 0.82836114 -0.527140045
## [20,] -1.4526684 -0.16713511 0.009863574
## [21,] -0.1165020 1.31237565 -0.008170449
## [22,] -0.4553111 0.15764108 -0.224225784
## [23,] 1.1724386 0.24674407 -1.058680582
## [24,] 0.6755048 1.45999694 -0.452883431
## [25,] 0.9393964 0.49036949 0.918375945
## [26,] 0.1757576 1.80227601 -0.342789182
## [27,] -0.3694155 -1.88356570 0.844722127
## [28,] 0.4258345 0.65979587 -0.353986861
## [29,] -0.9373584 0.23775841 0.506474049
## [30,] -0.8483556 0.92884569 -0.765735896
## [31,] 1.4003034 0.35993048 -1.305009463
## [32,] 0.3779029 0.77887401 -1.099799905
## [33,] 0.2381839 0.22047924 0.055995099
## [34,] -2.2590735 -1.31679483 -0.563389139
##
## $scores$corr.X.xscores
## [,1] [,2] [,3]
## X1 -0.8177336 0.3678225 -0.4427395
## X2 -0.8497526 0.2949835 -0.4369272
## X3 -0.8579913 0.3249537 -0.3978140
##
## $scores$corr.Y.xscores
## [,1] [,2] [,3]
## Y1 0.4807295 -0.005516707 0.0001049456
## Y2 0.4795781 -0.014058273 -0.0007954096
## Y3 0.4791014 -0.018933146 -0.0002376941
##
## $scores$corr.X.yscores
## [,1] [,2] [,3]
## X1 -0.3932349 0.08165630 -0.009366848
## X2 -0.4086323 0.06548609 -0.009243878
## X3 -0.4125942 0.07213945 -0.008416378
##
## $scores$corr.Y.yscores
## [,1] [,2] [,3]
## Y1 0.9996789 -0.02485012 0.004960429
## Y2 0.9972845 -0.06332578 -0.037596350
## Y3 0.9962933 -0.08528475 -0.011235004
plot(hasil$cor,type="b")
hasil$cor
## [1] 0.48088390 0.22199921 0.02115657
hasil$xcoef
## [,1] [,2] [,3]
## X1 1.2644667 1.890923 -1.182560
## X2 0.1297381 -2.883217 -2.634965
## X3 -1.6110390 1.012772 3.816965
hasil$ycoef
## [,1] [,2] [,3]
## Y1 1.3960219 14.689415 12.28876
## Y2 0.3931482 9.054677 -33.87048
## Y3 -0.7044044 -23.998129 21.73638
hasil$scores
## $xscores
## [,1] [,2] [,3]
## [1,] -0.6794862 0.37682535 -0.34150444
## [2,] 0.6716592 -0.02066714 -0.52511976
## [3,] 0.8821690 0.45887824 0.47946349
## [4,] 0.4372740 -0.35481185 0.42032348
## [5,] 0.3228516 -0.03102330 0.49513775
## [6,] 0.1179836 0.86433812 -0.36842147
## [7,] -0.1606463 -0.18874855 -1.72367907
## [8,] 0.8763834 0.72123899 -1.79608622
## [9,] 0.8077125 -0.02235471 0.94043162
## [10,] 0.6976774 -1.69144257 -0.75303025
## [11,] 0.7401287 -1.13571460 0.21554378
## [12,] 0.7074795 -0.67294157 -0.87816190
## [13,] 0.2915970 0.65268891 -0.42595161
## [14,] 1.1869204 1.65385084 -1.67009275
## [15,] 0.4037354 1.07563363 -0.11864763
## [16,] 0.5968116 0.04644390 0.65132739
## [17,] 0.7904089 -1.34143074 0.03120273
## [18,] -1.3421267 0.28685147 1.30512982
## [19,] -1.6975466 1.06162386 -0.25847995
## [20,] 0.4203899 -0.12354016 0.63110384
## [21,] 0.2936434 -1.32624872 0.69795439
## [22,] 1.0949283 -0.50298564 0.03991036
## [23,] 0.5611987 -0.67371567 0.16897204
## [24,] 1.1099876 -0.10509585 -0.71504330
## [25,] 0.1963191 0.14162050 1.00605216
## [26,] -0.6388690 0.56514933 0.71402185
## [27,] -0.4779946 -0.50403003 1.29285721
## [28,] -0.9049323 0.38332679 1.61458649
## [29,] -1.3519671 -0.63368441 -0.05601851
## [30,] -1.3941992 -1.92781393 0.75287220
## [31,] -0.4689360 3.34025330 0.66970951
## [32,] 0.4295193 0.57323503 1.30181075
## [33,] -1.3105358 -0.48483942 -2.61341990
## [34,] -3.2095389 -0.46086942 -1.18475411
##
## $yscores
## [,1] [,2] [,3]
## [1,] 0.6863783 0.42880739 0.991485926
## [2,] 0.8780215 -0.78803232 0.281713341
## [3,] 0.3271486 -0.28361687 0.505415506
## [4,] 0.5148918 1.20682214 0.941726948
## [5,] -0.2068897 -0.50803660 1.386622270
## [6,] -0.5123980 0.01742308 0.676246890
## [7,] 0.1567913 0.95758597 1.448304161
## [8,] -0.7545684 -0.04667938 0.750903476
## [9,] -0.6960884 0.55324138 1.872625082
## [10,] 1.5255043 -1.08640381 -0.776377906
## [11,] 2.5726569 -2.19714999 1.566431347
## [12,] -0.1607226 0.13780976 -1.381366462
## [13,] -1.1089838 -0.56091041 -0.812725032
## [14,] 0.9684989 0.17026497 0.050935772
## [15,] -0.9461587 0.09307942 -0.645186846
## [16,] 0.1603198 -0.52506548 -1.189387361
## [17,] 0.2849290 -2.13096333 -2.441041498
## [18,] -1.5255099 -1.55412835 1.140054329
## [19,] -1.1304586 0.82836114 -0.527140045
## [20,] -1.4526684 -0.16713511 0.009863574
## [21,] -0.1165020 1.31237565 -0.008170449
## [22,] -0.4553111 0.15764108 -0.224225784
## [23,] 1.1724386 0.24674407 -1.058680582
## [24,] 0.6755048 1.45999694 -0.452883431
## [25,] 0.9393964 0.49036949 0.918375945
## [26,] 0.1757576 1.80227601 -0.342789182
## [27,] -0.3694155 -1.88356570 0.844722127
## [28,] 0.4258345 0.65979587 -0.353986861
## [29,] -0.9373584 0.23775841 0.506474049
## [30,] -0.8483556 0.92884569 -0.765735896
## [31,] 1.4003034 0.35993048 -1.305009463
## [32,] 0.3779029 0.77887401 -1.099799905
## [33,] 0.2381839 0.22047924 0.055995099
## [34,] -2.2590735 -1.31679483 -0.563389139
##
## $corr.X.xscores
## [,1] [,2] [,3]
## X1 -0.8177336 0.3678225 -0.4427395
## X2 -0.8497526 0.2949835 -0.4369272
## X3 -0.8579913 0.3249537 -0.3978140
##
## $corr.Y.xscores
## [,1] [,2] [,3]
## Y1 0.4807295 -0.005516707 0.0001049456
## Y2 0.4795781 -0.014058273 -0.0007954096
## Y3 0.4791014 -0.018933146 -0.0002376941
##
## $corr.X.yscores
## [,1] [,2] [,3]
## X1 -0.3932349 0.08165630 -0.009366848
## X2 -0.4086323 0.06548609 -0.009243878
## X3 -0.4125942 0.07213945 -0.008416378
##
## $corr.Y.yscores
## [,1] [,2] [,3]
## Y1 0.9996789 -0.02485012 0.004960429
## Y2 0.9972845 -0.06332578 -0.037596350
## Y3 0.9962933 -0.08528475 -0.011235004
X_canonical <- as.matrix(X) %*% hasil$xcoef # Variabel kanonik untuk X
Y_canonical <- as.matrix(Y) %*% hasil$ycoef
library(zoo)
##
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
library(lmtest)
##
## Attaching package: 'lmtest'
## The following object is masked from 'package:RCurl':
##
## reset
# Konversi ke data frame agar mudah diakses
X_canonical <- as.data.frame(X_canonical)
Y_canonical <- as.data.frame(Y_canonical)
# Memberi nama kolom untuk identifikasi yang mudah
colnames(X_canonical) <- paste0("XCan", 1:ncol(X_canonical))
colnames(Y_canonical) <- paste0("YCan", 1:ncol(Y_canonical))
# Model regresi linier antara variabel kanonik pertama dari X dan Y
model <- lm(Y_canonical$YCan1 ~ X_canonical$XCan1)
model2 <- lm(Y_canonical$YCan2 ~ X_canonical$XCan2)
# Uji RESET (Regression Equation Specification Error Test) untuk memeriksa adanya bentuk non-linear
# Uji RESET untuk memeriksa non-linearitas (Linear jika > 0.05)
reset_result <- resettest(model, power = 2:3)
print(reset_result)
##
## RESET test
##
## data: model
## RESET = 0.7677, df1 = 2, df2 = 30, p-value = 0.473
reset_result2 <- resettest(model2, power = 2:3)
print(reset_result2)
##
## RESET test
##
## data: model2
## RESET = 0.28427, df1 = 2, df2 = 30, p-value = 0.7546