Library:
> # install.packages("knitr")
> # install.packages("rmarkdown")
> # install.packages("prettydoc")
> # install.packages("equatiomatic")Kualitas suatu produk adalah faktor utama yang menentukan daya saingnya di pasar, termasuk dalam industri minuman seperti anggur. Vinho Verde, salah satu varian anggur merah khas Portugal, dikenal karena keunikan rasanya yang dipengaruhi oleh berbagai senyawa kimia. Kualitas anggur ini tidak hanya dipengaruhi oleh proses produksinya, tetapi juga oleh karakteristik kimia seperti keasaman tetap (fixed acidity), kandungan asam sitrat (citric acid), alkohol (alcohol), pH, dan kadar sulfat (sulphates).
Namun, penilaian kualitas anggur sering kali bersifat subjektif karena melibatkan preferensi manusia. Untuk itu, pengembangan model prediktif berbasis data menjadi solusi yang potensial. Dataset yang digunakan dalam penelitian ini menggambarkan hubungan antara komposisi kimia anggur dan kualitasnya. Tantangannya terletak pada ketidakseimbangan data dan jumlah sampel yang relatif kecil. Oleh karena itu, penelitian ini bertujuan untuk mengembangkan model yang mampu memprediksi kualitas anggur secara akurat meskipun dengan keterbatasan tersebut.
Analisis korelasi kanonik merupakan suatu teknik statistika peubah ganda yang dapat digunakan untuk menyelidiki keeratan hubungan antara dua gugus peubah.Ide utama dari analisis korelasi kanonik ialah menentukan pasangan peubah baru yang masing-masingnya merupakan kombinasi linier dari peubah-peubah asal yang mempunyai korelasi terbesar. Pasangan kombinasi linier itu disebut peubah kanonik dan korelasinya disebut korelasi kanonik.
Indeks redundansi mengukur proporsi variabilitas dalam satu kelompok variabel yang dapat dijelaskan oleh fungsi kanonik yang berasal dari kelompok variabel lainnya. Ini adalah ukuran penting untuk mengevaluasi seberapa banyak informasi yang dapat dipertukarkan antara dua kelompok variabel.
Data merupakan data sekunder yang diambil dari kaggle Sumber : https://www.kaggle.com/datasets/yasserh/wine-quality-dataset
Variabel yang digunakan adalah : Variabel Kimia X1 : Fixed Acidity X2 : Citric acid X3 : Alcohol
Variabel Kualitas Y1 : Quality Y2 : pH Y3 : Sulphates
> library(candisc)
> library(readxl)
> library(dplyr)
> library(CCA)
> library(kableExtra)
> library(DT)> data_k1 <- read_excel("C:/Users/ASUS/Downloads/Data ANMUL Praktikum.xlsx",
+ sheet <- "X")
> data_k2 <- read_excel("C:/Users/ASUS/Downloads/Data ANMUL Praktikum.xlsx",
+ sheet <- "Y")
> str(data_k1)
tibble [50 × 3] (S3: tbl_df/tbl/data.frame)
$ X1: num [1:50] 7.4 7.8 7.8 11.2 7.4 7.4 7.9 7.3 7.8 7.5 ...
$ X2: num [1:50] 0 0 0.04 0.56 0 0 0.06 0 0.02 0.36 ...
$ X3: num [1:50] 9.4 9.8 9.8 9.8 9.4 9.4 9.4 10 9.5 10.5 ...> str(data_k2)
tibble [50 × 3] (S3: tbl_df/tbl/data.frame)
$ Y1: num [1:50] 5 5 5 6 5 5 5 7 7 5 ...
$ Y2: num [1:50] 3.51 3.2 3.26 3.16 3.51 3.51 3.3 3.39 3.36 3.35 ...
$ Y3: num [1:50] 0.56 0.68 0.65 0.58 0.56 0.56 0.46 0.47 0.57 0.8 ...> data_kanonik <- data.frame(data_k1, data_k2)
> colnames(data_kanonik) <- c("X1", "X2", "X3", "Y1", "Y2", "Y3")
> datatable(data_kanonik,
+ options = list(pageLength = 12),
+ caption = "Tabel 1. Data Analisis Korelasi Kanonik")> cc=cancor(data_k1, data_k2)
> cc
Canonical correlation analysis of:
3 X variables: X1, X2, X3
with 3 Y variables: Y1, Y2, Y3
CanR CanRSQ Eigen percent cum scree
1 0.7621 0.58087 1.38588 88.666 88.67 ******************************
2 0.3335 0.11121 0.12512 8.005 96.67 ***
3 0.2224 0.04946 0.05203 3.329 100.00 *
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 0.76215 0.35410 6.3389 9 107.23 3.645e-07 ***
2 0.33348 0.84483 1.9792 4 90.00 0.1044
3 0.22239 0.95054 2.3934 1 46.00 0.1287
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1> cc1=cc(data_k1, data_k2)
> cc2=comput(data_k1, data_k2, cc1)
>
> # n jumlah data, p jumlah variabel X, q jumlah variabel Y
> n=50
> p=3
> q=3
> #k dalah db dalam uji bartlett
> k=(n-1)-0.5*(p+q+1)
>
> #rumus: 1-lambda(i) dengan lambda = canonical r^2
> a=1-0.58087
> b=1-0.11121
> c=1-0.04946
>
> #statistik uji sekuensial bartlett masing-masing korelasi kanonik
> B1=-k*log(a*b*c)
> B2=-k*log(b*c)
> B3=-k*log(c)
> db1=p*q
> db2=(p-1)*(q-1)
> db3=(p-2)*(q-2)
> pv1=1-pchisq(B1, db1)
> pv2=1-pchisq(B2, db2)
> pv3=1-pchisq(B3, db3)
> B=rbind(B1,B2,B3)
> d=rbind(db1, db2, db3)
> p=rbind(pv1,pv2,pv3)
> result <- cbind(B , d, p)
> colnames(result) <- c("Bartlett", "db", "p-value")
> print(result)
Bartlett db p-value
B1 47.237803 9 3.543973e-07
B2 7.672179 4 1.043522e-01
B3 2.307989 1 1.287105e-01>
> cc
Canonical correlation analysis of:
3 X variables: X1, X2, X3
with 3 Y variables: Y1, Y2, Y3
CanR CanRSQ Eigen percent cum scree
1 0.7621 0.58087 1.38588 88.666 88.67 ******************************
2 0.3335 0.11121 0.12512 8.005 96.67 ***
3 0.2224 0.04946 0.05203 3.329 100.00 *
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 0.76215 0.35410 6.3389 9 107.23 3.645e-07 ***
2 0.33348 0.84483 1.9792 4 90.00 0.1044
3 0.22239 0.95054 2.3934 1 46.00 0.1287
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1> cc1
$cor
[1] 0.7621471 0.3334792 0.2223901
$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" "35" "36" "37" "38" "39" "40" "41" "42" "43" "44" "45"
[46] "46" "47" "48" "49" "50"
$xcoef
[,1] [,2] [,3]
X1 -0.5680871 -0.3131843 0.8137710
X2 -1.6098821 -2.9773716 -5.5761389
X3 0.7588255 -1.1789124 0.6630445
$ycoef
[,1] [,2] [,3]
Y1 -0.111750 -0.7968173 1.140180
Y2 7.127068 -3.4566019 0.102008
Y3 0.665324 -4.4323271 -2.437741
$scores
$scores$xscores
[,1] [,2] [,3]
[1,] 0.11400048 1.01286649 0.76103402
[2,] 0.19029582 0.41602782 1.35176020
[3,] 0.12590054 0.29693296 1.12871464
[4,] -2.64273442 -2.31612687 0.99594367
[5,] 0.11400048 1.01286649 0.76103402
[6,] 0.11400048 1.01286649 0.76103402
[7,] -0.26663602 0.67763205 0.83335117
[8,] 0.62610449 0.33683750 1.07748361
[9,] -0.06954947 0.71015411 1.04132408
[10,] 0.31234227 -1.38710932 -0.43564997
[11,] 0.23110582 1.22968826 -0.38730566
[12,] 0.31234227 -1.38710932 -0.43564997
[13,] 1.51597009 0.98714204 -0.37223147
[14,] -0.80774783 0.37782873 -0.72945122
[15,] -1.17967411 0.24294564 0.84537656
[16,] -1.19577293 0.21317192 0.78961517
[17,] -0.57772129 -2.29576793 -0.73710679
[18,] -0.81031005 0.07786468 -0.29694965
[19,] -0.31832028 1.24624172 0.04972512
[20,] -1.14284804 -0.42640268 -1.80852024
[21,] -1.51087363 -0.88604831 -0.69485622
[22,] -0.27103274 -0.32642927 -0.60590151
[23,] -0.43223578 0.11313508 0.06323478
[24,] -0.68798241 0.34085289 1.04280680
[25,] 0.40030821 0.39895291 -0.22759756
[26,] 0.40543266 0.99888101 -1.09260071
[27,] -0.31010609 0.11776922 -0.34818068
[28,] -0.43223578 0.11313508 0.06323478
[29,] 0.28442662 1.10682178 0.51690274
[30,] 0.19029582 0.41602782 1.35176020
[31,] 0.93014759 0.19844083 0.26519576
[32,] 1.30863465 -0.24523621 1.14980191
[33,] -0.28693360 -0.09784892 1.08950901
[34,] 0.20485820 0.81217406 -0.31498813
[35,] 0.80955658 1.19331154 -2.55590571
[36,] 0.03853072 0.65181030 1.21915130
[37,] 0.72373783 -1.17971658 1.23414522
[38,] -0.50677985 -0.39370027 -0.03173186
[39,] 1.23838944 0.80575141 -0.85901132
[40,] 0.42595970 -1.32447246 -0.59840416
[41,] 0.42595970 -1.32447246 -0.59840416
[42,] -1.24016869 -0.20091176 0.16116724
[43,] 0.56992340 -0.91072987 0.45653226
[44,] 0.04510837 -0.92240540 0.70066316
[45,] 0.49853768 1.02333840 0.22755312
[46,] 4.27081652 -2.91879901 0.09931906
[47,] -0.90044005 -0.12557609 -1.52518332
[48,] -1.38576893 -1.06039755 -1.01435152
[49,] 0.16004965 0.87703781 -1.46785778
[50,] 0.38913588 0.71075323 -2.89953400
$scores$yscores
[,1] [,2] [,3]
[1,] 1.18488962 0.17156972 -0.0002573339
[2,] -0.94466271 0.71123705 -0.3244087634
[3,] -0.53699833 0.63681075 -0.2451560469
[4,] -1.40802785 0.49591649 1.0554647829
[5,] 1.18488962 0.17156972 -0.0002573339
[6,] 1.18488962 0.17156972 -0.0002573339
[7,] -0.37832715 1.34068882 0.2220950874
[8,] 0.04626225 -0.60836330 2.4872579138
[9,] -0.10101740 -0.94789796 2.2404235606
[10,] 0.20423643 -0.33913248 -0.6016364900
[11,] -0.46764260 1.05523469 0.0250356370
[12,] 0.20423643 -0.33913248 -0.6016364900
[13,] 1.65717145 0.10690068 0.1043928743
[14,] 0.06844651 -3.39660691 -2.4635004636
[15,] -1.09668065 -0.03696430 -0.8160373089
[16,] -0.99214377 -0.29314667 -0.9369042842
[17,] -0.40888319 -1.53832073 1.7955096765
[18,] -1.18690447 -1.63706504 -1.7962341583
[19,] 0.33020128 1.68368494 -1.0074336699
[20,] -1.93061406 -1.30545484 -0.1756467417
[21,] 0.19793169 -0.07748559 1.2008136902
[22,] 1.31603946 -0.26190573 -0.2186339540
[23,] -1.00545025 -0.20450013 -0.8881494619
[24,] -1.25827336 1.47978417 0.0381921627
[25,] 0.54954682 -0.65898237 0.9611199005
[26,] -0.02671201 0.75919204 -0.0175987024
[27,] -0.43437640 0.83361834 -0.0968514189
[28,] -1.00545025 -0.20450013 -0.8881494619
[29,] 0.89315364 0.35415707 0.0200397553
[30,] 0.16658044 -0.30885919 1.0535291427
[31,] 0.03125219 0.81327256 0.0321762005
[32,] 0.72343944 -0.49674080 1.1104446090
[33,] -1.17178124 0.90358165 -0.2787141826
[34,] 0.61890255 -0.24055843 1.2313115844
[35,] 0.25171748 0.66525124 0.0108590308
[36,] 0.28250885 -0.20069815 1.1530789483
[37,] 0.45831642 -0.49144654 1.0332320535
[38,] -0.92108446 -1.20771205 1.8371239353
[39,] 1.17214301 1.35753926 -0.9464378816
[40,] 0.08165478 -0.40297026 -0.6768088845
[41,] 0.08165478 -0.40297026 -0.6768088845
[42,] -0.51839369 2.05415389 -1.0440520471
[43,] -0.83877075 -1.09525828 0.2804880278
[44,] 0.11401261 -1.93923323 -1.5818333394
[45,] 0.94446461 0.45256086 0.0941920693
[46,] 4.07619630 -0.37968766 -1.1006539510
[47,] -0.55504309 0.31679060 -0.4411954168
[48,] -0.65484169 0.98163966 -0.0755342492
[49,] -0.02671201 0.75919204 -0.0175987024
[50,] -0.15594690 0.73967753 -0.0683936857
$scores$corr.X.xscores
[,1] [,2] [,3]
X1 -0.8532589 -0.3158223 0.4149765
X2 -0.4875900 -0.6448645 -0.5885625
X3 0.6689638 -0.7184711 0.1904907
$scores$corr.Y.xscores
[,1] [,2] [,3]
Y1 -0.1920884 -0.16511497 0.18490850
Y2 0.7523133 0.02287511 0.03217634
Y3 -0.2709220 -0.24991662 -0.12422163
$scores$corr.X.yscores
[,1] [,2] [,3]
X1 -0.6503088 -0.1053202 0.09228666
X2 -0.3716153 -0.2150489 -0.13089046
X3 0.5098488 -0.2395952 0.04236325
$scores$corr.Y.yscores
[,1] [,2] [,3]
Y1 -0.2520358 -0.4951282 0.8314602
Y2 0.9870973 0.0685953 0.1446842
Y3 -0.3554721 -0.7494219 -0.5585754> cc2
$xscores
[,1] [,2] [,3]
[1,] 0.11400048 1.01286649 0.76103402
[2,] 0.19029582 0.41602782 1.35176020
[3,] 0.12590054 0.29693296 1.12871464
[4,] -2.64273442 -2.31612687 0.99594367
[5,] 0.11400048 1.01286649 0.76103402
[6,] 0.11400048 1.01286649 0.76103402
[7,] -0.26663602 0.67763205 0.83335117
[8,] 0.62610449 0.33683750 1.07748361
[9,] -0.06954947 0.71015411 1.04132408
[10,] 0.31234227 -1.38710932 -0.43564997
[11,] 0.23110582 1.22968826 -0.38730566
[12,] 0.31234227 -1.38710932 -0.43564997
[13,] 1.51597009 0.98714204 -0.37223147
[14,] -0.80774783 0.37782873 -0.72945122
[15,] -1.17967411 0.24294564 0.84537656
[16,] -1.19577293 0.21317192 0.78961517
[17,] -0.57772129 -2.29576793 -0.73710679
[18,] -0.81031005 0.07786468 -0.29694965
[19,] -0.31832028 1.24624172 0.04972512
[20,] -1.14284804 -0.42640268 -1.80852024
[21,] -1.51087363 -0.88604831 -0.69485622
[22,] -0.27103274 -0.32642927 -0.60590151
[23,] -0.43223578 0.11313508 0.06323478
[24,] -0.68798241 0.34085289 1.04280680
[25,] 0.40030821 0.39895291 -0.22759756
[26,] 0.40543266 0.99888101 -1.09260071
[27,] -0.31010609 0.11776922 -0.34818068
[28,] -0.43223578 0.11313508 0.06323478
[29,] 0.28442662 1.10682178 0.51690274
[30,] 0.19029582 0.41602782 1.35176020
[31,] 0.93014759 0.19844083 0.26519576
[32,] 1.30863465 -0.24523621 1.14980191
[33,] -0.28693360 -0.09784892 1.08950901
[34,] 0.20485820 0.81217406 -0.31498813
[35,] 0.80955658 1.19331154 -2.55590571
[36,] 0.03853072 0.65181030 1.21915130
[37,] 0.72373783 -1.17971658 1.23414522
[38,] -0.50677985 -0.39370027 -0.03173186
[39,] 1.23838944 0.80575141 -0.85901132
[40,] 0.42595970 -1.32447246 -0.59840416
[41,] 0.42595970 -1.32447246 -0.59840416
[42,] -1.24016869 -0.20091176 0.16116724
[43,] 0.56992340 -0.91072987 0.45653226
[44,] 0.04510837 -0.92240540 0.70066316
[45,] 0.49853768 1.02333840 0.22755312
[46,] 4.27081652 -2.91879901 0.09931906
[47,] -0.90044005 -0.12557609 -1.52518332
[48,] -1.38576893 -1.06039755 -1.01435152
[49,] 0.16004965 0.87703781 -1.46785778
[50,] 0.38913588 0.71075323 -2.89953400
$yscores
[,1] [,2] [,3]
[1,] 1.18488962 0.17156972 -0.0002573339
[2,] -0.94466271 0.71123705 -0.3244087634
[3,] -0.53699833 0.63681075 -0.2451560469
[4,] -1.40802785 0.49591649 1.0554647829
[5,] 1.18488962 0.17156972 -0.0002573339
[6,] 1.18488962 0.17156972 -0.0002573339
[7,] -0.37832715 1.34068882 0.2220950874
[8,] 0.04626225 -0.60836330 2.4872579138
[9,] -0.10101740 -0.94789796 2.2404235606
[10,] 0.20423643 -0.33913248 -0.6016364900
[11,] -0.46764260 1.05523469 0.0250356370
[12,] 0.20423643 -0.33913248 -0.6016364900
[13,] 1.65717145 0.10690068 0.1043928743
[14,] 0.06844651 -3.39660691 -2.4635004636
[15,] -1.09668065 -0.03696430 -0.8160373089
[16,] -0.99214377 -0.29314667 -0.9369042842
[17,] -0.40888319 -1.53832073 1.7955096765
[18,] -1.18690447 -1.63706504 -1.7962341583
[19,] 0.33020128 1.68368494 -1.0074336699
[20,] -1.93061406 -1.30545484 -0.1756467417
[21,] 0.19793169 -0.07748559 1.2008136902
[22,] 1.31603946 -0.26190573 -0.2186339540
[23,] -1.00545025 -0.20450013 -0.8881494619
[24,] -1.25827336 1.47978417 0.0381921627
[25,] 0.54954682 -0.65898237 0.9611199005
[26,] -0.02671201 0.75919204 -0.0175987024
[27,] -0.43437640 0.83361834 -0.0968514189
[28,] -1.00545025 -0.20450013 -0.8881494619
[29,] 0.89315364 0.35415707 0.0200397553
[30,] 0.16658044 -0.30885919 1.0535291427
[31,] 0.03125219 0.81327256 0.0321762005
[32,] 0.72343944 -0.49674080 1.1104446090
[33,] -1.17178124 0.90358165 -0.2787141826
[34,] 0.61890255 -0.24055843 1.2313115844
[35,] 0.25171748 0.66525124 0.0108590308
[36,] 0.28250885 -0.20069815 1.1530789483
[37,] 0.45831642 -0.49144654 1.0332320535
[38,] -0.92108446 -1.20771205 1.8371239353
[39,] 1.17214301 1.35753926 -0.9464378816
[40,] 0.08165478 -0.40297026 -0.6768088845
[41,] 0.08165478 -0.40297026 -0.6768088845
[42,] -0.51839369 2.05415389 -1.0440520471
[43,] -0.83877075 -1.09525828 0.2804880278
[44,] 0.11401261 -1.93923323 -1.5818333394
[45,] 0.94446461 0.45256086 0.0941920693
[46,] 4.07619630 -0.37968766 -1.1006539510
[47,] -0.55504309 0.31679060 -0.4411954168
[48,] -0.65484169 0.98163966 -0.0755342492
[49,] -0.02671201 0.75919204 -0.0175987024
[50,] -0.15594690 0.73967753 -0.0683936857
$corr.X.xscores
[,1] [,2] [,3]
X1 -0.8532589 -0.3158223 0.4149765
X2 -0.4875900 -0.6448645 -0.5885625
X3 0.6689638 -0.7184711 0.1904907
$corr.Y.xscores
[,1] [,2] [,3]
Y1 -0.1920884 -0.16511497 0.18490850
Y2 0.7523133 0.02287511 0.03217634
Y3 -0.2709220 -0.24991662 -0.12422163
$corr.X.yscores
[,1] [,2] [,3]
X1 -0.6503088 -0.1053202 0.09228666
X2 -0.3716153 -0.2150489 -0.13089046
X3 0.5098488 -0.2395952 0.04236325
$corr.Y.yscores
[,1] [,2] [,3]
Y1 -0.2520358 -0.4951282 0.8314602
Y2 0.9870973 0.0685953 0.1446842
Y3 -0.3554721 -0.7494219 -0.5585754> #nilai redudansi
> redundancy(cc)
Redundancies for the X variables & total X canonical redundancy
Xcan1 Xcan2 Xcan3 total X|Y
0.273648 0.038248 0.009148 0.321044
Redundancies for the Y variables & total Y canonical redundancy
Ycan1 Ycan2 Ycan3 total Y|X
0.22542 0.03008 0.01689 0.27239 > cc1$xcoef
[,1] [,2] [,3]
X1 -0.5680871 -0.3131843 0.8137710
X2 -1.6098821 -2.9773716 -5.5761389
X3 0.7588255 -1.1789124 0.6630445> cc1$ycoef
[,1] [,2] [,3]
Y1 -0.111750 -0.7968173 1.140180
Y2 7.127068 -3.4566019 0.102008
Y3 0.665324 -4.4323271 -2.437741\[ \text{Fungsi kanonik yang didapat }\\ U1=−0.5680X1-1.6098X2+0.7588X3\\ U2=-0.3131X1-2.9773X2-1.1789X3\\ U3=0.8137X1-5.5761X2+0.6630X3\\ V1=-0.1117Y1+7.1270Y2+0.6653Y3\\ V2=-0.7968Y1-3.4566Y2-4.4323Y3\\ V3=1.1401Y1+0.1020Y2-2.4377Y3\\ \]
> cc1$cor
[1] 0.7621471 0.3334792 0.2223901\[ \text{Korelasi Kanonik I =0.7621471}\\ \text{Korelasi Kanonik II =0.3334792}\\ \text{Korelasi Kanonik III =0.2223901}\\ \text{Berdasarkan hasil tersebut terlihat bahwa korelasi kanonik terbesar terjadi pada fungsi kanonik pertama.} \]
\[ \text{Uji yang digunakan adalah uji Rao F dengan kriteria Wilks Lambda} \] \[ \text{Hipotesis: } \\ H_0: \rho_1 = \rho_2 = \rho_3 = 0 \\ H_1: \text{setidaknya ada satu } i \text{ di mana } \rho_i \neq 0 \]
> cc
Canonical correlation analysis of:
3 X variables: X1, X2, X3
with 3 Y variables: Y1, Y2, Y3
CanR CanRSQ Eigen percent cum scree
1 0.7621 0.58087 1.38588 88.666 88.67 ******************************
2 0.3335 0.11121 0.12512 8.005 96.67 ***
3 0.2224 0.04946 0.05203 3.329 100.00 *
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 0.76215 0.35410 6.3389 9 107.23 3.645e-07 ***
2 0.33348 0.84483 1.9792 4 90.00 0.1044
3 0.22239 0.95054 2.3934 1 46.00 0.1287
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1> result
Bartlett db p-value
B1 47.237803 9 3.543973e-07
B2 7.672179 4 1.043522e-01
B3 2.307989 1 1.287105e-01\[ \text{Pengujian Pertama}\\ \text{Pada Pengujian pertama hipotesis yang digunakan adalah H0:ρ1=ρ1=ρ3=0}\\ \text{Berdasarkan output di atas dapat diputuskan untuk menolak H0, karena nilai-p = 3.543973e-07, sehingga dilanjutkan pengujian kedua}\\ \text{Pengujian Kedua}\\ \text{Pada Pengujian kedua hipotesis yang digunakan adalah H0:ρ2=ρ3=0}\\ \text{Nilai-p dari pengujian kedua adalah 1.043522e-01 sehingga H0 diterima, sehingga dapat disimpulkan korelasi yang signifikan hanya korelasi yang pertama ρ1 yaitu U1 dan V1 saja.}\\ \text{Pengujian Ketiga}\\ \text{Karena pada pengujian yang kedua keputusan yang dihasilkan adalah terima H0 , maka tidak dilakukan pengujian yang ketiga.} \]
> cc1$scores$corr.X.xscores
[,1] [,2] [,3]
X1 -0.8532589 -0.3158223 0.4149765
X2 -0.4875900 -0.6448645 -0.5885625
X3 0.6689638 -0.7184711 0.1904907> cc1$scores$corr.Y.yscores
[,1] [,2] [,3]
Y1 -0.2520358 -0.4951282 0.8314602
Y2 0.9870973 0.0685953 0.1446842
Y3 -0.3554721 -0.7494219 -0.5585754> cc1$scores$corr.X.yscores
[,1] [,2] [,3]
X1 -0.6503088 -0.1053202 0.09228666
X2 -0.3716153 -0.2150489 -0.13089046
X3 0.5098488 -0.2395952 0.04236325> cc1$scores$corr.Y.xscores
[,1] [,2] [,3]
Y1 -0.1920884 -0.16511497 0.18490850
Y2 0.7523133 0.02287511 0.03217634
Y3 -0.2709220 -0.24991662 -0.12422163> data <- data.frame(
+ Variabel = c("X1", "X2", "X3", "Y1", "Y2", "Y3"),
+ Group = c("", "$V_1$", "", "", "$U_1$", ""),
+ Crossloading = c(-0.6503, -0.3716, 0.5098, -0.1920, 0.7523, -0.2709)
+ )
> data %>%
+ kbl(caption = "Tabel 3. Nilai Crossloading Variabel Kanonik I", align = "c", escape = FALSE) %>%
+ kable_classic(full_width = FALSE, html_font = "Verdana")| Variabel | Group | Crossloading |
|---|---|---|
| X1 | -0.6503 | |
| X2 | \(V_1\) | -0.3716 |
| X3 | 0.5098 | |
| Y1 | -0.1920 | |
| Y2 | \(U_1\) | 0.7523 |
| Y3 | -0.2709 |
> redundancy(cc)
Redundancies for the X variables & total X canonical redundancy
Xcan1 Xcan2 Xcan3 total X|Y
0.273648 0.038248 0.009148 0.321044
Redundancies for the Y variables & total Y canonical redundancy
Ycan1 Ycan2 Ycan3 total Y|X
0.22542 0.03008 0.01689 0.27239 \[ \text{Berdasarkan output di atas dapat diperoleh beberapa informasi yaitu :}\\ \text{Keragaman himpunan variabel X dapat dijelaskan oleh variabel U1 sebesar 27.3648% dan dijelaskan bersama oleh U1, U2, U3 sebesar 32.1044%.}\\ \text{Keragaman himpunan variabel Y dapat dijelaskan oleh variabel V1 sebesar 22.542% dan dijelaskan bersama oleh V1, V2, V3 sebesar 27.239%.}\\ \]
Hasil analisis korelasi kanonik menunjukkan adanya hubungan signifikan antara variabel Kimia (Fixed Acidity,Citric acid,Alcohol) dengan variabel kualitas (Quality, pH,Sulphates). Hubungan tersebut terutama terlihat pada fungsi kanonik pertama (ρ₁ = 0,76215) dengan nilai-p sebesar 3,645e-07, yang mencerminkan keterkaitan yang sangat kuat antara kedua kelompok variabel. Sementara itu, fungsi kanonik kedua dan ketiga tidak menunjukkan signifikansi, sehingga hanya fungsi kanonik pertama yang dianggap relevan untuk dianalisis lebih lanjut.
Terdapat hubungan yang signifikan Kimia dengan Kualitas Anggur, sehingga diperoleh pasangan peubah kanonik pertama yang mampu menjelaskan sebesar 0,76215 keragaman data dengan bentuk sebagai berikut:
U1=−0.5680X1-1.6098X2+0.7588X3
V1=-0.1117Y1+7.1270Y2+0.6653Y3
Akhirman, R., & Azhar, A. (2022). Analisis Korelasi Kanonik pada Data Penelitian. Jurnal Matematika UNAND, 11(3), 123–135.
Hossam, Y. (2018). Wine Quality Dataset. Kaggle. https://www.kaggle.com/datasets/yasserh/wine-quality-dataset