analisis korelasi kanonik
MEISYA PUTERI SIAGIAN
2025-03-25
- Input Dataset
library(readxl)
wineclustering <- read_excel("D:/Meisya/Kuliah/Semester 4/Statistika Multivariat/wine_clustering.xlsx")
View(wineclustering)Dataset ini terdiri dari 13 variabel dan 178 objek.
- Menentukan variabel yang digunakan
resumecca <- wineclustering[,2:7]
resumecca## # A tibble: 178 × 6
## Ash Ash_Alcanity Magnesium Total_Phenols Alcohol Flavanoids
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 2.43 15.6 127 2.8 14.2 3.06
## 2 2.14 11.2 100 2.65 13.2 2.76
## 3 2.67 18.6 101 2.8 13.2 3.24
## 4 2.5 16.8 113 3.85 14.4 3.49
## 5 2.87 21 118 2.8 13.2 2.69
## 6 2.45 15.2 112 3.27 14.2 3.39
## 7 2.45 14.6 96 2.5 14.4 2.52
## 8 2.61 17.6 121 2.6 14.1 2.51
## 9 2.17 14 97 2.8 14.8 2.98
## 10 2.27 16 98 2.98 13.9 3.15
## # ℹ 168 more rowsSet kelompok 1 (X) terdiri dari variabel Ash, Ash_Alcanity, dan Magnesium. Sedangkan set kelompok 2 (Y) terdiri dari Total_Phenols, Alcohol, dan Flavanoiod.
- Uji asumsi
- Uji linearitas
library(ggplot2)
library(GGally)## Registered S3 method overwritten by 'GGally':
## method from
## +.gg ggplot2selected_vars <- scale(resumecca) # Standarisasi data
ggpairs(selected_vars,
title = "Scatterplot Matrix: Linearitas Variabel X dan Y",
lower = list(continuous = wrap("smooth", method = "lm", se = FALSE, color = "red")),
upper = list(continuous = wrap("cor", size = 4)),
diag = list(continuous = wrap("densityDiag", alpha = 0.5, fill = "lightblue"))) # Distribusi variabel
Beberapa pasangan variabel menunjukkan hubungan linear yang cukup kuat,
seperti Flavanoids vs Total Phenols (Corr = 0.865), Flavanoids vs
Alcohol (Corr = -0.538), dan Total Phenols vs Alcohol (Corr = -0.321).
Ada juga hubungan yang tidak terlalu linear, misalnya Magnesium vs
variabel lain (Corr ≈ -0.08 hingga 0.27). Secara keseluruhan, beberapa
variabel memiliki hubungan linear kuat, tetapi tidak semua pasangan
variabel menunjukkan pola linear.
- Uji normalitas
hist(selected_vars) # Histogram
qqnorm(selected_vars); qqline(selected_vars) # Q-Q Plot
Histogram berbentuk simetris, mendekati distribusi normal dan tidak ada
skewness yang signifikan (tidak terlalu condong ke kanan/kiri).
Sedangkan pada Q-Q Plot, sebagian besar titik berada di sepanjang garis
diagonal, yang menunjukkan bahwa data hampir normal. Ada sedikit
penyimpangan di ekor (bagian kiri dan kanan), yang bisa mengindikasikan
sedikit kurtosis (lebih banyak nilai ekstrem dari normal). Jadi, secara
visual, data ini sudah cukup mendekati distribusi normal.
- Uji multikolinearitas
corr_matrix <- cor(selected_vars)
corr_matrix## Ash Ash_Alcanity Magnesium Total_Phenols Alcohol
## Ash 1.0000000 0.44336719 0.28658669 0.1289795 0.2115446
## Ash_Alcanity 0.4433672 1.00000000 -0.08333309 -0.3211133 -0.3102351
## Magnesium 0.2865867 -0.08333309 1.00000000 0.2144012 0.2707982
## Total_Phenols 0.1289795 -0.32111332 0.21440123 1.0000000 0.2891011
## Alcohol 0.2115446 -0.31023514 0.27079823 0.2891011 1.0000000
## Flavanoids 0.1150773 -0.35136986 0.19578377 0.8645635 0.2368149
## Flavanoids
## Ash 0.1150773
## Ash_Alcanity -0.3513699
## Magnesium 0.1957838
## Total_Phenols 0.8645635
## Alcohol 0.2368149
## Flavanoids 1.0000000korelasi antar variabel independen di atas 0,8 dapat menjadi indikasi multikolinearitas.Berdasarkan matriks korelasi diatas, ada beberapa nilai korelasi antar anggota kelompok peubah berkisar pada ≤ 0,8, artinya tidak ada masalah multikolinearitas.
- Standarisasi data
std_data <- scale(resumecca)
std_data## Ash Ash_Alcanity Magnesium Total_Phenols Alcohol
## [1,] 0.23139979 -1.166303174 1.90852151 0.806721729 1.51434077
## [2,] -0.82566722 -2.483840525 0.01809398 0.567048088 0.24559683
## [3,] 1.10621386 -0.267982252 0.08810981 0.806721729 0.19632522
## [4,] 0.48655389 -0.806974805 0.92829983 2.484437221 1.68679140
## [5,] 1.83522559 0.450674485 1.27837900 0.806721729 0.29486844
## [6,] 0.30430096 -1.286079296 0.85828399 1.557699140 1.47738706
## [7,] 0.30430096 -1.465743481 -0.26196936 0.327374446 1.71142720
## [8,] 0.88751034 -0.567422559 1.48842650 0.487156874 1.30493643
## [9,] -0.71631546 -1.645407665 -0.19195352 0.806721729 2.25341491
## [10,] -0.35180959 -1.046527051 -0.12193769 1.094330099 1.05857838
## [11,] -0.24245783 -0.447646437 0.36817315 1.046395371 1.35420804
## [12,] -0.16955666 -0.806974805 -0.33198519 -0.151972837 1.37884384
## [13,] 0.15849862 -1.046527051 -0.75208020 0.487156874 0.92308146
## [14,] 0.08559744 -2.423952463 -0.61204853 1.286069013 2.15487169
## [15,] 0.04914686 -2.244288279 0.15812565 1.605633868 1.69910930
## [16,] 1.21556562 -0.687198682 0.85828399 0.886612943 0.77526663
## [17,] 1.28846679 0.151234178 1.41841067 0.806721729 1.60056608
## [18,] 0.92396093 0.151234178 1.06833150 1.046395371 1.02162467
## [19,] 0.41365272 -0.896806897 0.57822065 1.605633868 1.46506916
## [20,] 0.70525741 -1.286079296 1.13834733 0.646939302 0.78758453
## [21,] -0.31535901 -1.046527051 1.83850567 1.126286585 1.30493643
## [22,] 1.03331269 -0.267982252 0.15812565 0.183570261 -0.08698653
## [23,] -0.02375431 -0.866862867 0.08810981 0.503135117 0.87380985
## [24,] 0.55945507 -0.507534498 -0.33198519 0.295417961 -0.18552975
## [25,] 0.88751034 0.151234178 -0.26196936 0.375309174 0.61513390
## [26,] 3.11099611 1.648435713 1.69847400 0.535091602 0.06082829
## [27,] 0.92396093 -1.016583020 -0.47201686 0.886612943 0.47963697
## [28,] -0.82566722 -0.747086744 -0.40200103 0.167592018 0.36877585
## [29,] 1.58007149 -0.028430007 0.50820482 1.046395371 1.07089628
## [30,] -0.57051311 -1.046527051 -0.26196936 0.567048088 1.25566482
## [31,] 1.21556562 0.899834945 0.08810981 1.126286585 0.89844565
## [32,] -0.02375431 -0.118262099 0.43818899 0.902591186 0.71367712
## [33,] -0.02375431 -0.687198682 0.29815732 0.199548504 0.83685614
## [34,] 1.21556562 0.001514024 2.25860068 1.046395371 0.93539936
## [35,] 1.03331269 -0.148206130 0.71825232 0.087700804 0.62745180
## [36,] 0.15849862 0.300954331 0.01809398 0.646939302 0.59049809
## [37,] 1.72587383 -1.196247204 0.71825232 0.487156874 0.34414005
## [38,] 0.66880683 -0.447646437 -0.12193769 0.247483232 0.06082829
## [39,] -0.97146956 -1.196247204 -0.12193769 0.167592018 0.08546410
## [40,] 0.52300448 -1.884959911 1.97853734 1.126286585 1.50202286
## [41,] -0.20600725 -0.986638989 1.20836316 1.365960227 0.68904131
## [42,] -0.89856839 -0.208094191 -0.68206436 0.247483232 0.50427278
## [43,] 0.81460917 -1.345967358 0.08810981 1.525742654 1.08321419
## [44,] -0.27890842 -0.597366590 0.22814148 0.551069845 0.29486844
## [45,] -0.97146956 -0.747086744 0.50820482 1.126286585 0.06082829
## [46,] 0.26785038 -0.178150160 0.78826816 0.886612943 1.48970496
## [47,] -0.31535901 -1.046527051 0.15812565 1.525742654 1.69910930
## [48,] -0.89856839 -1.046527051 0.08810981 1.286069013 1.10784999
## [49,] 0.12204803 -0.208094191 0.22814148 0.726830515 1.35420804
## [50,] -0.35180959 -0.627310621 0.57822065 0.934547672 1.15712160
## [51,] -1.19017308 -2.124512156 -0.54203270 0.678895787 0.06082829
## [52,] 0.85105976 -0.687198682 -0.40200103 0.247483232 1.02162467
## [53,] 0.19494920 -1.645407665 0.78826816 2.532371949 1.00930677
## [54,] 1.14266445 -0.717142713 1.06833150 1.126286585 0.94771726
## [55,] -0.42471076 -0.926750928 1.27837900 0.487156874 0.91076355
## [56,] 0.34075155 0.300954331 1.13834733 1.062373614 0.68904131
## [57,] -0.24245783 -0.956694959 1.27837900 1.445851440 1.50202286
## [58,] 1.14266445 -0.806974805 0.15812565 1.126286585 0.35645795
## [59,] 0.48655389 -0.836918836 0.57822065 1.765416296 0.88612775
## [60,] -3.66881295 -2.663504709 -0.82209603 -0.503494178 -0.77678907
## [61,] -0.31535901 -1.046527051 0.08810981 -0.391646479 -0.82606067
## [62,] -1.26307425 -0.806974805 0.01809398 -0.439581207 -0.44420570
## [63,] -1.62758012 -0.447646437 -0.40200103 -0.311755265 0.82453824
## [64,] -0.75276604 -0.148206130 -0.89211187 1.925198724 -0.77678907
## [65,] 0.59590565 -0.148206130 0.29815732 -0.647298363 -1.02314711
## [66,] 0.70525741 -0.417702406 -0.12193769 0.199548504 -0.77678907
## [67,] -2.42949302 -1.345967358 -1.52225438 1.094330099 0.13473571
## [68,] -1.62758012 0.031458055 -1.52225438 -0.295777022 -0.77678907
## [69,] -0.02375431 -0.747086744 0.71825232 0.375309174 0.41804746
## [70,] -2.24724008 -0.806974805 3.58890153 -0.711211334 -0.97387550
## [71,] -0.57051311 0.271010300 0.22814148 -1.909579543 -0.87533228
## [72,] 1.10621386 1.648435713 -0.96212770 1.046395371 1.05857838
## [73,] -0.46116135 1.348995406 -0.89211187 -0.663276606 0.60281600
## [74,] 0.85105976 3.145637249 2.74871152 1.605633868 -0.01307912
## [75,] -0.24245783 0.450674485 0.08810981 1.733459810 -1.28182306
## [76,] -1.62758012 -1.046527051 -0.19195352 -1.094689161 -1.65136013
## [77,] -2.39304243 -1.046527051 -0.96212770 -0.551428907 0.03619249
## [78,] -0.49761194 -0.447646437 0.85828399 -0.918928490 -1.42963789
## [79,] -1.51822836 -1.405855419 2.53866402 -0.631320120 -0.82606067
## [80,] 0.12204803 1.049555099 0.08810981 0.854656458 -0.37029829
## [81,] -1.33597542 -0.148206130 -0.96212770 0.199548504 -1.23255145
## [82,] -0.60696370 -0.208094191 -0.96212770 -0.151972837 -0.34566248
## [83,] 0.52300448 1.348995406 -1.52225438 -0.471537693 -1.13400823
## [84,] -0.16955666 0.899834945 -1.03214354 -1.030776190 0.06082829
## [85,] 0.77815859 -0.447646437 -0.40200103 -0.151972837 -1.42963789
## [86,] -0.46116135 -0.447646437 -0.05192185 -0.151972837 -0.40725200
## [87,] -0.20600725 0.989667037 -0.68206436 -0.823059034 -1.03546501
## [88,] 0.92396093 1.947876020 -0.82209603 -0.599363635 -1.66367803
## [89,] 0.34075155 0.630338669 -1.10215937 -0.551428907 -1.67599593
## [90,] -0.24245783 1.229219283 -2.08238105 -0.151972837 -1.13400823
## [91,] -0.16955666 -0.297926283 -1.31220687 -1.110667404 -1.13400823
## [92,] 0.19494920 0.750114792 -0.96212770 -1.350341045 -1.23255145
## [93,] -0.38826018 0.360842393 -1.38222271 -1.462188745 -0.38261619
## [94,] -0.53406252 -0.447646437 -0.82209603 0.247483232 -0.87533228
## [95,] -0.31535901 -0.447646437 -0.12193769 1.158243070 -1.70063174
## [96,] -0.60696370 -0.148206130 4.35907571 0.327374446 -0.65361004
## [97,] 1.36136797 0.600394638 2.39863235 -1.110667404 -1.46659160
## [98,] -1.40887660 -1.046527051 -1.03214354 0.407265660 -0.87533228
## [99,] -0.97146956 -0.297926283 -0.82209603 1.957155209 -0.77678907
## [100,] -0.57051311 -0.447646437 -0.82209603 0.886612943 -0.87533228
## [101,] -2.42949302 -0.597366590 -0.19195352 -0.104038109 -1.13400823
## [102,] -1.70048129 -0.297926283 -0.82209603 -1.350341045 -0.49347731
## [103,] 0.34075155 0.450674485 -0.12193769 0.423243903 -0.81374277
## [104,] -1.77338246 0.001514024 -0.96212770 0.327374446 -1.45427369
## [105,] -1.40887660 0.300954331 -1.03214354 -0.151972837 -0.60433843
## [106,] -0.35180959 0.750114792 -0.68206436 -0.982841462 -0.71519955
## [107,] -0.89856839 -0.148206130 -1.38222271 -1.030776190 -0.92460389
## [108,] -0.31535901 0.899834945 -1.10215937 -1.462188745 -0.34566248
## [109,] -1.55467894 -0.148206130 -0.54203270 0.103679047 -0.96155760
## [110,] 1.21556562 0.151234178 -0.40200103 0.710852273 -1.71294964
## [111,] -1.99208598 0.001514024 0.50820482 1.413894955 -1.89771818
## [112,] -0.71631546 0.450674485 -0.82209603 0.407265660 -0.59202053
## [113,] 2.01747852 0.151234178 0.22814148 -0.870993762 -1.52818111
## [114,] 0.48655389 0.450674485 -0.82209603 0.295417961 -1.95930769
## [115,] 0.48655389 0.899834945 -1.10215937 0.423243903 -1.13400823
## [116,] -0.60696370 0.600394638 -1.03214354 0.263461475 -2.42738798
## [117,] -1.37242601 0.390786423 -0.96212770 -0.503494178 -1.45427369
## [118,] -0.64341428 0.899834945 0.57822065 -0.471537693 -0.71519955
## [119,] -1.40887660 -1.046527051 -1.38222271 -1.062732675 -0.28407297
## [120,] -1.33597542 -0.148206130 -0.89211187 -0.471537693 -1.23255145
## [121,] 0.19494920 0.151234178 -0.26196936 0.966504157 -1.91003608
## [122,] 3.14744670 2.696476788 1.34839483 1.413894955 -1.77453915
## [123,] 1.32491738 2.097596174 0.15812565 -0.151972837 -0.71519955
## [124,] -0.86211780 0.600394638 -0.96212770 0.519113359 0.06082829
## [125,] 0.08559744 0.450674485 -1.24219104 0.902591186 -1.39268418
## [126,] -0.71631546 0.450674485 -1.03214354 0.487156874 -1.14632613
## [127,] -0.27890842 0.600394638 -0.96212770 0.710852273 -0.70288165
## [128,] 1.50717031 2.696476788 -0.54203270 -0.263820537 -1.49122740
## [129,] -0.24245783 1.498715559 -0.82209603 -0.120016352 -0.77678907
## [130,] 0.04914686 0.750114792 -1.38222271 -0.311755265 -1.18327984
## [131,] -0.16955666 -0.447646437 1.55844234 -1.254471589 -0.17321185
## [132,] 0.12204803 0.151234178 0.29815732 -1.590014687 -0.14857605
## [133,] 0.12204803 1.348995406 -0.12193769 -1.829688329 -0.23480136
## [134,] -0.02375431 0.600394638 0.43818899 -0.950884976 -0.37029829
## [135,] -0.42471076 -0.597366590 -1.03214354 -0.471537693 -0.60433843
## [136,] -0.60696370 -0.297926283 -0.40200103 -1.078710918 -0.49347731
## [137,] 0.63235624 0.450674485 -0.75208020 -1.462188745 -0.92460389
## [138,] 0.99686210 1.648435713 -0.26196936 -0.807080791 -0.57970263
## [139,] -0.64341428 0.001514024 -0.82209603 -1.078710918 0.60281600
## [140,] 0.88751034 1.348995406 0.08810981 0.039766076 -0.19784766
## [141,] 1.21556562 0.450674485 -0.26196936 -1.206536860 -0.08698653
## [142,] -0.06020490 0.151234178 -0.75208020 -1.430232259 0.44268327
## [143,] 1.28846679 1.199275252 -0.19195352 -1.190558618 0.63976970
## [144,] -0.06020490 0.151234178 -0.54203270 -0.471537693 0.76294873
## [145,] -0.60696370 -0.297926283 0.85828399 -1.462188745 -0.92460389
## [146,] -0.78921663 0.450674485 0.15812565 -1.270449832 0.19632522
## [147,] -0.49761194 0.151234178 -1.38222271 -2.101318456 1.08321419
## [148,] 0.41365272 0.600394638 -0.96212770 -0.950884976 -0.16089395
## [149,] 0.04914686 0.600394638 -0.54203270 -0.583385392 0.39341166
## [150,] -0.02375431 0.600394638 0.92829983 -1.414254017 0.09778200
## [151,] 0.92396093 1.348995406 1.62845817 -1.430232259 0.61513390
## [152,] 0.41365272 0.750114792 0.85828399 -1.302406317 -0.25943717
## [153,] 1.39781855 1.798155867 1.13834733 -0.151972837 0.13473571
## [154,] -0.31535901 -0.297926283 -0.12193769 -0.791102548 0.28255053
## [155,] -0.97146956 0.151234178 0.22814148 -1.302406317 -0.51811312
## [156,] -0.16955666 0.750114792 -0.47201686 -0.886972005 0.20864312
## [157,] 0.04914686 0.001514024 -0.75208020 -0.791102548 1.03394258
## [158,] 0.99686210 2.247316327 -0.19195352 -0.631320120 -0.67824585
## [159,] 1.21556562 1.648435713 -0.12193769 0.806721729 1.64983769
## [160,] 0.99686210 0.899834945 -0.75208020 0.487156874 0.59049809
## [161,] 0.04914686 0.450674485 -0.82209603 0.007809591 -0.78910697
## [162,] 0.63235624 0.151234178 0.50820482 -0.743167820 0.84917404
## [163,] 0.77815859 0.750114792 0.43818899 -1.030776190 -0.18552975
## [164,] -0.06020490 -0.297926283 0.43818899 -1.446210502 -0.05003283
## [165,] -0.24245783 0.750114792 -0.68206436 -1.510123473 0.96003516
## [166,] -0.38826018 0.899834945 -0.82209603 -1.621971173 0.89844565
## [167,] 0.85105976 1.049555099 0.78826816 -0.950884976 0.55354439
## [168,] -0.24245783 0.001514024 -0.82209603 -1.302406317 -0.22248346
## [169,] 1.17911504 1.498715559 0.36817315 -1.190558618 0.71367712
## [170,] 1.79877500 1.648435713 0.85828399 -0.503494178 0.49195487
## [171,] -0.16955666 -0.148206130 -0.26196936 -1.669905901 -0.98619340
## [172,] -0.31535901 0.001514024 -0.96212770 -1.446210502 -0.28407297
## [173,] 0.41365272 0.151234178 -0.61204853 -0.982841462 1.42811545
## [174,] 0.30430096 0.300954331 -0.33198519 -0.982841462 0.87380985
## [175,] 0.41365272 1.049555099 0.15812565 -0.791102548 0.49195487
## [176,] -0.38826018 0.151234178 1.41841067 -1.126645647 0.33182214
## [177,] 0.01269627 0.151234178 1.41841067 -1.030776190 0.20864312
## [178,] 1.36136797 1.498715559 -0.26196936 -0.391646479 1.39116174
## Flavanoids
## [1,] 1.0319080692
## [2,] 0.7315652835
## [3,] 1.2121137407
## [4,] 1.4623993954
## [5,] 0.6614853002
## [6,] 1.3622851335
## [7,] 0.4912910549
## [8,] 0.4812796287
## [9,] 0.9518166597
## [10,] 1.1220109049
## [11,] 1.2922051502
## [12,] 0.4011882192
## [13,] 0.7315652835
## [14,] 1.6626279192
## [15,] 1.6125707883
## [16,] 0.8817366764
## [17,] 1.1119994787
## [18,] 1.3722965597
## [19,] 1.9029021478
## [20,] 1.0018737906
## [21,] 1.1420337573
## [22,] 0.3811653668
## [23,] 0.8517023978
## [24,] 0.3411196621
## [25,] 0.5813938906
## [26,] 0.6514738740
## [27,] 0.9117709549
## [28,] 0.1609139906
## [29,] 0.9418052335
## [30,] 0.3010739573
## [31,] 1.2221251668
## [32,] 1.1620566097
## [33,] 0.6614853002
## [34,] 0.7115424311
## [35,] 0.5013024811
## [36,] 0.9518166597
## [37,] 0.6514738740
## [38,] 0.4011882192
## [39,] 0.6114281692
## [40,] 1.0118852168
## [41,] 1.2621708716
## [42,] 0.6514738740
## [43,] 1.5324793788
## [44,] 0.6014167430
## [45,] 0.9718395121
## [46,] 0.6214395954
## [47,] 1.1420337573
## [48,] 1.3622851335
## [49,] 0.8917481025
## [50,] 1.5124565264
## [51,] 1.2421480192
## [52,] 0.9618280859
## [53,] 1.7126850502
## [54,] 0.7615995621
## [55,] 0.8717252502
## [56,] 0.7515881359
## [57,] 0.9718395121
## [58,] 1.2021023145
## [59,] 1.6426050669
## [60,] -1.4609370523
## [61,] -0.9403428904
## [62,] -0.6199772522
## [63,] -0.2395430570
## [64,] 1.0719537740
## [65,] -0.2795887618
## [66,] 0.6214395954
## [67,] 1.1520451835
## [68,] -0.0293031070
## [69,] -0.7301029403
## [70,] -0.7501257927
## [71,] -1.0104228737
## [72,] 0.8316795454
## [73,] -0.1894859260
## [74,] 0.8617138240
## [75,] 0.1108568597
## [76,] -0.4597944332
## [77,] 0.0007311716
## [78,] -0.7100800880
## [79,] -0.1794744999
## [80,] 0.5213253335
## [81,] 0.2309939740
## [82,] 0.5013024811
## [83,] -0.4497830070
## [84,] -0.4397715808
## [85,] 0.1809368430
## [86,] -0.0893716641
## [87,] -0.3396573189
## [88,] -0.4197487284
## [89,] -0.3396573189
## [90,] -0.4397715808
## [91,] -0.5298744165
## [92,] -0.7801600713
## [93,] -0.5699201213
## [94,] 0.2209825478
## [95,] 0.2309939740
## [96,] 0.2410054002
## [97,] -1.0404571523
## [98,] 0.4712682025
## [99,] 1.7226964764
## [100,] 0.9618280859
## [101,] 0.1408911382
## [102,] -0.6700343832
## [103,] 0.0808225811
## [104,] -0.3897144499
## [105,] -0.1093945165
## [106,] -0.1894859260
## [107,] 0.0007311716
## [108,] -0.2695773356
## [109,] 0.0107425978
## [110,] 0.8917481025
## [111,] 0.5513596121
## [112,] 0.2410054002
## [113,] 0.0007311716
## [114,] -0.0192916808
## [115,] 0.2610282525
## [116,] 0.1408911382
## [117,] -0.4297601546
## [118,] 0.0607997287
## [119,] -0.7801600713
## [120,] -0.3897144499
## [121,] 0.7615995621
## [122,] 3.0542161597
## [123,] 0.1008454335
## [124,] 0.6214395954
## [125,] 1.0018737906
## [126,] 0.6214395954
## [127,] 1.1220109049
## [128,] 0.2109711216
## [129,] 0.4212110716
## [130,] -0.2795887618
## [131,] -0.7801600713
## [132,] -0.8101943499
## [133,] -0.9403428904
## [134,] -0.8302172023
## [135,] -1.4509256261
## [136,] -1.3708342166
## [137,] -1.5610513142
## [138,] -1.4309027737
## [139,] -1.5510398880
## [140,] -1.4309027737
## [141,] -1.5310170356
## [142,] -1.5310170356
## [143,] -1.5109941832
## [144,] -1.2306742499
## [145,] -1.2506971023
## [146,] -1.4809599046
## [147,] -1.6911998547
## [148,] -1.3808456427
## [149,] -1.2707199546
## [150,] -0.6400001046
## [151,] -0.4597944332
## [152,] -0.6700343832
## [153,] -0.7501257927
## [154,] -1.2006399713
## [155,] -1.4509256261
## [156,] -1.4008684951
## [157,] -1.2006399713
## [158,] -1.4509256261
## [159,] -0.7200915142
## [160,] -0.9303314642
## [161,] -1.1105371356
## [162,] -1.4709484785
## [163,] -1.4309027737
## [164,] -1.3307885118
## [165,] -1.3508113642
## [166,] -1.5610513142
## [167,] -1.1105371356
## [168,] -1.3708342166
## [169,] -1.1906285451
## [170,] -1.0704914308
## [171,] -1.5410284618
## [172,] -1.5210056094
## [173,] -1.3307885118
## [174,] -1.4208913475
## [175,] -1.2807313808
## [176,] -1.3407999380
## [177,] -1.3508113642
## [178,] -1.2707199546
## attr(,"scaled:center")
## Ash Ash_Alcanity Magnesium Total_Phenols Alcohol
## 2.366517 19.494944 99.741573 2.295112 13.000618
## Flavanoids
## 2.029270
## attr(,"scaled:scale")
## Ash Ash_Alcanity Magnesium Total_Phenols Alcohol
## 0.2743440 3.3395638 14.2824835 0.6258510 0.8118265
## Flavanoids
## 0.9988587standarisasi data diperlukan karena tiap variabel memiliki satuan yang berbeda.
- Analisis korelasi kanonik
X <- wineclustering[,2:4]
X## # A tibble: 178 × 3
## Ash Ash_Alcanity Magnesium
## <dbl> <dbl> <dbl>
## 1 2.43 15.6 127
## 2 2.14 11.2 100
## 3 2.67 18.6 101
## 4 2.5 16.8 113
## 5 2.87 21 118
## 6 2.45 15.2 112
## 7 2.45 14.6 96
## 8 2.61 17.6 121
## 9 2.17 14 97
## 10 2.27 16 98
## # ℹ 168 more rowsY <- wineclustering[,5:7]
Y## # A tibble: 178 × 3
## Total_Phenols Alcohol Flavanoids
## <dbl> <dbl> <dbl>
## 1 2.8 14.2 3.06
## 2 2.65 13.2 2.76
## 3 2.8 13.2 3.24
## 4 3.85 14.4 3.49
## 5 2.8 13.2 2.69
## 6 3.27 14.2 3.39
## 7 2.5 14.4 2.52
## 8 2.6 14.1 2.51
## 9 2.8 14.8 2.98
## 10 2.98 13.9 3.15
## # ℹ 168 more rowslibrary(CCA) ## Warning: package 'CCA' was built under R version 4.4.3## Loading required package: fda## Warning: package 'fda' was built under R version 4.4.3## Loading required package: splines## Loading required package: fds## Warning: package 'fds' was built under R version 4.4.3## Loading required package: rainbow## Warning: package 'rainbow' was built under R version 4.4.3## Loading required package: MASS## Loading required package: pcaPP## Loading required package: RCurl## Warning: package 'RCurl' was built under R version 4.4.3## Loading required package: deSolve## Warning: package 'deSolve' was built under R version 4.4.3##
## Attaching package: 'fda'## The following object is masked from 'package:graphics':
##
## matplot## Loading required package: fields## Warning: package 'fields' was built under R version 4.4.3## Loading required package: spam## Warning: package 'spam' was built under R version 4.4.3## Spam version 2.11-1 (2025-01-20) 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.cancor_result <- cancor(X, Y)
cancor_result$cor ## [1] 0.61998890 0.09019750 0.02461195Korelasi kanonik pertama = 0.62 menunjukkan hubungan kuat antara kombinasi variabel dari X dan Y. Korelasi kanonik kedua = 0.09 dan korelasi kanonik ketiga = 0.02 menunjukkan hubungan yang lemah dan hampir tidak ada hubungan. Dapat disimpulkan bahwa hanya pasangan kanonik pertama yang memiliki hubungan yang cukup berarti, sedangkan dua lainnya sangat lemah.
cancor_result$xcoef## [,1] [,2] [,3]
## Ash 0.196850839 -0.086312233 -0.247668147
## Ash_Alcanity -0.021954248 -0.013168559 0.003922992
## Magnesium 0.001046548 -0.003096211 0.004628132Untuk koefisien variabel dalam X yang terdiri dari Ash, Ash_Alcanity, dan Magnesium. Ash memiliki pengaruh terbesar pada semua kombinasi di X.
cancor_result$ycoef## [,1] [,2] [,3]
## Total_Phenols 0.00905679 -0.11187530 0.21512204
## Alcohol 0.06242076 -0.05457323 -0.04986541
## Flavanoids 0.03943973 0.11627623 -0.08581775Untuk koefisien variabel dalam Y yang terdiri dari Total_Phenols, Alcohol, dan Flavonoids. Alcohol memiliki kontribusi tersebar dalam kombinasi pertama Y, Flavonoids memiliki kontribusi terbesar pada kombinasi kedua Y, dan Total_Phenols memiliki kontribusi terbesar pada kombinasi ketiga Y.
cancor_result$xcenter## Ash Ash_Alcanity Magnesium
## 2.366517 19.494944 99.741573cancor_result$ycenter## Total_Phenols Alcohol Flavanoids
## 2.295112 13.000618 2.029270Ini merupakan data yang telah dimean-centering, artinya nilai variabel dikurangi dengan rata-rata sebelum analisis dilakukan.
- Uji hipotesis
- Uji korelasi kanonik secara keseluruhan
H0:Σ12 = 0 ( 𝜌1 ∗ = 𝜌2 ∗ = ⋯ = 𝜌𝑝 ∗ = 0) (semua korelasi kanonik tidak signifikan)
H1: ada 𝜌𝑖 ≠ 0 ,𝑖 = 1,2,…,𝑘 (paling tidak ada satu korelasi kanonik signifikan)
# Uji Bartlett untuk signifikansi korelasi kanonik
rho <- cancor_result$cor # Korelasi kanonik
rho ## [1] 0.61998890 0.09019750 0.02461195n <- nrow(X) # Jumlah sampel
p <- ncol(X) # Jumlah variabel X
q <- ncol(Y) # Jumlah variabel Y
# Hitung statistik uji Bartlett
stat_bartlett <- -((n - 1) - ((p + q + 1) / 2)) * log(prod(1 - rho^2))
stat_bartlett ## [1] 85.69344# Hitung p-value
df <- (p*q)
p_value <- pchisq(stat_bartlett, df = df, lower.tail = FALSE)
p_value ## [1] 1.18591e-14# Hasil
cat("Statistik Uji Bartlett:", stat_bartlett, "\n") ## Statistik Uji Bartlett: 85.69344cat("p-value:", p_value, "\n") ## p-value: 1.18591e-14Karena p-value 1.18591e-14 < 0.05, maka tolak H0 atau dapat disimpulkan bahwa semua korelasi kanonik signifikan.
- Uji korelasi kanonik secara sebagian
H0^(𝑘) : 𝜌1 ∗ = 0,𝜌2 ∗ = 0,…,𝜌𝑘∗ = 0 (korelasi kanonik tidak signifikan)
H1^(𝑘) : 𝜌𝑖 ≠ 0 ,𝑖 = 1,2,…,𝑘 (korelasi kanonik signifikan)
rho3 <- c(0.61998890, 0.09019750, 0.02461195)
log(prod(1 - rho3^2)) ## [1] -0.4939103rho2 <- c(0.09019750, 0.02461195)
log(prod(1 - rho2^2)) ## [1] -0.008774795rho1 <- (0.02461195)
log(prod(1 - rho1^2)) ## [1] -0.0006059316stat_bartlett <- -((n - 1) - (((p-1) + (q-1) + 1) / 2)) * log(prod(1 - rho3^2))
stat_bartlett ## [1] 86.18735stat_bartlett <- -((n - 1) - (((p-2) + (q-2) + 1) / 2)) * log(prod(1 - rho2^2))
stat_bartlett ## [1] 1.539977stat_bartlett <- -((n - 1) - (((p-3) + (q-3) + 1) / 2)) * log(prod(1 - rho1^2))
stat_bartlett## [1] 0.1069469Hipotesis nol ditolak pada taraf signifikan α jika 𝐵 > 𝜒2 dengan derajat bebas (𝑝−𝑟)(𝑞−𝑟). 𝜒2 hitung = 86.18735 > 𝜒2 kritis = 30,579.5 sehingga dapat disimpulkan hanya pasangan korelasi kanonik 1 yang ada hubungan signifikan antara dua set variabel secara keseluruhan.
- Redudansi
#Uji Redudansi
X <- as.matrix(wineclustering[,2:4])
Y <- as.matrix(wineclustering[,5:7])
#Kanonik
rhosq<-cancor_result$cor^2
RIx<-colMeans(cancor_result$xcoef^2)*rhosq
RIy<-colMeans(cancor_result$ycoef^2)*rhosq
RIx ## [1] 5.026918e-03 2.069911e-05 1.239286e-05RIy ## [1] 7.090478e-04 7.868330e-05 1.133329e-05RIX menunjukkan bahwa variabel kanonik dari Y hanya menjelaskan varians kecil dari X (nilai sangat kecil). RIY menunjukkan bahwa variabel kanonik dari X juga hanya menjelaskan varians kecil dari Y. Karena nilai-nilai ini sangat kecil (< 0.01 atau 1%), ini menunjukkan hubungan antara X dan Y tidak terlalu kuat dalam menjelaskan varians satu sama lain.