pacman::p_load(pacman,dplyr,GGally,ggplot2,ggthemes,ggvis,httr,lubridate,plotly,rio,rmarkdown,shiny,stringr,tidyr,tidyverse,lattice,caret,pls,MASS,yarrr,psych,ggcorrplot,GGally,CCA,CCP)
library(tidyverse)
theme_set(theme_bw(16))
library(CCA)
library(stats)
Y=read.csv("sensorialCSV.csv",sep=",")
Y<-Y[,c('Aroma', 'Flavor', 'Aftertaste', 'Acidity', 'Body', 'Balance')]
X=read.csv("apolarCSV.csv",sep=",")
X <- X[, c('A25', 'A58', 'A1', 'A15', 'A40', 'A72', 'A34', 'A14', 'A69', 'A13', 'A46')]
X
## A25 A58 A1 A15 A40 A72 A34
## 1 19.370000 0.4533333 16.543333 8.736667 0.6000000 0.03666667 0.0000000
## 2 21.316667 0.9800000 0.000000 12.213333 0.8233333 0.18000000 0.1366667
## 3 11.443333 0.9733333 9.526667 18.383333 0.6600000 0.11000000 0.1833333
## 4 14.000000 0.9266667 20.610000 9.060000 0.5700000 0.12666667 0.1600000
## 5 17.210000 0.9566667 6.876667 19.186667 1.3966667 0.06333333 0.0000000
## 6 15.210000 0.7233333 16.190000 10.170000 0.8133333 0.13666667 0.1466667
## 7 12.236667 1.0566667 15.453333 15.730000 0.7833333 0.12666667 0.1133333
## 8 16.996667 0.8966667 13.613333 10.906667 0.9233333 0.08666667 0.1133333
## 9 11.596667 1.1066667 20.816667 13.970000 0.7333333 0.07000000 0.1666667
## 10 11.936667 1.2533333 16.423333 14.733333 0.8433333 0.06000000 0.3533333
## 11 13.473333 1.2900000 8.676667 14.356667 0.9666667 0.13666667 0.3033333
## 12 17.526667 0.7233333 22.580000 8.370000 0.6866667 0.08666667 0.1633333
## 13 16.943333 1.0633333 15.406667 17.133333 0.8366667 0.09000000 0.0000000
## 14 14.723333 0.9666667 21.490000 14.553333 0.8400000 0.00000000 0.0000000
## 15 11.193333 0.6433333 16.930000 11.800000 2.2233333 0.13666667 0.1633333
## 16 9.086667 0.6533333 21.066667 17.583333 1.9866667 0.10333333 0.1433333
## A14 A69 A13 A46
## 1 20.27000 0.00000000 2.110000 0.5333333
## 2 16.81000 0.03666667 2.516667 0.4600000
## 3 17.37000 0.03000000 1.780000 0.4600000
## 4 15.24667 0.00000000 1.863333 0.3233333
## 5 15.71000 0.02000000 2.386667 0.6000000
## 6 16.07667 0.02666667 1.550000 0.4766667
## 7 14.86667 0.03333333 2.003333 0.3833333
## 8 16.26000 0.03000000 2.736667 0.5100000
## 9 15.46333 0.02000000 2.223333 0.2900000
## 10 14.00333 0.01333333 1.866667 0.2833333
## 11 16.26667 0.00000000 2.243333 0.3500000
## 12 14.89000 0.01333333 2.003333 0.3700000
## 13 14.94000 0.02333333 1.883333 0.4900000
## 14 11.72667 0.02000000 1.983333 0.4700000
## 15 12.80333 0.01666667 3.350000 0.2666667
## 16 13.28000 0.02000000 2.830000 0.2333333
Y
## Aroma Flavor Aftertaste Acidity Body Balance
## 1 8.50 8.42 8.47 8.42 8.36 8.75
## 2 8.39 8.36 8.31 8.44 8.39 8.58
## 3 8.31 8.44 8.33 8.42 8.36 8.64
## 4 8.36 8.25 8.17 8.28 8.31 8.39
## 5 8.17 8.08 8.14 8.33 8.33 8.44
## 6 8.39 8.36 8.25 8.33 8.33 8.58
## 7 8.31 8.39 8.31 8.42 8.36 8.67
## 8 8.50 8.44 8.33 8.61 8.56 8.58
## 9 8.44 8.39 8.31 8.47 8.39 8.67
## 10 8.42 8.39 8.28 8.33 8.47 8.50
## 11 8.47 8.14 8.31 8.42 8.19 8.50
## 12 8.53 8.31 8.25 8.47 8.28 8.61
## 13 8.42 8.47 8.39 8.53 8.42 8.64
## 14 8.56 8.47 8.42 8.53 8.33 8.64
## 15 8.16 8.13 8.03 8.16 8.22 8.22
## 16 8.07 7.89 7.89 8.11 8.00 8.25
#Correlatsion matrices
mat_cor <-matcor(X,Y)
mat_cor
## $Xcor
## A25 A58 A1 A15 A40 A72
## A25 1.00000000 -0.18135639 -0.43085120 -0.40275513 -0.419975534 -0.01825580
## A58 -0.18135639 1.00000000 -0.30172536 0.44880878 -0.310536587 0.06820285
## A1 -0.43085120 -0.30172536 1.00000000 -0.29210867 0.031280286 -0.46898725
## A15 -0.40275513 0.44880878 -0.29210867 1.00000000 0.294046156 -0.10936872
## A40 -0.41997553 -0.31053659 0.03128029 0.29404616 1.000000000 0.16200851
## A72 -0.01825580 0.06820285 -0.46898725 -0.10936872 0.162008508 1.00000000
## A34 -0.46732026 0.44853553 -0.04290717 -0.07364446 0.008578171 0.39303208
## A14 0.51064973 -0.19008092 -0.44103729 -0.25507348 -0.492925389 0.12640453
## A69 0.05861037 0.10287365 -0.35893143 0.36259933 0.050740697 0.26426427
## A13 -0.12449413 -0.29310138 -0.12170794 0.03028465 0.809255779 0.19689497
## A46 0.72436738 -0.11557843 -0.46283931 0.05901247 -0.364399100 -0.24739540
## A34 A14 A69 A13 A46
## A25 -0.467320263 0.5106497 0.05861037 -0.12449413 0.72436738
## A58 0.448535526 -0.1900809 0.10287365 -0.29310138 -0.11557843
## A1 -0.042907173 -0.4410373 -0.35893143 -0.12170794 -0.46283931
## A15 -0.073644460 -0.2550735 0.36259933 0.03028465 0.05901247
## A40 0.008578171 -0.4929254 0.05074070 0.80925578 -0.36439910
## A72 0.393032081 0.1264045 0.26426427 0.19689497 -0.24739540
## A34 1.000000000 -0.1021803 -0.18656346 -0.02347316 -0.66409496
## A14 -0.102180264 1.0000000 -0.12548042 -0.24400168 0.49992626
## A69 -0.186563462 -0.1254804 1.00000000 0.07430970 0.24983090
## A13 -0.023473162 -0.2440017 0.07430970 1.00000000 -0.27349364
## A46 -0.664094959 0.4999263 0.24983090 -0.27349364 1.00000000
##
## $Ycor
## Aroma Flavor Aftertaste Acidity Body Balance
## Aroma 1.0000000 0.7460524 0.8403546 0.8118285 0.5585906 0.7369988
## Flavor 0.7460524 1.0000000 0.8804859 0.7854296 0.8221883 0.8334571
## Aftertaste 0.8403546 0.8804859 1.0000000 0.8529577 0.6921323 0.9119873
## Acidity 0.8118285 0.7854296 0.8529577 1.0000000 0.7165935 0.8201281
## Body 0.5585906 0.8221883 0.6921323 0.7165935 1.0000000 0.6099369
## Balance 0.7369988 0.8334571 0.9119873 0.8201281 0.6099369 1.0000000
##
## $XYcor
## A25 A58 A1 A15 A40
## A25 1.00000000 -0.18135639 -0.430851202 -0.40275513 -0.419975534
## A58 -0.18135639 1.00000000 -0.301725356 0.44880878 -0.310536587
## A1 -0.43085120 -0.30172536 1.000000000 -0.29210867 0.031280286
## A15 -0.40275513 0.44880878 -0.292108670 1.00000000 0.294046156
## A40 -0.41997553 -0.31053659 0.031280286 0.29404616 1.000000000
## A72 -0.01825580 0.06820285 -0.468987253 -0.10936872 0.162008508
## A34 -0.46732026 0.44853553 -0.042907173 -0.07364446 0.008578171
## A14 0.51064973 -0.19008092 -0.441037291 -0.25507348 -0.492925389
## A69 0.05861037 0.10287365 -0.358931425 0.36259933 0.050740697
## A13 -0.12449413 -0.29310138 -0.121707941 0.03028465 0.809255779
## A46 0.72436738 -0.11557843 -0.462839308 0.05901247 -0.364399100
## Aroma 0.47987188 0.21756819 0.129362597 -0.49806772 -0.771264360
## Flavor 0.36894284 0.20904091 0.001415696 -0.22626186 -0.763870859
## Aftertaste 0.50997520 0.27310672 -0.155076544 -0.17934135 -0.807842942
## Acidity 0.52628653 0.34199917 -0.142644893 -0.10585283 -0.696231144
## Body 0.44478432 0.32190921 -0.220988604 -0.15348048 -0.601675397
## Balance 0.46002302 0.15847236 -0.072210914 -0.12179748 -0.829185297
## A72 A34 A14 A69 A13
## A25 -0.01825580 -0.467320263 0.5106497 0.05861037 -0.12449413
## A58 0.06820285 0.448535526 -0.1900809 0.10287365 -0.29310138
## A1 -0.46898725 -0.042907173 -0.4410373 -0.35893143 -0.12170794
## A15 -0.10936872 -0.073644460 -0.2550735 0.36259933 0.03028465
## A40 0.16200851 0.008578171 -0.4929254 0.05074070 0.80925578
## A72 1.00000000 0.393032081 0.1264045 0.26426427 0.19689497
## A34 0.39303208 1.000000000 -0.1021803 -0.18656346 -0.02347316
## A14 0.12640453 -0.102180264 1.0000000 -0.12548042 -0.24400168
## A69 0.26426427 -0.186563462 -0.1254804 1.00000000 0.07430970
## A13 0.19689497 -0.023473162 -0.2440017 0.07430970 1.00000000
## A46 -0.24739540 -0.664094959 0.4999263 0.24983090 -0.27349364
## Aroma -0.35177414 -0.005735030 0.2486802 -0.18417950 -0.48798410
## Flavor -0.26931620 -0.170462632 0.2714448 0.27109350 -0.55396964
## Aftertaste -0.34440454 -0.216665962 0.4588940 0.02369976 -0.55937954
## Acidity -0.30817677 -0.263953482 0.2786702 0.23971656 -0.36226707
## Body -0.20771172 -0.100360715 0.3043094 0.30963048 -0.31966161
## Balance -0.32986242 -0.281594235 0.5104018 0.18778275 -0.62320807
## A46 Aroma Flavor Aftertaste Acidity
## A25 0.72436738 0.47987188 0.368942837 0.50997520 0.5262865
## A58 -0.11557843 0.21756819 0.209040910 0.27310672 0.3419992
## A1 -0.46283931 0.12936260 0.001415696 -0.15507654 -0.1426449
## A15 0.05901247 -0.49806772 -0.226261857 -0.17934135 -0.1058528
## A40 -0.36439910 -0.77126436 -0.763870859 -0.80784294 -0.6962311
## A72 -0.24739540 -0.35177414 -0.269316197 -0.34440454 -0.3081768
## A34 -0.66409496 -0.00573503 -0.170462632 -0.21666596 -0.2639535
## A14 0.49992626 0.24868015 0.271444773 0.45889397 0.2786702
## A69 0.24983090 -0.18417950 0.271093504 0.02369976 0.2397166
## A13 -0.27349364 -0.48798410 -0.553969642 -0.55937954 -0.3622671
## A46 1.00000000 0.28189707 0.410396473 0.54487713 0.5515343
## Aroma 0.28189707 1.00000000 0.746052422 0.84035457 0.8118285
## Flavor 0.41039647 0.74605242 1.000000000 0.88048587 0.7854296
## Aftertaste 0.54487713 0.84035457 0.880485874 1.00000000 0.8529577
## Acidity 0.55153429 0.81182848 0.785429604 0.85295767 1.0000000
## Body 0.48735985 0.55859059 0.822188317 0.69213230 0.7165935
## Balance 0.53277374 0.73699879 0.833457108 0.91198732 0.8201281
## Body Balance
## A25 0.4447843 0.46002302
## A58 0.3219092 0.15847236
## A1 -0.2209886 -0.07221091
## A15 -0.1534805 -0.12179748
## A40 -0.6016754 -0.82918530
## A72 -0.2077117 -0.32986242
## A34 -0.1003607 -0.28159424
## A14 0.3043094 0.51040177
## A69 0.3096305 0.18778275
## A13 -0.3196616 -0.62320807
## A46 0.4873598 0.53277374
## Aroma 0.5585906 0.73699879
## Flavor 0.8221883 0.83345711
## Aftertaste 0.6921323 0.91198732
## Acidity 0.7165935 0.82012809
## Body 1.0000000 0.60993686
## Balance 0.6099369 1.00000000
cc1 <- cc(X, Y)
# display the canonical correlations
cc1$cor
## [1] 1.0000000 1.0000000 0.9807809 0.9459939 0.6022575 0.5244332
# canonical vectors
cc1[3:4]
## $xcoef
## [,1] [,2] [,3] [,4] [,5]
## A25 -0.12122232 0.08741659 -0.058323720 0.1926928 -0.5063744
## A58 -3.45338335 1.98220520 1.887393915 -2.2602260 -3.3661593
## A1 -0.06756581 0.17751323 -0.168415509 0.2544482 -0.3538928
## A15 0.21557891 0.27861429 -0.211460693 0.2766940 -0.1911074
## A40 -0.64723073 -1.70292936 1.832342233 -2.9295898 -4.2835399
## A72 12.10401693 14.83618510 -9.290449412 22.1816098 -2.8298197
## A34 -2.82643700 4.35542228 -2.203682375 13.9260880 -10.8251705
## A14 -0.25156186 -0.03710752 -0.008916911 -0.6200673 -0.8858299
## A69 -36.10718354 -19.48785279 -68.671750582 -35.5423510 -55.8575382
## A13 0.28488329 3.21575180 -0.903230736 3.4776590 0.6546994
## A46 -1.15607403 13.59315413 -1.428673052 14.1454821 -0.8955144
## [,6]
## A25 0.3727698
## A58 -6.4688128
## A1 0.2440669
## A15 0.7634864
## A40 -5.3802716
## A72 26.0556494
## A34 8.6533718
## A14 -0.3855186
## A69 -100.1378574
## A13 3.2822327
## A46 4.8103434
##
## $ycoef
## [,1] [,2] [,3] [,4] [,5] [,6]
## Aroma -8.601644 -8.147004 3.676741 6.488945 -4.837793 2.297379
## Flavor 3.575096 -5.506885 -10.289474 4.553118 11.062029 -3.117002
## Aftertaste 3.463244 6.928188 15.671556 -10.516516 11.565301 -1.141995
## Acidity 3.744878 13.017124 -6.495353 7.456519 4.384930 5.104057
## Body -6.942830 2.210205 4.603664 -2.476606 -11.009861 -8.349326
## Balance -4.232448 -5.103435 -7.039717 -6.756198 -13.216140 4.625235
# Standarized coefficients of X
std_coef_x<-cc1$xcoef*apply(X,2,sd)
std_coef_x
## [,1] [,2] [,3] [,4] [,5] [,6]
## A25 -0.4082558 0.29440394 -0.19642419 0.6489560 -1.70538143 1.2554242
## A58 -0.7850883 0.45063230 0.42907800 -0.5138372 -0.76525886 -1.4706126
## A1 -0.4180194 1.09824725 -1.04196104 1.5742321 -2.18948098 1.5100045
## A15 0.7584143 0.98017505 -0.74392629 0.9734195 -0.67232283 2.6859725
## A40 -0.3103048 -0.81644336 0.87848837 -1.4045469 -2.05367749 -2.5794887
## A72 0.5424034 0.66483689 -0.41632222 0.9939990 -0.12680945 1.1676018
## A34 -0.2878816 0.44361369 -0.22445210 1.4184166 -1.10257824 0.8813736
## A14 -0.4992707 -0.07364669 -0.01769725 -1.2306374 -1.75809210 -0.7651324
## A69 -0.4162779 -0.22467446 -0.79171312 -0.4097660 -0.64397871 -1.1544843
## A13 0.1315806 1.48527650 -0.41718002 1.6062450 0.30238953 1.5159824
## A46 -0.1252809 1.47305635 -0.15482175 1.5329108 -0.09704467 0.5212850
# Standarized coefficients of Y
std_coef_y<-cc1$ycoef*apply(Y,2,sd)
std_coef_y
## [,1] [,2] [,3] [,4] [,5] [,6]
## Aroma -1.2107660 -1.1467710 0.5175374 0.9133829 -0.6809669 0.3233788
## Flavor 0.5949742 -0.9164662 -1.7123938 0.7577386 1.8409640 -0.5187373
## Aftertaste 0.5052411 1.0107302 2.2862709 -1.5342193 1.6872231 -0.1666018
## Acidity 0.4936460 1.7159044 -0.8562110 0.9829109 0.5780171 0.6728117
## Body -0.8671129 0.2760398 0.5749668 -0.3093114 -1.3750577 -1.0427748
## Balance -0.6370033 -0.7680910 -1.0595105 -1.0168396 -1.9890913 0.6961197
# Calculate structure correlations
struc_cor_x <- cor(X, cc1$scores$xscores)
struc_cor_y <- cor(Y, cc1$scores$yscores)
# Compute redundancy indices
can_cor <- cc1$cor
redundancy_x <- colMeans(struc_cor_x^2) * can_cor^2
redundancy_y <- colMeans(struc_cor_y^2) * can_cor^2
print(redundancy_x)
## [1] 0.16316268 0.12240024 0.07163330 0.09863615 0.01182328 0.01584773
print(redundancy_y)
## [1] 0.57526829 0.06957837 0.06960760 0.07370398 0.04340058 0.02221592
# Total redundancy
total_redundancy_x <- sum(redundancy_x)
total_redundancy_y <- sum(redundancy_y)
# Print results
print(paste("Total redundancy for X:", total_redundancy_x))
## [1] "Total redundancy for X: 0.483503383507049"
print(paste("Total redundancy for Y:", total_redundancy_y))
## [1] "Total redundancy for Y: 0.853774748337202"
# compute canonical loadings
cc2 <- comput(X, Y, cc1)
# display canonical loadings
cc2[3:6]
## $corr.X.xscores
## [,1] [,2] [,3] [,4] [,5] [,6]
## A25 -0.52275581 0.29951651 0.10220669 -0.16131032 -0.015863223 0.17036707
## A58 -0.21231799 0.38893380 0.10542190 0.01433344 0.227965027 -0.15033843
## A1 -0.06693200 -0.55668935 -0.22272047 0.37920513 0.029756157 0.28818831
## A15 0.53622935 0.46681675 -0.15182832 -0.30015735 0.020198894 -0.01863829
## A40 0.77740430 0.04415157 0.19438559 0.31824151 -0.281996221 -0.26086620
## A72 0.32977538 -0.03065069 -0.01463453 0.10546667 -0.122425262 -0.26132148
## A34 -0.06784469 -0.32052330 0.26532105 0.27055655 -0.215730367 -0.27895449
## A14 -0.35917252 0.10000667 0.11075679 -0.64528405 -0.278898871 0.16898996
## A69 0.12649833 0.33928451 -0.74586794 -0.05313587 0.006249432 -0.44811420
## A13 0.47395200 0.27074424 0.20784327 0.39031097 -0.268258760 -0.23163145
## A46 -0.31155370 0.52302995 -0.06894990 -0.44174722 0.119225648 0.04050190
##
## $corr.Y.xscores
## [,1] [,2] [,3] [,4] [,5]
## Aroma -0.8953783 -9.958044e-16 0.006371812 0.06165458 0.20811181
## Flavor -0.7195839 5.242400e-02 -0.388461399 -0.22844380 0.29156255
## Aftertaste -0.7484019 1.942610e-01 -0.083534593 -0.38078488 0.27895869
## Acidity -0.7348205 4.950887e-01 -0.282316535 -0.04223105 0.17682230
## Body -0.7393491 3.426343e-01 -0.216987643 -0.14553521 0.07645323
## Balance -0.6967086 1.203062e-01 -0.364607290 -0.46719904 0.13097724
## [,6]
## Aroma 0.14323943
## Flavor -0.09067209
## Aftertaste 0.07101052
## Acidity 0.10985072
## Body -0.26076240
## Balance 0.13946276
##
## $corr.X.yscores
## [,1] [,2] [,3] [,4] [,5] [,6]
## A25 -0.52275581 0.29951651 0.10024237 -0.15259858 -0.009553745 0.089346148
## A58 -0.21231799 0.38893380 0.10339579 0.01355935 0.137293641 -0.078842460
## A1 -0.06693200 -0.55668935 -0.21843999 0.35872574 0.017920868 0.151135513
## A15 0.53622935 0.46681675 -0.14891031 -0.28394702 0.012164935 -0.009774538
## A40 0.77740430 0.04415157 0.19064967 0.30105453 -0.169834332 -0.136806895
## A72 0.32977538 -0.03065069 -0.01435327 0.09977082 -0.073731529 -0.137045657
## A34 -0.06784469 -0.32052330 0.26022182 0.25594485 -0.129925226 -0.146292993
## A14 -0.35917252 0.10000667 0.10862815 -0.61043477 -0.167968930 0.088623945
## A69 0.12649833 0.33928451 -0.73153304 -0.05026621 0.003763767 -0.235005958
## A13 0.47395200 0.27074424 0.20384871 0.36923180 -0.161560843 -0.121475222
## A46 -0.31155370 0.52302995 -0.06762474 -0.41789018 0.071804538 0.021240542
##
## $corr.Y.yscores
## [,1] [,2] [,3] [,4] [,5]
## Aroma -0.8953783 -9.404684e-16 0.006496673 0.06517440 0.3455529
## Flavor -0.7195839 5.242400e-02 -0.396073573 -0.24148549 0.4841161
## Aftertaste -0.7484019 1.942610e-01 -0.085171512 -0.40252361 0.4631884
## Acidity -0.7348205 4.950887e-01 -0.287848726 -0.04464199 0.2935992
## Body -0.7393491 3.426343e-01 -0.221239668 -0.15384371 0.1269444
## Balance -0.6967086 1.203062e-01 -0.371752026 -0.49387109 0.2174771
## [,6]
## Aroma 0.2731319
## Flavor -0.1728954
## Aftertaste 0.1354043
## Acidity 0.2094656
## Body -0.4972271
## Balance 0.2659305
# tests of canonical dimensions
rho <- cc1$cor
## Define number of observations, number of variables in first set, and number of variables in the second set.
n <- dim(X)[1]
p <- length(X)
q <- length(Y)
## Calculate p-values using the F-approximations of different test statistics:
p.asym(rho, n, p, q, tstat = "Wilks")
## Wilks' Lambda, using F-approximation (Rao's F):
## stat approx df1 df2 p.value
## 1 to 6: 0.000000e+00 Inf 66 0.1050906 0.000000e+00
## 2 to 6: 8.208768e-19 621.4740283 50 3.3642102 3.216798e-05
## 3 to 6: 1.848450e-03 0.6646059 36 5.4847775 7.912900e-01
## 4 to 6: 4.855551e-02 0.4902057 24 6.4018255 9.040948e-01
## 5 to 6: 4.620131e-01 0.2019445 14 6.0000000 9.935366e-01
## 6 to 6: 7.249698e-01 0.2529118 6 4.0000000 9.339501e-01
p.asym(rho, n, p, q, tstat = "Hotelling")
## Warning in pf(approx[rhostart], df1[rhostart], df2[rhostart]): Se han producido
## NaNs
## Warning in pf(approx[rhostart], df1[rhostart], df2[rhostart]): Se han producido
## NaNs
## Hotelling-Lawley Trace, using F-approximation:
## stat approx df1 df2 p.value
## 1 to 6: Inf -Inf 66 -16 NaN
## 2 to 6: 2.251800e+15 -3.002400e+13 50 -4 NaN
## 3 to 6: 3.473190e+01 1.286367e+00 36 8 0.3749573
## 4 to 6: 9.463675e+00 1.314399e+00 24 20 0.2693943
## 5 to 6: 9.485221e-01 3.613418e-01 14 32 0.9768808
## 6 to 6: 3.793677e-01 4.636717e-01 6 44 0.8313388
# Canonical variates (linear combinations of X and Y)
X_canon <- as.matrix(X) %*% cc1$xcoef
Y_canon <- as.matrix(Y) %*% cc1$ycoef
# Plot the first canonical variates
plot(X_canon[,1], Y_canon[,1],
xlab = "Canonical Variate 1 (X)",
ylab = "Canonical Variate 1 (Y)",
main = "Scatter plot of first pair of canonical variates")
plot(X_canon[,2], Y_canon[,2],
xlab = "Canonical Variate 2 (X)",
ylab = "Canonical Variate 2 (Y)",
main = "Scatter plot of the second pair of canonical variates")
plot(X_canon[,3], Y_canon[,3],
xlab = "Canonical Variate 3 (X)",
ylab = "Canonical Variate (Y)",
main = "Scatter plot of the third pair of canonical variates")
# Create a data frame of canonical correlations
canon_corr_df <- data.frame(Variable = 1:length(cc1$cor),
Correlation = cc1$cor)
# Bar plot of canonical correlations
ggplot(canon_corr_df, aes(x = as.factor(Variable), y = Correlation)) +
geom_bar(stat = "identity") +
xlab("Canonical Pair") +
ylab("Canonical Correlation") +
ggtitle("Canonical Correlations for Each Canonical Pair")
plt.cc(cc1, var.label = TRUE, d1 = 1, d2 = 2, type = "b")
plt.cc(cc1,d1=1,d2=2, type = "b")
