#####################################################################################
#
# The sales performance data
#
# Source: David Hitchcock's Applied Multivariate Statistics course.
# David is Associate Professor of Statistics, Department of Statistics
# University of South Carolina, Columbia, SC.
# http://www.stat.sc.edu/~hitchcock/stat530.html
# http://www.stat.sc.edu/~hitchcock/chapter8_R_examples.txt
#
# Variables:
# X1 = Sales growth 
# X2 = Sales profitability 
# X3 = New account sales 
# X4 = Creativity Test 
# X5 = Mechanical Reasoning Test 
# X6 = Abstract Reasoning Test 
# X7 = Mathematics Test
# X8 = Historical Facts Test 
# X9 = Sports Trivia Test 
# X10 = Music Trivia Test
#
#####################################################################################
install.packages("GGally")
install.packages("CCA")
library(GGally)
library(CCA)

salesdata = read.table("http://www.stat.sc.edu/~hitchcock/salesmat.txt", header=T)

attach(salesdata)

X = cbind(x1,x2,x3)
Y = cbind(x4,x5,x6,x7,x8,x9,x10)


# scatterplot Y
ggpairs(Y)

# scatterplot X
ggpairs(X)

# correlations
matcor(X,Y)


# Ajustando modelo de correlacoes canonicas
# -----------------------------------------
fit = cc(X,Y)

# correlacoes canonicas
fit$cor

# pesos canonicos
fit$ycoef
fit$xcoef

# Variaveis canonicas
A = X%*%fit$xcoef
B = Y%*%fit$ycoef

par(mfrow=c(1,3))
plot(A[,1],B[,1],xlab="1a variavel canonica (X)",ylab="1a variavel canonica (Y)")
title(paste("1a correlacao canonica=",round(fit$cor[1],4),sep=""))
plot(A[,2],B[,2],xlab="2a variavel canonica (X)",ylab="2a variavel canonica (Y)")
title(paste("2a correlacao canonica=",round(fit$cor[2],4),sep=""))
plot(A[,3],B[,3],xlab="3a variavel canonica (X)",ylab="3a variavel canonica (Y)")
title(paste("3a correlacao canonica=",round(fit$cor[3],4),sep=""))


# Cargas canonicas
CCXA=cor(X,A)
CCYB=cor(Y,B)
round(CCXA,3)
round(CCYB,3)

# Determinação da % da variância explicada pelas componentes
CCYB^2
CCXA^2

# Determinação das cargas cruzadas 
cor(Y,A)
cor(X,B)