##############################################################
#
# Correlacao canonica
#
##############################################################
#
# 50 vendedores avaliados
#
# Analise do desempenho
#   y1: indice de crescimento de vendas
#   y2: indice de lucratividade
#   y3: indice de captacao de novas vendas
#
# Analise de habilidades
#   x1: criatividade
#   x2: raciocinio mecanico
#   x3: raciocionio abstrato
#   x4: habilidade matematica
#
##############################################################
install.packages("GGally")
install.packages("CCA")
library(GGally)
library(CCA)

data = read.csv("vendedores.csv",header=TRUE)

attach(data)

names(data) = c("cres.venda","lucrat","novas.venda","criativ","mecan","abstr","matem")

Y = as.matrix(data[,1:3])
X = as.matrix(data[,4:7])

# scatterplot Y
ggpairs(Y)

# scatterplot X
ggpairs(x)

# correlations
matcor(X,Y)

write.csv(cor(data),"corr.csv")

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

# correlacoes canonicas
fit$cor
# 0.9944827 0.8781065 0.3836057

# pesos canonicos
fit$ycoef
fit$xcoef

#Y1 -0.06237788 -0.1740703  0.3771529
#Y2 -0.02092564  0.2421641 -0.1035150
#Y3 -0.07825817 -0.2382940 -0.3834151
#
#X1 -0.06974814 -0.19239132 -0.24655659
#X2 -0.03073830  0.20157438  0.14189528
#X3 -0.08956418 -0.49576326  0.28022405
#X4 -0.06282997  0.06831607 -0.01133259
 

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

par(mfrow=c(1,1))
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)