data = read.table("vinho.txt",header=TRUE)

attach(data)

summary(data)

boxplot(data)

plot(Aroma,Corpo)

plot(Aroma,Sabor)

plot(Corpo,Sabor)

corAC = round(cor(Aroma,Corpo),4)
corAS = round(cor(Aroma,Sabor),4)
corCS = round(cor(Corpo,Sabor),4)


L=min(data)
U=max(data)

par(mfrow=c(1,3))
plot(Aroma,Corpo,main=corAC,xlim=c(L,U),ylim=c(L,U))
plot(Aroma,Sabor,main=corAS,xlim=c(L,U),ylim=c(L,U))
plot(Corpo,Sabor,main=corCS,xlim=c(L,U),ylim=c(L,U))

# calculando distancias de Mahalanobis
# ------------------------------------
pairs(data)

x    = cbind(Aroma,Corpo,Sabor)
n    = nrow(x)
xbar = apply(x,2,mean)
S    = var(x)
iS   = solve(S)  
dist = x-matrix(xbar,n,3,byrow=TRUE)
Dm   = diag(dist%*%iS%*%t(dist))
pval = round(1-pchisq(Dm,3),4)
rDm  = round(sqrt(Dm),2)

par(mfrow=c(1,1))
plot(Dm,xlab="Observation",ylab="Mahalanobis distance")
abline(h=qchisq(0.95,3),col=2,lwd=2)
abline(h=qchisq(0.99,3),col=4,lwd=2)
abline(h=qchisq(0.999,3),col=6,lwd=2)
legend(10,20,c("Cut-off for 5% level","Cut-off for 1% level","Cut-off for 0.1% level"),
       col=c(2,4,6),bty="n",lwd=2)
       
       
data[c(6,38,39),]       
#   Aroma Corpo Sabor
#6    4.3   5.5   3.5
#38   7.7   6.6   6.7
#39   7.7   2.6   2.5