######################################################
#
# X1: população em milhares de habitantes
# X2: densidade populacional
# X3: % de população urbana
# X4: expectativa de vida feminina
# X5: expectativa de vida masculina
# X6: crescimento populacional
# X7: mortalidade infantil
# X8: PIB per capita
# X9: % de homens alfabetizados
# X10: % de mulheres alfabetizadas
#
######################################################
wants  =  c("graphics")
has    =  wants %in% rownames(installed.packages())
if(any(!has)) install.packages(wants[!has])
library(graphics)

p = 10

x = matrix(scan("mundo.txt"),byrow=TRUE,ncol=p)

n = nrow(x)

boxplot(x)

mu = matrix(apply(x,2,mean),n,p,byrow=TRUE)
iD  = sqrt(diag(1/apply(x,2,var)))
x = x-mu

x = x%*%iD

boxplot(x)

pairs(x)

round(cor(x),2)

pca.cor = princomp(x,scores=TRUE,cor=TRUE)

summary(pca.cor)

vd.cor = pca.cor$sd^2/sum(pca.cor$sd^2)

svd.cor = cumsum(vd.cor)

100*cbind(vd.cor,svd.cor)

loadings(pca.cor)[,1:3]


par(mfrow=c(1,1))
biplot(pca.cor)

par(mfrow=c(1,1))
screeplot(pca.cor)

round(cor(x,pca.cor$scor),2)