# Generating data
x<-sort(scale(rnorm(200)))
y<-scale(x+0.5*rnorm(200))
data<-data.frame(x,y)
plot(data,xlim=c(-3,3),ylim=c(-3,3))
title("Highly correlated data")

# Performing PCA and plotting the first PC
pca = princomp(data)
arrows(0,0,pca$loadings[1],pca$loadings[2],0.1,col="red",lwd=3)
plot(pca$scores[,1])

# Recreating the information from the first PC
plot(data,xlim=c(-3,3),ylim=c(-3,3))
points(pca$scores[,1]%*%t(pca$loadings[1]),pca$scores[,1]%*%t(pca$loadings[2]),col="red")

# PC2
plot(pca$scores[,2])
plot(data,xlim=c(-3,3),ylim=c(-3,3))
arrows(0,0,pca$loadings[1],pca$loadings[2],0.1,col="red",lwd=3)
arrows(0,0,pca$loadings[3],pca$loadings[4],0.1,col="red",lwd=3)

# Both PCs
plot(pca$scores[,1],pca$scores[,2],xlab="PC1",ylab="PC2")
title("All principal components")

# More commands
summary(pca)
screeplot(pca)
loadings(pca)
biplot(pca) #Later