# Perform PCA on exams data
exams<-matrix(scan(file='exams.txt'),byrow=T,ncol=5)
nr<-length(exams[,1])
dimnames(exams)<-list(1:nr,c("X1","X2","X3","X4","X5"))
exams.prc<-princomp(exams,cor=F)
# cor=F (the default) means use covariances not correlations
print(summary(exams.prc,loadings=T))
# Plot of PC variances
plot(exams.prc)
# Draw a screeplot with lines
screeplot(exams.prc,type='lines')
# Apply Kaiser's criterion by first computing mean eigenvalue
exams.eigen<-exams.prc$sdev^2
print(sqrt(mean(exams.eigen)))
# Plot prediction scores of original data
pr<-predict(exams.prc)
plot(1:88,pr[,1],xlab='Student',ylab='Component 1')
plot(1:88,pr[,2],xlab='Student',ylab='Component 2')
plot(1:88,pr[,3],xlab='Student',ylab='Component 3')
plot(1:88,pr[,4],xlab='Student',ylab='Component 4')
# Print prediction scores for new data
exam2<-matrix(scan(file='exam2.txt'),byrow=T,ncol=5)
dimnames(exam2)<-list(1:6,c("X1","X2","X3","X4","X5"))
print(predict(exams.prc,newdata=exam2))
# Biplot
biplot(exams.prc)