## Read in data and assign variable names
lpga2008 <- read.fwf("http://www.stat.ufl.edu/~winner/data/lpga2008.dat", 
   width=c(30,8,8,8,8,8,8,8,8,8,8), 
   col.names=c("golfer","drive","frwy","grnreg",
      "puttrnd","sandrnd","sandsv","przrnd","lnprzrnd","rounds","golferid"))
attach(lpga2008)
# lpga2008

## Create new variables for analysis that remove outlying golfer(s)
drive1 <- drive[grnreg >= 50]
frwy1 <- frwy[grnreg >= 50]
grnreg1 <- grnreg[grnreg >= 50]
puttrnd1 <- puttrnd[grnreg >= 50]

## Create new data frame with only the 4 variables of interest
lpga1 <- data.frame(drive1,frwy1,grnreg1,puttrnd1)

detach(lpga2008)
attach(lpga1)

X <- cbind(drive1, frwy1)



lpga.pc1 <- princomp(X,cor=FALSE)
summary(lpga.pc1, loadings=TRUE)

qqnorm(lpga.pc1$scores[,2]); qqline(lpga.pc1$scores[,2])

par(pty="s")
plot(lpga.pc1$scores[,2],lpga.pc1$scores[,1],
   xlim=range(lpga.pc1$scores[,1]),xlab="PC2",ylab="PC1")

lpga.pc1$scores[,1]



lpga.pc2 <- princomp(X,cor=TRUE)
summary(lpga.pc2, loadings=TRUE)

qqnorm(lpga.pc2$scores[,2]); qqline(lpga.pc2$scores[,2])

par(pty="s")
plot(lpga.pc2$scores[,2],lpga.pc2$scores[,1],
   xlim=range(lpga.pc2$scores[,1]),xlab="PC2",ylab="PC1")

lpga.pc2$scores[,1]

lpga.pc3 <- princomp(lpga1,cor=FALSE)
summary(lpga.pc3, loadings=TRUE)

lpga.pc4 <- princomp(lpga1,cor=TRUE)
summary(lpga.pc4, loadings=TRUE)


library(graphics)

par(pty="s")
biplot(lpga.pc3, cex=0.5)
## Scale for vars (arrows) appears to be loading * sqrt(n-1)