data <- read.table("C:/Documents and Settings/steeleb/My Documents/Math 543/counties.txt",sep=",",header=TRUE)
head(data)

data <- na.omit(data)
dem <- data$democrat > data$republican
I <- data$pop>1000000
data <- data[I,1:11]
dem <- dem[I]

X <- data[,4:dim(data)[2]]
X.names <- c("pop.dens","pop","p.chng","a6574","a75","crime","colge","income")
colnames(X) <- X.names
p <- dim(data)[2] - 3
v.names <- colnames(data)
e <- eigen(cor(X))

############################# examine eigenvalues and vectors - cleaner output ####################

m <- cbind(1:p,e$values,100*e$values/sum(e$values),100*cumsum(e$values)/sum(e$values))
colnames(m) <- c("e-pair","eigenvalue","%acc't by","% cumulative acc't by")
options(digits = 3)
m

vectrs <- e$vectors
rownames(vectrs) <-colnames(X)
colnames(vectrs) <- c("PC 1","PC 2","PC 3","PC 4","PC 5","PC 6","PC 7","PC 8")

vectrs
sort(vectrs[,1])
sort(vectrs[,2])
sort(vectrs[,3])

s <- 1:p
par(mfrow=c(2,1))
plot(1:p,vectrs[,1],xaxt="n",xlab="Variable",ylab="Coefficient",pch=16)
axis(1,at=1:p,labels=colnames(X))
abline(h=0)

plot(1:p,vectrs[,2],xaxt="n",xlab="Variable",ylab="Coefficient",pch=16)
axis(1,at=1:p,labels=colnames(X))
abline(h=0)
plot(1:p,vectrs[,3],xaxt="n",xlab="Variable",ylab="Coefficient",pch=16)
axis(1,at=1:p,labels=colnames(X))
abline(h=0)

############################# plot principal components #####################
par(mfrow=c(1,1))
PC <- scale(X)%*%vectrs
plot(PC[,1],PC[,2],xlab="PC 1",ylab="PC 2",type="p")
points(PC[dem,1],PC[dem,2],col=3,pch=16)
points(PC[dem==F,1],PC[dem==F,2],col=2,pch=16)
identify(PC[,1],PC[,2],labels = data$county)

plot(PC[,3],PC[,2],xlab="PC 1",ylab="PC 2",type="p")
identify(PC[,3],PC[,2],labels = data$county)