x <- sample(-10:10,200,replace=TRUE)
y <- -2*x + 50 + rnorm(200,sd=5) # normal population of ys for each x
plot(x,y)
m0 <- lm(y~x)
abline(m0)
for (i in -10:10) {
  points(i,mean(y[x==i]),col='green')}
pc <- predict(m0,newdata=data.frame(x=-10:10),interval='confidence')
pp <- predict(m0,newdata=data.frame(x=-10:10),interval='prediction')
lines(-10:10,pc[,2],col='red')
lines(-10:10,pp[,2],col='blue')
lines(-10:10,pc[,3],col='red')
lines(-10:10,pp[,3],col='blue')



Prostate <- read.table('http://math.uttyler.edu/nathan/classes/statistics/data/prostate.data',header=TRUE)

attach(Prostate)
names(Prostate)

plot(Prostate)

m1 <- lm(lpsa ~ .,data=Prostate)
summary(m1) 

grandpa <- data.frame(lcavol=1, lweight=3, age=68, lbph=1.2, svi=0, lcp=.12,
                      gleason=6,pgg45=282.35)

men.like.grandpa <- data.frame(lcavol=1, lweight=3, age=68, lbph=1.2,
                               svi=0, lcp=.12, gleason=6,pgg45=282.35)

predict(m1,newdata=grandpa,interval='prediction')
predict(m1,newdata=men.like.grandpa,interval='confidence')