trees<-read.table("trees.txt")
names(trees)<-c("Diameter","Height","Volume")
trees.fit <- lm(Volume~ Diameter+Height, trees)
trees.fit
summary(trees.fit)
anova(trees.fit)
trees.res <- residuals(trees.fit)
trees.prd <- predict(trees.fit)

s <- summary(trees.fit)$sigma
h <- lm.influence(trees.fit)$hat
trees.res <- trees.res/(s*sqrt(1-h))

par(mfrow=c(2,1))
plot(trees[,"Diameter"], trees.res, xlab="Diameter",ylab="Std. Residuals")
abline(h=0, lty=2)
title("Std. Residuals versus Diameter")
plot(trees[,"Height"], trees.res, xlab="Height",ylab="Std. Residuals")
abline(h=0, lty=2)
title("Std. Residuals versus Height")
par(mfrow=c(1,1))
plot(trees.prd, trees.res, xlab="Predicted Volume",ylab="Std. Residuals")
abline(h=0,lty=2)
title("Std. Residuals vs Fitted Values")
qqnorm(trees.res,ylab="Std. Residuals",main="Normal Plot of Std. Residuals")
qqline(trees.res)

h <- lm.influence(trees.fit)$hat
h
plot(1:31,h, type="n", xlab="i", ylab="Diagonal of Hat Matrix")
abline(h=mean(h))
segments(1:31, h, 1:31, mean(h))

trees1.fit <- lm(Volume~Diameter+I(Diameter*Diameter)+Height,trees)
trees1.fit
summary(trees1.fit)
trees1.res<-residuals(trees1.fit)
trees1.prd<-predict(trees1.fit)

attach(trees)
trees.drop1 <- drop1(trees.fit)
trees.drop1

trees0.fit <- lm(Volume~1)
trees.add1 <- add1(trees0.fit,~ Height+Diameter)
trees.add1

trees1.drop1 <- drop1(trees1.fit)
trees1.drop1
trees10.fit <- lm(Volume~1)
trees1.add1 <- add1(trees10.fit,~ Height+Diameter+I(Diameter*Diameter))
trees1.add1