install.packages("alr3")
library(alr3)
data(heights)
names(heights)

fit1 = lm(Dheight ~ Mheight, heights)
fit1

summary(fit1)

aov(fit1)
sigma = 7051.957/1373
sigma


anova1 = aov(Dheight ~ Mheight, heights)
summary(anova1)

confint(fit1, level=0.99)

#partb
fmeans = mean(heights)
fcov = var(heights)*(1375-1)
xbar <- fmeans[1] 
ybar <- fmeans[2]
SXX <- fcov[1,1] 
SXY<- fcov[1,2]
SYY <- fcov[2,2]
betahat1 <- SXY/SXX ; print(round(betahat1,4))
betahat0 <- ybar - betahat1*xbar ; print(round(betahat0,4))

alpha = betahat0+ betahat1*xbar
alpha
xbar
fit_dev = alpha+betahat1*(heights$Mheight-xbar)


#partc
predict(fit1, newdata=data.frame(Mheight=c(64)),interval="prediction",level=.99,se.fit=TRUE)