#
# Epage 41
#
# Written by:
# -- 
# John L. Weatherwax                2009-04-21
# 
# email: wax@alum.mit.edu
# 
# Please send comments and especially bug reports to the
# above email address.
# 
#-----

library(alr3)
data(heights)
attach(heights)

# 2.4.1:
#
postscript("../../WriteUp/Graphics/Chapter2/prob_4.eps", onefile=FALSE, horizontal=FALSE)
plot( Mheight, Dheight, xlab="Mheight", ylab="Dheight" )
dev.off()

m <- lm( Dheight ~ Mheight ) 
summary( m )

anova(m)

# 2.4.2:
#
Mheight0 <- Mheight - mean( Mheight )
m0 <- lm( Dheight ~ Mheight0 )
summary(m0)

# get the standard error of beta_1: 
n   <- length( m0$residuals )
RSS <- sum( m0$residuals ^ 2 )
sigma_hat <- sqrt( RSS/(n-2) )
SXX <- sum( ( Mheight0 - mean(Mheight0) )^2 ) 
se_beta_1 <- sigma_hat / sqrt( SXX ) 

# get the confidence interval of beta_1:
#
alpha = 1 - 0.99
quant = qt( 1 - alpha/2, n-2 ) 

m0$coefficients[2] - quant * se_beta_1
m0$coefficients[2] + quant * se_beta_1

# 2.4.3:
# 
predict( m0, newdata=data.frame(Mheight0=64-mean(Mheight)), interval="prediction", level=0.99 )
#
#          fit      lwr      upr
# [1,] 64.58925 58.74045 70.43805
#