# 
# 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(oldfaith)
attach(oldfaith)

# 2.12.1:
#

m = lm( Interval ~ Duration )

# plot this data:
#
postscript("../../WriteUp/Graphics/Chapter2/prob_12.eps", onefile=FALSE, horizontal=FALSE)
plot(Duration,Interval,bty="l")
abline( m )
dev.off()

# 2.12.2:
#
predict( m, newdata=data.frame(Duration=250), interval="confidence", level=0.95 )

# 2.12.3:
#
predict( m, newdata=data.frame(Duration=250), interval="prediction", level=0.95 )

# 2.12.4:
#
SXX = sum( ( Duration - mean(Duration) )^2 )
bar_x = mean(Duration)
n   = length( Duration ) 
sigma = summary(m)$sigma 

alpha=0.1
F = qf(1-alpha,2,n-2)
sqrt( 2 * F )