#
# Epage 65
#
# 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(water)
attach(water)

# 
# 
# plot the scatter plot matrix: BSAAM will be the y-axis of the first row 
postscript("../../WriteUp/Graphics/Chapter3/prob_5.eps", onefile=FALSE, horizontal=FALSE)
pairs(BSAAM~OPBPC+OPRC+OPSLAKE)
dev.off()

f = water[,c(8,5,6,7)]
summary(f)
round(cor(f),4)

m = lm( BSAAM ~ OPBPC+OPRC+OPSLAKE)
summary(m)

# 3.5.3:
#

m1 <- lm( BSAAM ~ OPBPC + OPRC + OPSLAKE )
anova(m1)

m2 <- lm( BSAAM ~ OPBPC + OPSLAKE + OPRC )
anova(m2) 

m3 <- lm( BSAAM ~ OPSLAKE + OPRC + OPBPC )
anova(m3) 

# show that the t-statistics squared for each coefficient are the F-statistics
# of the {\em last} variable added in the sequential ANOVA table
#
s <- summary(m1)
t <- s$coefficients[,3]^2 # <- the t values squared
t

# 3.5.4:
#
mLarger  = m3 # all three inputs
mSmaller = lm( BSAAM ~ OPSLAKE ) 
anova(mSmaller,mLarger)