#
# Epage 
#
# 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(snowgeese)
attach(snowgeese)

# a scatterplot matrix
#
postscript("../../WriteUp/Graphics/Chapter5/prob_5.eps", onefile=FALSE, horizontal=FALSE)
pairs(photo~obs1+obs2)
dev.off()

# 5.5.2:
#
plot( obs1, photo )
m_obs1 <- lm( photo ~ obs1 )
abline( m_obs1 ) 

param_bootstrap( obs1, photo, 1000 )

# 5.5.3:
#
sqrt_photo <- sqrt( photo )
sqrt_obs1  <- sqrt( obs1 )

plot( sqrt_obs1, sqrt_photo )

param_bootstrap( sqrt_obs1, sqrt_photo, 1000 )

m_obs1 <- lm( photo ~ obs1 )
m_obs2 <- lm( photo ~ obs2 )
m_both <- lm( photo ~ obs1 + obs2 ) 
summary(m_obs1)
summary(m_obs2)
summary(m_both)

summary(m_obs1)$r.squared
summary(m_obs2)$r.squared
summary(m_both)$r.squared

summary(m_obs1)$sigma^2
summary(m_obs2)$sigma^2
summary(m_both)$sigma^2

summary(m_obs1)$fstatistic[1]
summary(m_obs2)$fstatistic[1]
summary(m_both)$fstatistic[1]

avgerage <- 0.5 * ( obs1 + obs2 )
diff <- obs1 - obs2

m_both2 <- lm( photo ~ avgerage + diff )
summary( m_both2 )

m_wobs1 <- lm( photo ~ obs1, weights=1/obs1 )
summary(m_wobs1)