#
# 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.
# 
#-----

if(is.null(version$language) == FALSE) require(alr3) else library(alr3)

data(mantel)

# start with backwards ellimination:
#
mNone <- lm( Y ~ 1, data=mantel )              # <- our most basic model
mAll  <- lm( Y ~ X1 + X2 + X3, data=mantel )   # <- the full model

# us the R function "step" to do backwards ellimination:
#

# using the AIC:
# 
step( mAll, scope=list(lower=~1,upper=~1+X1+X2+X3),direction="backward",data=mantel, k=2 )

# using the BIC:
#
step( mAll, scope=list(lower=~1,upper=~1+X1+X2+X3),direction="backward",data=mantel, k=log(length(mAll$residuals)) )

# using the C_p criterion:
#
step( mAll, scope=list(lower=~1,upper=~1+X1+X2+X3),direction="backward",data=mantel, scale=sigma.hat(mAll)^2 )


# us the R function "step" to do forward ellimination:
#

# using the AIC:
# 
step( mNone, scope=list(lower=~1,upper=~1+X1+X2+X3),direction="forward",data=mantel, k=2 )

# using the BIC:
#
step( mNone, scope=list(lower=~1,upper=~1+X1+X2+X3),direction="forward",data=mantel, k=log(length(mNone$residuals)) )

# using the C_p criterion:
#
step( mNone, scope=list(lower=~1,upper=~1+X1+X2+X3),direction="forward",data=mantel, scale=sigma.hat(mNone)^2 )

# lets compute the correlation of these variables:
# 
cor(as.matrix(mantel)[,c(2,3,4)])