# Part (a):
#
N = 6
X = matrix( data=c(  1, 999,  60, 150, 851,  80,
                    92, 910, 110, 903, 100, 130,
                   450, 554, 150,  75, 930, 175 ),
            nrow=N, ncol=3, byrow=TRUE )
DF = data.frame(X)
Y = 0:(N-1)
DF$Y = Y

print( cor(DF) )

# Part (b):
#
null = lm( Y ~ 1, data=DF )
full = lm( Y ~ ., data=DF )

# Forward selection:
step( null, scope=list(lower=null, upper=full), direction="forward" )

# Now try the leaps package:
#
if( ! require("leaps") ){ install.packages("leaps") }
rss = regsubsets( Y~., data=DF )
print( summary( rss ))