# Part (a):
#
DF = data.frame(
    x=seq( 1, 5 ),
    y=c( 5.1, 2.2, 0.9, 1.9, 5.2 )
)

# Build some linear models:
#
m0 = lm( y ~ 1, data=DF )
summary(m0)

m1 = lm( y ~ x, data=DF )
summary(m1)

m2 = lm( y ~ x + I(x^2), data=DF )
summary(m2)

# Compare the models sequentially using the anova command:
#
anova( m0, m1, m2 )

# Lets plot the data and models:
#
#postscript("../../WriteUp/Graphics/Chapter2/ex_2_21_part_a.eps", onefile=FALSE, horizontal=FALSE)
plot( DF$x, DF$y, type='p', pch=19, cex=1.5, xlab='x', ylab='y' )
abline(m0, col='blue')
abline(m1, col='red')
points( DF$x, m2$fitted, type='l', col='green')
grid()
#dev.off()


# Part (b):
#
DF = data.frame(
    x = seq( 1, 10 ),
    y = c( 15.5, 11.0, 13.5, 18.0, 24.5, 28.0, 32.0, 40.0, 43.0, 44.0 )
)

m0 = lm( y ~ 1, data=DF )
m1 = lm( y ~ x, data=DF )
m2 = lm( y ~ x + I(x^2), data=DF )
m3 = lm( y ~ x + I(x^2) + I(x^3), data=DF )
anova( m0, m1, m2, m3 )

# Lets plot the data and models:
#
#postscript("../../WriteUp/Graphics/Chapter2/ex_2_21_part_b.eps", onefile=FALSE, horizontal=FALSE)
plot( DF$x, DF$y, type='p', pch=19, cex=1.5, xlab='x', ylab='y' )
abline(m1, col='blue')
points( DF$x, m2$fitted, type='l', col='green')
points( DF$x, m3$fitted, type='l', col='red')
grid()
#dev.off()