DF = data.frame(
    x=c( 10, 10, 20, 33, 33, 40, 40, 40, 47, 50 ),
    y=c( 6, 4, 11, 17, 19, 19, 21, 23, 20, 17 )
)

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

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

anova( m, m2 ) 

#postscript("../../WriteUp/Graphics/Chapter2/ex_2_28_plot.eps", onefile=FALSE, horizontal=FALSE)
plot( DF$x, DF$y, type='p', xlab='x', ylab='y', pch=19, cex=1.5 )
abline(m, col='blue')
points( DF$x, m2$fitted.values, type='l', col='purple' )
legend( 'topleft', c('linear fit', 'quadratic fit'), col=c('blue', 'purple'), lty=c(1, 1) )
grid()
#dev.off()