DF = data.frame(
    x=seq( 1, 5 ),
    y=c( 22.1, 17.3, 18.0, 22.8, 24.1 )
)

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

m_zero_intercept = lm( y ~ x - 1, data=DF )
summary(m_zero_intercept)

# Compare the two models:
#
print( anova( m_zero_intercept, m_full ) )

#postscript("../../WriteUp/Graphics/Chapter2/ex_2_23_plot.eps", onefile=FALSE, horizontal=FALSE)
plot( DF$x, DF$y, type='p', xlab='x', ylab='y', pch=19, cex=1.5 )
abline(m_full, col='blue')
abline(m_zero_intercept, col='purple')
legend( 'topleft', c('beta_0 + beta_1 x', 'beta_1 x'), col=c('blue', 'purple'), lty=c(1, 1) )
grid()
#dev.off()

# Compute REG/Total
Total = sum( ( DF$y - mean(DF$y) )^2 )
REG_zero_intercept = Total - sum( ( DF$y - m_zero_intercept$fitted.values )^2 ) # How can this be negative?
REG_full = Total - sum( ( DF$y - m_full$fitted.values )^2 )

cor( DF$y, m_zero_intercept$fitted.values )^2
cor( DF$y, m_full$fitted.values )^2