source('../../Data/data_loaders.R')

DF = load_exercise_3_4_data()

# Part (a):
#
m1 = lm( Y ~ X, data=DF )

#postscript("../../WriteUp/Graphics/Chapter3/ex_3_4_part_a.eps", onefile=FALSE, horizontal=FALSE)
par(mfrow=c(1,2))
plot( DF$X, DF$Y, type='p', pch=19, cex=1.5, xlab='X', ylab='Y' )
abline(m1, col='red')
grid()
plot(m1, which=1)
par(mfrow=c(1,1))
#dev.off()

m2 = lm( Y ~ X + I(X^2), data=DF )
anova( m1, m2 )

#postscript("../../WriteUp/Graphics/Chapter3/ex_3_4_part_a_linear_N_quadratic.eps", onefile=FALSE, horizontal=FALSE)
par(mfrow=c(1,2))
plot( DF$Y, m1$residuals, type='p', pch=19, cex=1.5, xlab='Y', ylab='residuals', main='linear fit' )
grid()
plot( DF$Y, m2$residuals, type='p', pch=19, cex=1.5, xlab='Y', ylab='residuals', main='quadratic fit' )
grid()
par(mfrow=c(1,1))
#dev.off()


# Part (b):
#
DF$Y_OVER_X = DF$Y / DF$X
m_y_over_x = lm( Y_OVER_X ~ X, data=DF )

plot( DF$Y, m_y_over_x$residuals, type='p', pch=19, cex=1.5, xlab='Y', ylab='residuals', main='y/x fit' )
grid()


# Part (c):
#
predict( m1, newdata=data.frame( X=c( 1 ) ), interval='prediction' )
1 * predict( m_y_over_x, newdata=data.frame( X=c( 1 ) ), interval='prediction' )


# Part (d):
#
summary(m1)$r.squared
summary(m_y_over_x)$r.squared