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

DF = load_appendix_refinery_data()

# Part (a):
#
m = lm( WATER ~ PROD, data=DF )

# Lets plot the data and models:
#
#postscript("../../WriteUp/Graphics/Chapter3/ex_3_3_part_a.eps", onefile=FALSE, horizontal=FALSE)
par(mfrow=c(1,2))
plot( DF$PROD, DF$WATER, type='p', pch=19, cex=1.5, xlab='WATER', ylab='PROD' )
abline(m, col='red')
grid()
plot( DF$PROD, m$residuals, type='p', pch=19, cex=1.5, xlab='PROD', ylab='residuals' )
grid()
par(mfrow=c(1,1))
#dev.off()


# Part (b):
#

# Build the two models suggested:
#
m_no_intercept = lm( WATER ~ PROD - 1, data=DF )

DF$WATER_OVER_PROD = DF$WATER / DF$PROD
m_water_over_prod = lm( WATER_OVER_PROD ~ 1, data=DF )

# Plot the variance as a function of WATER for each model:
#
#postscript("../../WriteUp/Graphics/Chapter3/ex_3_3_part_b.eps", onefile=FALSE, horizontal=FALSE)
par(mfrow=c(1,2))
plot( DF$PROD, m_no_intercept$residuals, type='p', pch=19, cex=1.5, xlab='PROD', ylab='residuals', main='WATER = beta_1 PROD' )
grid()
plot( DF$PROD, m_water_over_prod$residuals, type='p', pch=19, cex=1.5, xlab='PROD', ylab='residuals', main='WATER/PROD = beta_0' )
grid()
par(mfrow=c(1,1))
#dev.off()

coefficients(m_no_intercept)
coefficients(m_water_over_prod)


# Part (c):
#
DF$CAP_OVER_PROD = DF$CAP / DF$PROD

DF$ratio_difference = DF$WATER_OVER_PROD - DF$CAP_OVER_PROD
m_ratio_difference = lm( ratio_difference ~ 1, data=DF )

#postscript("../../WriteUp/Graphics/Chapter3/ex_3_3_part_c.eps", onefile=FALSE, horizontal=FALSE)
plot( DF$PROD, m_ratio_difference$residuals, type='p', pch=19, cex=1.5, xlab='PROD', ylab='residuals' )
grid()
#dev.off()