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

DF = load_appendix_Indianapolis_500_data()

# Part (a)-(b):
#
m = lm( SPEED ~ YEAR, data=DF )
m2 = lm( SPEED ~ YEAR + I(YEAR^2), data=DF )
m3 = lm( SPEED ~ YEAR + I(YEAR^2) + I(YEAR^3), data=DF )

DF$YEARC = DF$YEAR - mean(DF$YEAR)
mc = lm( SPEED ~ YEARC, data=DF )
mc2 = lm( SPEED ~ YEARC + I(YEARC^2), data=DF )
mc3 = lm( SPEED ~ YEARC + I(YEARC^2) + I(YEARC^3), data=DF )

# Print the coefficients:
# 
print('Uncentered coefficients:')
print( rbind( c( coefficients(m), 0, 0 ), c( coefficients(m2), 0 ), coefficients(m3) ) )
print('Centered coefficients:')
print( rbind( c( coefficients(mc), 0, 0 ), c( coefficients(mc2), 0 ), coefficients(mc3) ) )

# Print the ANOVAs:
# 
print( anova( m, m2, m3 ) )
print( anova( mc, mc2, mc3 ) )