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

DF = load_appendix_highway_fatality_data()

# Part (a):
#
m = lm( FATAL ~ NOV, data=DF )

print(summary(m))
print(anova(m))

# Part (b):
#
m2 = lm( FATAL ~ NOV + I(NOV^2), data=DF )
print(coefficients(m2))

DF$NOVC = DF$NOV - mean(DF$NOV)
m2_centered = lm( FATAL ~ NOVC + I(NOVC^2), data=DF )
print(coefficients(m2_centered))

# Plot (c):
#
plot( m, which=1 )

# Lets plot some models to see how well they fit:
# 
plot( DF$NOV, DF$FATAL, type='p', xlab='NOV', ylab='FATAL' )
abline(m)
points( DF$NOV, m2$fitted.values, type='l' )
grid()