library(car)

save_figs = FALSE

source('../../Data/data_loaders.R')
DF = load_appendix_bodyfat_data()

#pairs(DF)
scatterplotMatrix(DF)

print(summary(DF))

m = lm(FAT ~ ., data=DF)
print(summary(m))

if( save_figs ){ postscript("../../WriteUp/Graphics/Chapter5/ex_5_4_residuals_vs_fitted.eps", onefile=FALSE, horizontal=FALSE) }
plot(m, which=1)
if( save_figs ){ dev.off() }

if( save_figs ){ postscript("../../WriteUp/Graphics/Chapter5/ex_5_4_qq_plot.eps", onefile=FALSE, horizontal=FALSE) }
plot(m, which=2)
if( save_figs ){ dev.off() }

# The added variable plots:
#
if( save_figs ){ postscript("../../WriteUp/Graphics/Chapter5/ex_5_4_av_plots.eps", onefile=FALSE, horizontal=FALSE) }
avPlots(m )
if( save_figs ){ dev.off() }

XTX = cor(DF) # Duplicates the numbers in Table 5.1
print(XTX) # notice no r_ij > 0.95
print(vif(m)) # gives the VIFs near the middle of Page 168 all of which are larger than the heuristic of 10

ES = eigen(XTX[ 1:3, 1:3 ])
print('Eigenvalues:')
print(ES$values) # one eigenvalue is less than 0.05