library(car)

save_figs = TRUE

# Get the data:
#
N = 6
X = matrix( data=c(  1, 999,  60, 150, 851,  80,
                    92, 910, 110, 903, 100, 130,
                   450, 554, 150,  75, 930, 175 ),
            nrow=N, ncol=3, byrow=TRUE )
DF = data.frame(X)
Y = 0:(N-1)
DF$Y = Y


# Drop X3:
#
DF$X3 = NULL
m = 2

C = cor(DF)

XTX = C[1:m, 1:m]
XTy = C[, m+1]
print(XTX)

m_full = lm( Y ~ ., data=DF )
print(summary(m_full))

print('Variance inflation factors:')
print(vif(m_full))

ES = eigen(XTX)
print('Eigenvalues')
print(ES$values)

#
# Compute the principal components (and a scatter plot of them):
#
DFs = scale(DF)
Z = as.matrix(DFs[, 1:m]) %*% ES$vectors
colnames(Z) = c('Z1', 'Z2')
print(summary(Z))

if( save_figs ){ postscript("../../WriteUp/Graphics/Chapter5/ex_5_14_scatter_plot_of_Z.eps", onefile=FALSE, horizontal=FALSE) }
pairs(Z, xlim=c(-3, +3), ylim=c(-3, +3))
if( save_figs ){ dev.off() }

# PC regression:
#
source('../../../Hastie/Code/Chapter3/pcr_wwx.R')
#source('http://www.waxworksmath.com/Authors/G_M/Hastie/Code/Chapter3/pcr_wwx.R')
res = pcr_wwx(DF, DF)

print(sprintf('Linear model with just one principle component:'))
R = regression_coefficients_given_pcr(DF$Y, res, M=1)
print(R[1, ])

print(sprintf('Linear model with just all principle components (duplicates LS results):'))
R = regression_coefficients_given_pcr(DF$Y, res, M=m)
print(R[1, ])