# This program illustrate partial/overal F-tests stat and
# the effect of multicollinearity
# cf. Table 7.1--7.8. in NKNW

# Load the data  (Body Fat Example, P 261)
t<-matrix(scan("CH07TA01.DAT"),ncol=4,byrow=T)

bfat <-data.frame(y=t[,4],x1=t[,1],x2=t[,2],x3=t[,3])
attach(bfat)

# Prelim plots and correlation matrix calc
windows()
pairs(bfat,main="Scatter plot matrix of y, x1, x2, x3")
cor(bfat)

# Regress Y on X1, X2, X1 and X2 respectively

m1<-lm(y~x1);m1s<-summary(m1);m1s;anova(m1);
m2<-lm(y~x2);m2s<-summary(m2);m2s;anova(m2);
m12<-lm(y~x1+x2);m12s<-summary(m12);m12s;anova(m12);
m123<-lm(y~x1+x2+x3);m123s<-summary(m123);m123s;anova(m123);

#
m1$fitted.values
m2$fitted.values
m12$fitted.values
m123$fitted.values

m1$coef; m1s$cov.unscaled
m2$coef; m2s$cov.unscaled
m12$coef; m12s$cov.unscaled
m123$coef; m123s$cov.unscaled


detach(bfat)

# Standardized Version
stbfat <-data.frame(y=scale(t[,4]),x1=scale(t[,1]),x2=scale(t[,2]),x3=scale(t[,3]))
attach(stbfat)
# Prelim plots and correlation matrix calc
windows()
pairs(stbfat,main="Scatter plot matrix of y, x1, x2, x3")
cor(stbfat)