data.source<-"http://www.math.mcgill.ca/dstephens/Regression/Data/2-1-RocketProp.csv"
RocketProp<-read.csv(file=data.source)
names(RocketProp)<-c('i','Strength','Age')
x<-RocketProp$Age
y<-RocketProp$Strength

############################################
#Fit the simple linear regression using lm

fit.RP<-lm(y~x)

RP.resids<-residuals(fit.RP)
RP.fitted<-fitted(fit.RP)

#Sum of residuals
sum(RP.resids)

#Sum of x times residuals
sum(x*RP.resids)
t(x) %*% RP.resids

#Sum of fitted values times residuals
sum(RP.fitted*RP.resids)
t(RP.fitted) %*% RP.resids


#Sum of y values times residuals
sum(y*RP.resids)
t(y) %*% RP.resids
##Non-zero !!

#par(mfrow=c(2,1))
plot(x,RP.resids,xlab='x',ylab='Residuals',pch=19,ylim=range(-250,250));abline(h=0,lty=2)
title('Residuals vs X (Age)')
plot(RP.fitted,RP.resids,xlab=expression(hat(y)),ylab='Residuals',
pch=19,ylim=range(-250,250));abline(h=0,lty=2)
title('Residuals vs Fitted values')
#dev.copy2pdf(file='RocketProp-Resids.pdf',width=9,height=11)