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
plot(x,y)

plot(x,y,pch=19)

plot(x,y,pch=19,xlab='Age',ylab='Shear Strength')

(xmean<-mean(x))
(ymean<-mean(y))

abline(v=xmean,h=ymean,lty=2)
dev.copy2pdf(file='RocketPropPlot.pdf',paper='USr',width=11,height=9)

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

fit.RP<-lm(y~x)
summary(fit.RP)

coef(fit.RP)
abline(coef(fit.RP),col='red')
title('Line of best fit for Rocket Propulsion Data')

############################################
#Using the matrix formulae

X<-cbind(rep(1,n),x)

(XtX<-t(X)%*%X)

Xty<-t(X) %*% y

(beta.hat<-solve(XtX,Xty))

############################################
#New material

plot(x[1:12],y[1:12],pch=19,xlab='Age',ylab='Shear Strength')
fit.RP2<-lm(y[1:12]~x[1:12])
summary(fit.RP2)

fit.RP<-lm(Strength~Age,data=RocketProp)

fit.RP0<-lm(Strength~Age-1,data=RocketProp)

plot(x,y,pch=19,xlab='Age',ylab='Shear Strength')
coef(fit.RP0)
abline(coef(fit.RP0),0)

fit.RP2<-lm(Strength~Age,subset=(i >= 1 & i <= 12),data=RocketProp)

fit.RP3<-lm(Strength~I(Age-1),subset=(i >= 1 & i <= 12),data=RocketProp)

fit.RP4<-lm(Strength~log(Age),data=RocketProp)

plot(log(x),y,pch=19,xlab='log(Age)',ylab='Shear Strength')
abline(coef(fit.RP4))
abline(coef(fit.RP4),col='white')

fit.RP5<-lm(Strength~Age^2,data=RocketProp)

plot(x^2,y,pch=19,xlab='Age squared',ylab='Shear Strength')
abline(coef(fit.RP5))

############################################