data.source.root<-"http://www.math.mcgill.ca/dstephens/Regression/Data/"

file1<-paste(data.source.root,'bloodtype.csv',sep='')
Blood<-read.csv(file=file1)
names(Blood)

x<-Blood$AB.Conc
y<-Blood$WickingLength

plot(x,y,pch=19,xlab='Conc',ylab='Wicking Length (mm)',ylim=range(0,25))

#Fit the simple linear regression using lm

fit.Blood<-lm(y~x)
summary(fit.Blood)
abline(coef(fit.Blood),col='red',lwd=2)
title('Line of best fit')
#dev.copy2eps(file='Ex1-Blood.eps',width=11,height=9)

plot(x,log(y),pch=19,xlab='Conc',ylab='log(Wicking Length (mm))',ylim=range(2,4))
fit.Blood2<-lm(log(y)~x)
summary(fit.Blood2)
abline(coef(fit.Blood2),col='red')
title('Line of best fit (logged response)')


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

file2<-paste(data.source.root,'liquid.csv',sep='')
Liquid<-read.csv(file=file2)
names(Liquid)

x<-Liquid$TIME
y<-Liquid$MASS

plot(x,y,pch=19,xlab='Time (min)',ylab='Mass (lbs)')
#dev.copy2eps(file='Ex1-Liquid-Data.eps',width=11,height=9)

#Fit the simple linear regression using lm

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

#Fit a quadratic regression using lm

fit.Liquid2<-lm(y~x+I(x^2))
summary(fit.Liquid2)


plot(x,y,pch=19,xlab='Time (min)',ylab='Mass (lbs)')
dev.copy2eps(file='Ex1-Liquid-Fits.eps',width=11,height=9)
abline(coef(fit.Liquid),col='red',lwd=2)
title('Lines of best fit')
yhat<-predict(fit.Liquid2)
lines(x,yhat,col='blue',lwd=2)
legend(40,5,c('Straight Line', 'Quadratic'),col=c('red','blue'),lty=1,lwd=2)
#dev.copy2eps(file='Ex1-Liquid-Fit.eps',width=11,height=9)

newx<-data.frame(x=25)
(y25.1<-predict(fit.Liquid,newdata=newx))
(y25.2<-predict(fit.Liquid2,newdata=newx))
points(25,y25.1,pch=3,col='green',lwd=2)
points(25,y25.2,pch=3,col='cyan',lwd=2)
abline(v=25,lty=2)

e1<-residuals(fit.Liquid)
e2<-residuals(fit.Liquid2)
sum(e1)
sum(e2)
par(mfrow=c(1,2))
plot(x,residuals(fit.Liquid),pch=19,ylim=range(-2,2),xlab='Time',ylab='Residuals');abline(h=0,lty=2)
title('Residuals from straight line fit')
plot(x,residuals(fit.Liquid2),pch=19,ylim=range(-2,2),xlab='Time',ylab='Residuals');abline(h=0,lty=2)
title('Residuals from quadratic fit')
#dev.copy2eps(file='Ex1-Liquid-Resids.eps',width=11,height=9)
dev.off()

##########################################################################
file3<-paste(data.source.root,'brainpain.csv',sep='')
Brain<-read.csv(file=file3)
names(Brain)

x<-Brain$EMPATHY
y<-Brain$ACTIVITY

plot(x,y,pch=19,xlab='Empathy Score',ylab='Brain Activity')

#Fit the simple linear regression using lm

fit.Brain<-lm(y~x)
summary(fit.Brain)
abline(coef(fit.Brain),col='red')
title('Brain data: Line of best fit')
#dev.copy2eps(file='Ex1-Brain-Fit.eps',width=11,height=9)

ei<-residuals(fit.Brain)
yhat<-fitted(fit.Brain)
par(mfrow=c(1,2))
plot(x,ei,pch=19,ylim=range(-0.5,0.5),xlab='Empathy level',ylab='Residuals');abline(h=0,lty=2)
title('Residuals from straight line fit')
plot(yhat,ei,pch=19,ylim=range(-0.5,0.5),xlab='Fitted value',ylab='Residuals');abline(h=0,lty=2)
#dev.copy2eps(file='Ex1-Brain-Resids.eps',width=11,height=9)
dev.off()

##########################################################################
file4<-paste(data.source.root,'casino.csv',sep='')
Casino<-read.csv(file=file4)
names(Casino)

x<-Casino$EMPLOYEES
y<-Casino$CRIMERAT

plot(x,y,pch=19,xlab='Number of Employees',ylab='Crime rate (per 1000)')

#Fit the simple linear regression using lm

fit.Casino<-lm(y~x)
summary(fit.Casino)
abline(coef(fit.Casino),col='red',lwd=2)
title('Casino data: Line of best fit')
#dev.copy2eps(file='Ex1-Casino-Fit.eps',width=11,height=9)

#Compute the sample correlation
cor(x,y)