### R code for Section 8.3-2 and 8.3-3

## Example 8.3-2 on page 464
## read table 8.3-1 on page 464
data = read.table("table831.dat", head=T)
y = data[,1]
x = data[,2]
fit0 = lm(y~x)
summary(fit0)

# scatter plot and residual plot
par(mfrow=c(1,2))
plot(x,y,xlab="Temperature",ylab="Steam", main="Scatter Plot")
abline(fit0$coef[1],fit0$coef[2])
plot(fit0$fitted,fit0$residual,xlab="Fitted value",ylab="Residual", main="Residual Plot")
abline(0,0)

# plot residual versus lagged residuals
n = length(x)         # number of observations
r = fit0$residual     # residuals
par(mfrow=c(1,1))
plot(r[1:(n-1)], r[2:n], xlab="Lagged residual", ylab="Residual", main="Lagged Residual Plot")
temp = lm(r[2:n]~r[1:(n-1)])
abline(temp$coef[1],temp$coef[2])

# lag 1 autocorrelation
r1 = sum(r[1:(n-1)]*r[2:n])/sum(r^2)

# Durbin-Watson test
# need to install R package "lmtest" first, go to R menu "Packages" ==> "Install package(s)..."
library("lmtest")
dwtest(y~x)


## read data set "exercise832.dat"
data = read.table("exercise832.dat", head=T)
X = data$X
Y1 = data$Y1
Y2 = data$Y2
Y3 = data$Y3
X4 = data$X4
Y4 = data$Y4

## linear regression
fit1 = lm(Y1~X)
fit2 = lm(Y2~X)
fit3 = lm(Y3~X)
fit4 = lm(Y4~X4)

## scatter plots
par(mfrow=c(2,2))
plot(c(0,20), c(0,15), xlab="X", ylab="Y1", main="(a)", type="n")
points(X, Y1)
abline(fit1$coef[1], fit1$coef[2])
plot(c(0,20), c(0,15), xlab="X", ylab="Y2", main="(b)", type="n")
points(X, Y2)
abline(fit2$coef[1], fit2$coef[2])
plot(c(0,20), c(0,15), xlab="X", ylab="Y3", main="(c)", type="n")
points(X, Y3)
abline(fit3$coef[1], fit3$coef[2])
plot(c(0,20), c(0,15), xlab="X4", ylab="Y4", main="(d)", type="n")
points(X4,Y4)
abline(fit4$coef[1], fit4$coef[2])

## plot fitted results
par(mfrow=c(2,3))
for(i in 1:6) plot(fit1, i);

## Cook's distance
par(mfrow=c(2,2))
plot(fit1, 4, main="(a)")
plot(fit2, 4, main="(b)")
plot(fit3, 4, main="(c)")
plot(fit4, 4, main="(d)")

## calculate Cook's distance directly
cooks.distance(fit1)