fv <- read.table("florida-election-data1.txt")
gore <- fv[,2]
bush <- fv[,3]
buchanan <- fv[,4]

plot(bush,buchanan)
lm1 <- lm(buchanan ~ bush)
abline(lm1)
summary(lm1)

r1 <- lm1$residuals
plot(r1)
abline(0,0)

plot(log(bush),log(buchanan))
lm2 <- lm(log(buchanan) ~ log(bush))
abline(lm2)
summary(lm2)

r2 <- lm2$residuals
plot(r2)
abline(0,0)

resid=log(buchanan)+2.34149-0.73096*log(bush)
sigma=sqrt(sum(resid^2)/64)

%prediction interval

Y=log(3407)
Ystar=-2.34149+0.73096*log(152846)
Y-Ystar

Xstar=152846
sigma=0.4198
u=sum((log(bush)-log(152846))^2)
m=mean(log(bush))
l=sum(66*(log(bush)-m)^2)
Prestd=sqrt(u/l+1)*sigma

(Y-Ystar)/Prestd