par(mfrow =c(1,1))

galton <- read.table("Galton.txt", header=TRUE)

father.son.dat <- galton[galton[,4]=="M",]

plot(father.son.dat$Father, father.son.dat$Height,
pch=17,col="blue", xlab = "Father", ylab = "Son",
main="Scatterplot of Father versus Son's Height")

m1 <- lm(father.son.dat$Height~father.son.dat$Father)
abline(m1,col="red",lty=2)
legend(62,78,legend="Least Squares Line",col="red",lty=2)

anova(m1)
MSE <- 5.88
x <- father.son.dat$Father
xseq <- father.son.dat$Father
yhat <- m1$coef[1] + m1$coef[2]*xseq
Sxx <- sum((x - mean(x))^2)
SYhhat <- sqrt(MSE*(1/50 + (xseq - mean(x))^2/Sxx))
W <- sqrt(2*qf(.95,2,nrow(father.son.dat)-2))
lwr.band <- yhat - W*SYhhat
upr.band <- yhat + W*SYhhat
m1 <- lm(father.son.dat$Height~father.son.dat$Father)
plot(father.son.dat$Father, father.son.dat$Height,
pch=17,col="blue", xlab = "Father", ylab = "Son",
main="Scatterplot of Father versus Son's Height")
abline(m1,col="red",lty=1)
lines(xseq,lwr.band,col="purple",lty=3)
lines(xseq,upr.band,col="purple",lty=3)
legend(62,78,legend=c("Least Squares Line",
                  "95% Conf. Bands"),
   col=c("red","purple"),
   lty=c(1,3))

Problem I: (20 Points). Be sure to show all work for full credit....