Soilution to Problem 6.
======================

> cathed = read.table(file="cathed.txt")
  names(cathed) = c("Town","Style","Height","Length")
        ### 25 x 4: first col is factor of town names
> plot(cathed[,4], cathed[,3], type="n", xlab="Length (feet)",
    ylab="Height (feet)", main=
    "English Cathedral Heights vs Lengths, by Style")
  points(cathed[cathed[,2]==0,4],cathed[cathed[,2]==0,3], pch=5)
  points(cathed[cathed[,2]==1,4],cathed[cathed[,2]==1,3], pch=18)
  tm0 = lm(Height ~ Length, data=cathed[cathed[,2]==0,])$coef
  abline(tm0[1],tm0[2], lty=3)
  tm1 = lm(Height ~ Length, data=cathed[cathed[,2]==1,])$coef
  abline(tm1[1],tm1[2], lty=1)
  legend(locator(), legend=c("Romanesque","Gothic"),
       pch=c(5,18), lty=c(3,1))

## A slightly more detailed fit and plot (not needed for HW):

plot(cathed[,4], cathed[,3], type="n", xlab="Length (feet)",
    ylab="Height (feet)", main=
    "English Cathedral Heights vs Lengths, by Style")
  points(cathed[cathed[,2]==0,4],cathed[cathed[,2]==0,3], pch=5)
  points(cathed[cathed[,2]==1,4],cathed[cathed[,2]==1,3], pch=18)
  tm0 = lm(Height ~ Length + I(Length^2), data=cathed[cathed[,2]==0,])
  tm1 = lm(Height ~ Length, data=cathed[cathed[,2]==1,])
  ordR = order(cathed$Length[cathed$Style==0])
  ordG = order(cathed$Length[cathed$Style==1])
  lines(cathed$Length[cathed$Style==0][ordR],tm0$fit[ordR], lty=7)
  lines(cathed$Length[cathed$Style==1][ordG],tm1$fit[ordG], lty=2)
  legend(locator(),   legend=c("Roman. obs","Gothic obs","Roman. fit",
       "Gothic fit"),  pch=c(5,18,-1,-1), lty=c(0,0,7,2))