Data given in Appendix D, Table 15 for 50 U.S. oil refineries, show the monthly totals of gallons of water used (WATER) and the number of barrels of crude oil processed (PROD). Also shown is the capacity (CAP) of the cooling towers. (The data have been coded since it is proprietary.)

a. Fit the linear model for regressing WATER on PROD. Examine the plot of the observed and predicted values against PROD. Also examine the residual plot and note the apparent problem with variance homogeneity.

b. Fit the linear model as in part

(a) forcing the intercept to be zero. Compare that model with the model WATER/PROD constant. Compare parameter estimates, prediction intervals and variance homogeneity. Use the results on weighted least squares Fit the model WATER/PROD constant + CAP/PROD and examine the results with regard to satisfaction of the model assumptions.