Reconsider the heat treating data in Exercises 12-10 and 12-24, where we fit a model to PITCH using regressors x1 = SOAKTIME SOAKPCT and x2 = DIFFTIME DIFFPCT.
(a) Using the model with regressors x1 and x2, find a 95% confidence interval on mean PITCH when SOAKTIME 1.00, SOAKPCT  1.10, DIFFTIME  1.00, and DIFFPCT = 0.80.
(b) Compare the length of this confidence interval with the length of the confidence interval on mean PITCH at the same point from Exercise 12-33 part (b), where an additive model in SOAKTIME, SOAKPCT, DIFFTIME, and DIFFPCT was used. Which confidence interval is shorter? Does this tell you anything about which model is preferable?