Consider Example 12.3. Displays a SAS printout of an analysis of the model containing variables x1, x2, and x3. Focus on the confidence interval of the mean response µY at the (x1, x2, x3) locations representing the 13 data points. Consider an item in the printout indicated by C.V. This is the coefficient of variation, which is defined by
C.V. = s/y • 100.
where s = √s2 is the root mean squared error. The coefficient of variation is often used as yet another criterion for comparing competing models. It is a scale-free quantity which expresses the estimate of a, namely s, as a percent of the average response y. In competition for the "best" among a group of competing models, one strives for the model with a "small" value of C.V. Do a regression analysis of the data set shown in Example 12.3 but eliminate x3. Compare the full (x1, x2, x3) model with the restricted model (x1.x2) and focus on two criteria: (i) C.V.; (ii) the widths of the confidence intervals on µY. For the second criterion you may want to use the average width. Comment.