<p> This example can be solved partly with StatPro and partly with Excel’s built-in functions. The end results appear in Figure 12.30. We first use StatPro’s multiple regression procedure to obtain the usual regression output for sales as a function of promotional expenses. (We could use the simple regression option, but it is just as easy to use multiple regression, even when there is a single explanatory variable.) We then calculate the point predictions and prediction intervals in rows 23–27 (for individual values) and rows 31–35 (for means). To calculate any point prediction in column H, we substitute the given promotional expense into the regression equation. For example, the formula in cell H23, which is then copied down, is =$G$18+$G$19*G23 The more difficult part is calculating the standard errors of prediction from equations (12.5) and (12.6). Fortunately, Excel has a built-in function, DEVSQ, for calculating the sum of squared deviations of the X’s around their mean—the sum in the denominator of each equation. In addition, the standard error of estimate has already been calculated in cell G9 by StatPro. Therefore, we can implement equations (12.5) and (12.6) in cells I23 and I31 with the formulas =$G$9*SQRT(1+1/50+(G23-AVERAGE($B$4:$B$53))^2/DEVSQ($B$4:$B$53)) and =$G$9*SQRT(1/50+(G31-AVERAGE($B$4:$B$53))^2/DEVSQ($B$4:$B$53)) (The trick is to get the parentheses correct!) Each of these formulas is then copied down. Finally, the lower and upper limits of the prediction intervals are found in the usual way, by subtracting and adding a t-multiple of the appropriate standard error to the point prediction. This t-multiple is found from the Excel function TINV(0.05,48), which evaluates to approximately 2.</p>