12.64 A small experiment was conducted to fit a multiple regression equation relating the yield y to temperature x1 , reaction time x2 , and concentration of one of the reactants x3 . Two levels of each variable were chosen, and measurements corresponding to the coded independent variables were recorded as follows:

y x1 x2 x3 7.6 5.5 9.2 10.3 11.6 11.1 10.2 14.0

−1 1

−1

−1 11

−1 1

−1

−1 1

−1 1

−1 11

−1

−1

−1 1

−1 111

(a) Using the coded variables, estimate the multiple linear regression equation

μY |x1 ,x2 ,x3 = β0 + β1x1 + β2x2 + β3x3 .

(b) Partition SSR, the regression sum of squares, into three single-degree-of-freedom components attributable to x1 , x2, and x3 , respectively. Show an analysis-of-variance table, indicating significance tests on each variable. Comment on the results.