A small experiment was conducted to fit a multiple regression equation relating the yield y to… 1 answer below »

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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

−1

−1

−1

5.5

1

−1

−1

9.2

−1

1

−1

10.3

−1

−1

1

11.6

1

1

−1

11.1

1

−1

1

10.2

−1

1

1

14

1

1

1

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

μY |x1,x2,x3 = β0 + β1×1 + β2×2 + β3×3.

(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.

 
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