The article “Response Surface Methodology for Protein Extraction Optimization of Red Pepper Seed” (Food Sci. and Tech., 2010: 226–231) gave data on the response variable and the independent variables and .

a. Fitting the model with the four xi

’s as predictors gave the following output:

Predictor Coef SE Coef T P Constant 4.586 2.542 1.80 0.084 x1 0.01317 0.02707 0.49 0.631 x2 1.6350 0.2707 6.04 0.000 x3 0.02883 0.01353 2.13 0.044 x4 0.05400 0.02707 1.99 0.058 Source DF SS MS F P Regression 4 19.8882 4.9721 11.31 0.000 Residual Error 24 10.5513 0.4396 Total 28 30.4395 x 4 5 solvent/meal ratio temperature (8C), x 2 5 pH, x 3 5 extraction time ( min ), x y 5 protein yield (%) 1 5 n 5 13 SST 5 2715.76 x x 3 5 % 4 5 %

x x 1 5 % 2 5 %

y 5 cumulative k (k 5 1, 2, 3, 4 Calculate and interpret the values of R2 and adjusted R2 .
Does the model appear to be useful?

b. Fitting the complete second-order model gave the following results:

Does at least one of the second-order predictors appear to be useful? Carry out an appropriate test of hypotheses.

c. From the output in (b), a reasonable conjecture is that none of the predictors involving x1 are providing useful information. When these predictors are eliminated, the value of SSE for the reduced regression model is 1.1887.
Does this support the conjecture?

d. Here is output from Minitab’s best subsets option, with just the single best subset of each size identified. Which model(s) would you consider using (subject to checking model adequacy)?