The article “Response Surface Methodology for Protein Extraction Optimization of Red Pep...

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

a. Fitting the model with the four x_i’s as predictors gave the following output:

Calculate and interpret the values of R² and adjusted R^2. 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)?