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 y protein yield (%) and the independent variables 1 temperature (°C), 2 pH, 3 extraction time (min), and 4 solvent/meal ratio.
a. Fitting the model with the four i ’s as predictors yielded the following output: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 part (b), we conjecture that none of the predictors involving 1 are providing useful information. When these predictors were eliminated, the value of SSResid 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)?