Soluble dietary fiber (SDF) can provide health benefits by lowering blood cholesterol and glucose levels. The article “Effects of Twin-Screw Extrusion on Soluble Dietary Fiber and Physicochemical Properties of Soybean Residue” (Food Chemistry, 2013: 884–889) reported the following data on y 5 SDF content (%) in soybean residue and the three predictors x1 5 extrusion temperature (in C), x2 = feed moisture (in %), and x3 5 screw speed (in rpm) of a twin-screw extrusion process.
a. The authors fit the complete second-order model with predictors 1, 2, 3, 12 , 22 , 32 , 12, 13, and 23, which resulted in SSResid .215 and SSTo 16.798. Determine the corresponding values of R2 and adjusted R2 .
b. If we include in the model only the predictors 1, 2, and 3, the corresponding SSResid 11.428. Carry out a test at significance level .01 to decide whether at least one of the second-order predictors provides useful information about SDF content.