Table B. 12 presents data on a heat treating process used to carburize gears. The thickness of the carburized layer is a critical factor in overall reliability of this component. The response variable \(y=\) PITCH is the result of a carbon analysis on the gear pitch for a cross-sectioned part. Use all possible regressions and the \(C_{p}\) criterion to find an appropriate regression model for these data. Investigate model adequacy using residual plots.

Temp Soaktime Soakpct Difftime Diffpct Pitch 1650 0.58 1.10 0.25 0.90 0.013 1650 0.66 1.10 0.33 0.90 0.016 1650 0.66 1.10 0.33 0.90 0.015 1650 0.66 1.10. 0.33 0.95 0.016 1600 0.66 1.15 0.33 1.00 0.015 1600 0.66 1.15 0.33 1.00 0.016 1650 1.00 1.10 0.50 0.80 0.014 1650 1.17 1.10 0.58 0.80 0.021 1650 1.17 1.10 0.58 0.80 0.018 1650 1.17 1.10 0.58 0.80 0.019 1650 1.17 1.10 0.58 0.90 0.021 1650 1.17 1.10 0.58 0.90 0.019 1650 1.17 1.15 0.58 0.90 0.021 1650 1.20 1.15 1.10 0.80 0.025 1650 2.00 1.15 1.00 0.80 0.025 1650 2.00 1.10 1.10 0.80 0.026 1650 2.20 1.10 1.10 0.80 0.024 1650 2.20 1.10 1.10 0.80 0.025 1650 2.20 1.15 1.10 0.80 0.024 1650 2.20 1.10 1.10 0.90 0.025 1650 2.20 1.10 1.10 0.90 0.027 1650 2.20 1.10 1.50 0.90 0.026 1650 3.00 1.15 1.50 0.80 0.029 1650 3.00 1.10 1.50 0.70 0.030 1650 3.00 1.10 1.50 0.75 0.028 1650 3.00 1.15 1.66 0.85 0.032 1650 3.33 1.10 1.50 0.80 0.033 1700 4.00 1.10 1.50 0.70 0.039 1650 4.00 1.10 1.50 0.70 0.040 1650 4.00 1.15 1.50 0.85 0.035 1700 12.50 1.00 1.50 0.70 0.056 1700 18.50 1.00 1.50 0.70 0.068