15.39 A molding machine that contains different cavi- ties is used in producing plastic parts. The product char- acteristics of interest are the product length (in.) and weight (g). The mold cavities were filled with raw mate- rial powder and then vibrated during the experiment. The factors that were varied were the vibration time (seconds), the vibration pressure (psi), the vibration amplitude (%), the raw material density (g/mL), and the quantity of raw material (scoops). The experiment was conducted in two different cavities on the molding machine. The data are stored in Molding . (Data extracted from M. Lopez and M. McShane-Vaughn, "Maximizing Product, Minimize ing Costs," Six Sigma Forum Magazine, February 2008, pp. 18-23.) a. Develop the most appropriate multiple regression model to predict the product length in cavity 1. Be sure to per- form a thorough residual analysis. In addition, provide a detailed explanation of your results. b. Repeat (a) for cavity 2. c. Compare the results for length in the two cavities. d. Develop the most appropriate multiple regression model to predict the product weight in cavity 1. Be sure to per- form a thorough residual analysis. In addition, provide a detailed explanation of your results. e. Repeat (d) for cavity 2. f. Compare the results for weight in the two cavities