The article ??Use of Taguchi Methods and Multiple Regression Analysis for Optimal Process Development of High Energy Electron Beam Case Hardening of Cast Iron?? (M. Jean and Y. Tzeng, Surface Engineering, 2003:150??156) describes a factorial experiment designed to determine factors in a high-energy electron beam process that affect hardness in metals. Results for two factors, each with three levels, are presented in the following table. Factor A is the travel speed in mm/s, and factor B is accelerating voltage in volts. The outcome is Vickers hardness. There were six replications for each treatment. In the article, a total of seven factors were studied; the two presented here are those that were found to be the most significant.

a. Estimate all main effects and interactions.

b. Construct an ANOVA table. You may give ranges for the P-values.

c. Is the additive model plausible? Provide the value of the test statistic and the P-value.

d. Can the effect of travel speed on the hardness be described by interpreting the main effects of travel speed? If so, interpret the main effects, using multiple comparisons at the 5% level if necessary. If not, explain why not.

e. Can the effect of accelerating voltage on the hardness be described by interpreting the main effects of accelerating voltage? If so, interpret the main effects, using multiple comparisons at the 5% level if necessary. If not, explain why not.

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A B Hardness 10 10 875 896 921 686 642 613 10 25 712 719 698 621 632 645 10 50 568 546 559 757 723 734 20 10 876 835 868 812 796 772 20 25 889 876 849 768 706 615 20 50 756 732 723 681 723 712 30 10 901 926 893 856 832 841 30 25 789 801 776 845 827 831 30 50 792 786 775 706 675 568