hw4 - Problem 6-1. (a) Estimate the factor effects. Which...

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Unformatted text preview: Problem 6-1. (a) Estimate the factor effects. Which effects appear to be large? Using Minitab we obtain the following table: Estimated Effects and Coefficients for Response (coded units) Term Effect Coef StDev Coef T P Constant 40,833 1,121 36,42 0,000 A 0,333 0,167 1,121 0,15 0,884 B 11,333 5,667 1,121 5,05 0,000 C 6,833 3,417 1,121 3,05 0,008 A*B -1,667 -0,833 1,121 -0,74 0,468 A*C -8,833 -4,417 1,121 -3,94 0,001 B*C -2,833 -1,417 1,121 -1,26 0,224 A*B*C -2,167 -1,083 1,121 -0,97 0,348 The plot for the main effects: C B A 1- 1 1-1 1- 1 47 44 41 38 35 Response Main Effects Plot (data means) for Response The effect of factor A is almost zero, but factor B and C both have positive large effects. The plot for the interaction effects: 1-1 1-1 50 40 30 50 40 30 A B C 1-1 1-1 Interaction Plot (data means) for Response The effect of the interaction AC is significant, the effects of the other interactions are inessential. b). Use the analysis of variances to confirm your conclusion for part a). Using Minitab (ANOVA->General Linear Model) we get the following table: General Linear Model Factor Type Levels Values A fixed 2 -1 1 B fixed 2 -1 1 C fixed 2 -1 1 Analysis of Variance for Response, using Adjusted SS for Tests Source DF Seq SS Adj SS Adj MS F P A 1 0,67 0,67 0,67 0,02 0,884 B 1 770,67 770,67 770,67 25,55 0,000 C 1 280,17 280,17 280,17 9,29 0,008 A*B 1 16,67 16,67 16,67 0,55 0,468 B*C 1 48,17 48,17 48,17 1,60 0,224 A*C 1 468,17 468,17 468,17 15,52 0,001 A*B*C 1 28,17 28,17 28,17 0,93 0,348 Error 16 482,67 482,67 30,17 Total 23 2095,33 The P-values for factors B,C and interaction AC are less than level of significance 5%. Thus, the factors B and C significantly affect the life of a machine tool. Moreover, there is a significant interaction between factors A and C....
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hw4 - Problem 6-1. (a) Estimate the factor effects. Which...

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