Solution HW4 - Designed Experimentation Solutions for HW4...

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Unformatted text preview: Designed Experimentation Solutions for HW4 8-1 Suppose that in the chemical process development experiment in Problem 6-7, it was only possible to run a one-half fraction of the 2 4 design. Construct the design and perform the statistical analysis, using the data from replicate 1. The required design is a 2 4-1 with I=ABCD . A B C D=ABC-1-1-1-1 90 1-1-1 1 72-1 1-1 1 87 1 1-1-1 83-1-1 1 1 99 1-1 1-1 81-1 1 1-1 88 1 1 1 1 80 By observing the Pareto chart (below), we see that terms A, AB, AD are the most significant. We will include those in the model along with B and D to preserve hierarchy. Term Effect B D AC C AD AB A 25 20 15 10 5 22.58 Factor D Name A A B B C C D Pareto Chart of the Effects (response is C9, Alpha = .05) Lenth's PSE = 6 Factorial Fit: C9 versus A, B, D Estimated Effects and Coefficients for C9 (coded units) Term Effect Coef SE Coef T P Constant 85.000 1.458 58.31 0.000 A -12.000 -6.000 1.458 -4.12 0.054 B -1.000 -0.500 1.458 -0.34 0.764 D -1.000 -0.500 1.458 -0.34 0.764 A*B 6.000 3.000 1.458 2.06 0.176 A*D -5.000 -2.500 1.458 -1.71 0.228 S = 4.12311 R-Sq = 92.41% R-Sq(adj) = 73.44% Analysis of Variance for C9 (coded units) Source DF Seq SS Adj SS Adj MS F P Main Effects 3 292.00 292.00 97.33 5.73 0.152 2-Way Interactions 2 122.00 122.00 61.00 3.59 0.218 Residual Error 2 34.00 34.00 17.00 Total 7 448.00 Now, by observing that only factor A is statistically significant in the revised model (p~0.05), we remove the other terms and run the model another time. This is necessary especially since we see that the ANOVA for MEs and interactions (highlighted above) show that neither is statistically significant. Factorial Fit: C9 versus A Estimated Effects and Coefficients for C9 (coded units) Term Effect Coef SE Coef T P Constant 85.000 1.826 46.56 0.000 A -12.000 -6.000 1.826 -3.29 0.017 S = 5.16398 R-Sq = 64.29% R-Sq(adj) = 58.33% Analysis of Variance for C9 (coded units) Source DF Seq SS Adj SS Adj MS F P Main Effects 1 288.0 288.0 288.00 10.80 0.017 Residual Error 6 160.0 160.0 26.67 Pure Error 6 160.0 160.0 26.67 Total 7 448.0 Now we see that the final model with only factor A is statistically significant. After verification of NID(0, 2) residuals, the final regression model is y=85 6 (A). 8-2 Suppose that in Problem 6-15, only a one-half fraction of the 2...
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Solution HW4 - Designed Experimentation Solutions for HW4...

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