Solution HW4

# Solution HW4 - Designed Experimentation Solutions for HW4...

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 ME’s 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, σ 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...
View Full Document

## This note was uploaded on 08/27/2011 for the course EIN 4905 taught by Professor Staff during the Spring '08 term at University of Florida.

### Page1 / 10

Solution HW4 - Designed Experimentation Solutions for HW4...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online