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Unformatted text preview: Stat 201A HW6 Solution 1. (a) The inner array is a 2 5- 2 fractional factorial design with a defining relation of I =- ACD =- BCE = ABDE . The outer array is a 2 3- 1 fractional factorial design with a defining relation of I =- F GH . Both arrays have resolution III. (b) A =- CD , B =- CE , C =- AD =- BE , D =- AC , E =- BC , AB = DE , AE = BD . (c) We can estimate 5 main effects and 2 two-factor interactions using 8 runs. The half- normal plots for the mean model (using y ) and variance model (using ln ( s 2 )) are 0.0 1.0 2.0 40 80 Mean Model half normal quantiles absolute effects E A C 0.0 1.0 2.0 1.4 1.6 Variance Model half normal quantiles absolute effects A:B A E Factors A, C, and E are significant for the mean model. For the variance model, E is most significant, followed by A and AB. However, it is not clear whether they are significant as all the points are close to a straight line. Further note that AB=DE, we cannot distinguish AB and DE. So I conclude that none effect is significant for the variance model. The mean model is y = 197 . 125- 27 . 500 A...
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- Spring '10