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Unformatted text preview: Stat 201A HW5 Solution 1. (a) The correlation between A and DF is 0.5. Main effect A is partially aliased with 16 2-factor interactions (2fis) which form 4 groups: BC = DG = EF = HK, BF = CE = DK = GH, BG = CD = EK = F H, BK = CH = DF = EG The correlation between A and the group of BG is- . 5 while the correlation between A and other groups is 0 . 5. A is not aliased with other 3 groups: BD = CG = EH = F K, BE = CF = DH = GK, BH = CK = DE = F G (b) The main effects analysis suggests D and C are important and followed by F, E, H . But the residuals plot reveals the model is not adequate. Since A and DF is not fully aliased, it is possible to include them in the same model. In the analysis, we can include all 9 main effects plus 6 2fis. We can include one 2fi from the 3 groups that are not aliased with A , say BD, BE, BH . For the 4 groups that are partially aliased with A , we can include at most 3 2fis from the 4 groups. Of course, we dont know which to include and have to do variable selections here. There are many procedures. I apply the Dantzig selector to a model with 9 main effects and 7 2fis ( BC, BD, BE, BF , BG, BH, BK ). By inspecting the profile plot, I conclude C, D, E, F, H, BG = CD, BH = DE, BK = DF are important (using = 20). As we are interested in testing whether A is negligible, I include A in the model, the summary is Estimate Std. Error t value Pr(>|t|)Estimate Std....
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