hw10ans - Statistics 500 Fall 2009 Solutions to Homework 10...

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Statistics 500 – Fall 2009 Solutions to Homework 10 1 1. Model selection practice --- My results are based on considering 4 possible X variables (X 1 , X 2 , X 3 , and X 4 ). From your e-mails, some of you created all possible interactions and all possible quadratics. That is also a reasonable thing to do. I know the results are not the same for C p because you’re starting with a different ‘full’ model. I don’t know whether AIC and BIC results differ. If you started with more X variables, your answers (if appropriate) should be marked correct, even if they differ from my answers. a) 4 2 1 33143 . 1 82934 . 0 29157 . 2 36234 . 1 ˆ X X X Y + + + = Note: You could also indicate just the variables going into the model for full credit. b) Yes, in this case we do. c) The models with smallest Cp are the ones that include: (1) x1, x2, x4, (2) x1,x2,x3, and (3) all four variables. No in Model C(p) R-Square AIC SBC Variables in Model 3 3.0184 0.8069 140.2875 147.93557 x1 x2 x4 3 3.0736 0.8067 140.3488 147.99686 x1 x2 x3 4 5.0000 0.8070 142.2670 151.82715 x1 x2 x3 x4 3 6.5302 0.7919 144.0432 151.69133 x2 x3 x4 d) Using AIC we choose the same three models as in (c). However, using SBC instead of selecting the model with all four variables we select the one with x2, x3 and x4. 2. Residential house price models --- There are many possible answers here. What you learn by doing this problem is way more important than the points you get for you. Full credit goes to anyone who identified a model by any reasonable method (C p , AIC or BIC), then evaluated diagnostics and reselected the model if major changes were made. If you look at diagnostics, you will probably notice house 108. You may notice other curiosities, such as a house with 4 bedrooms and 7 bathrooms (lots of teenagers?). To repeat the moral one last time: if I was being paid to analyze these data, I would spend a lot of time looking for and checking curiosities before spending a lot of time on modeling. I would definitely fit a preliminary model or two to help me identify curiosities. 3. Drug side effects --- ANCOVA My SAS code for all parts: data heart; infile 'heart.txt' firstobs = 2 ; input drug $ pre post; run ; proc glm ; class drug; model post = drug; lsmeans drug / stderr ; estimate 'Drug A - placebo (C)' drug 1 0 - 1 ; title 'ANOVA on post-trt values' ; run ; proc glm ; class drug; model post = pre drug;
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Statistics 500 – Fall 2009 Solutions to Homework 10 2 lsmeans drug / stderr ; estimate 'Drug A - placebo (C)' drug 1 0 - 1 ; title 'ANCOVA using pre-trt values' ; run ; proc glm ; class drug; model post = pre drug pre*drug; title 'Check interaction' ; run ; proc means ; class drug; var pre; title 'Pre treatment means for each drug'
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This note was uploaded on 02/11/2012 for the course STAT 500 taught by Professor Staff during the Fall '08 term at Iowa State.

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hw10ans - Statistics 500 Fall 2009 Solutions to Homework 10...

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