Regression -Assignment 6

The goal here is to do model selection anddiagnostics on the Cravens data. Therules here are the same as the other assignments.

You’regoing to first run a forward selection so everything is entered, and then abackward elimination so everything is removed. You will be asked to do the stopping, not the computer. To do this in Minitab, set alpha-to-enter to1 in the forward selection, and set it to 0 in the backward elimination.  If you’re using another program, setF-to-enter and F-to-remove so that everything comes in on forward selection andeverything is removed on backward elimination.

1. Inthe forward selection, suppose you keep the model in which all the variablesare significant at the 0.05 level. Which model would be chosen? Give a summary of the selection procedure to the point.  For the chosen model, what are theR-squared, F-test (show the ANOVA table),and what is the estimated model? [OUTPUT].

2. Repeatquestion 1 for the backward elimination procedure. [OUTPUT]

3. Themethods in questions 1 and 2 do not yield the same model. Briefly explain thereason for the difference for this particular data set; that is, whichvariables are causing the discrepancy and why are they causing this problem?  Show any output you have that helps supportyour claims. [OUTPUT]

4. Usingbest subset regression, which model would be selected based on Mallow’s C_pmethod? For the chosen model, what are the R-squared, F-test  (show the ANOVA table), and what is theestimated model? [OUPUT]

5. Withjustification, which model would you choose as the best model?

6. Forthe model selected in 5, run a complete set of diagnostics and state yourconclusions. [OUTPUT]