DSC 410/510 - Multivariate Statistical Methods

Assignment 12 (deadline: 4pm on Wednesday, November 10)

Practical matters

Illustrative Example from p314-321:

• Reproduce the analysis described in the book with the help of the "Illustrative Example from p314-321" handout. This provides guidance on using SAS to run logistic regression analyses on the hatco data (available in the "hatco.xls" spreadsheet on the data page).
• The procedure performs a stepwise analysis in which first X₇ enters the model, then X₃, then X₅. However, when X₅ enters the model the regression coefficients become unstable so that it is actually better to then remove X₅.
• Investigate the (X₇, X₃, X₅) three-predictor model further. (To fit this model in SAS just select these three variables in the main dialog and change "selection method" from "stepwise" to "full model.") Send an e-mail to ipardoe at lcbmail.uoregon.edu with a brief discussion (two or three sentences) of how we know there are problems with the three-predictor model and why it is better to remove X₅ from the final model.
• Hints:
  • The "Likelihood Ratio" part of the "Testing Global Null Hypothesis: BETA=0" table refers to a simultaneous null hypothesis equivalent to "none of X₇, X₃, or X₅ help me to predict whether X₁₁ is 0 or 1" - can we reject this null hypothesis? (Remember: reject a null hypothesis if the p-value is small enough; the p-value is given in the right-hand column of the table.)
  • The right-hand column of the "Analysis of Maximum Likelihood Estimates" table provides individual p-values for each variable that test null hypotheses like "this variable does not help me to predict whether X₁₁ is 0 or 1, after I've already accounted for the other two variables" - can we reject the null hypotheses for each of the three variables?
  • Although this may appear at first sight to lead to a contradiction, it is not. Explaining why it is not a contradiction will help you to answer the question.
  • It may also help to compare the three-predictor model results with the results for the model with just X₇ and X₃.

This assignment is worth 15 points rather than the usual 10.

Review questions

We may discuss some of the following questions in class on Thursday November 11. I will also provide suggested solutions to allow you to check your answers.

• Page 322: questions 2, 6, 9, and 10.