Homework 4 Due: Thursday, Oct 25, 2001

• Reading. The current material on ANOVA models is most like what is in RPD, Chapters 9 and 17. This will become more obvious on Tue Oct 23 (I hope!).

• Problems to be turned in:

1. RPD, p. 150, #4.3.

2. RPD, pp. 157–158, #4.12

3. In a regression study, three types of banks were involved, namely, commercial, mutual savings, and savings and loan. Consider the following system of indicator variables for type of bank:

             Type of Bank       X2     X3
-----------------------------------------
               Commercial        1      0
           Mutual Savings        0      1
         Savings and Loan       -1     -1

(a) Develop a first–order linear regression model for relating last year’s profit or loss (Y) to size of bank (X_{1}) and type of bank (X_{2},X_{3}).

(b) State the response functions for the three types of banks.

(c) Interpret each of the following quantities: (1) β_{2}, (2) β_{3}, (3) −β_{2} − β_{3}.

4. RPD, p. 233, #7.13. You can essentially repeat your solution for #3.13 from HW#3 for part (a). After you finish this exercise, write one paragraph entitled: Whether to include more regressors: the bias/variance tradeoff for coefficients of regressors already in the model. Audience: yourself (and me, of course). Write what you would want to remember about this in five years when you are teaching a regression course yourself and you come to this issue in your course.

5. Think about RPD, p. 204, #6.9. You don’t have to turn anything in for this question.

36-707: Applied Regression Analysis Fall 2001