I Use this problem for question 1.

In an effort to model executive compensation, 38 firms were selected and data were gathered for the following variables:

y = compensation (thousands of dollars) X1= Sales (millions of dollars)

X2= Profits (millions of dollars) X3= Employment

1. For the second order linear model, what are the following equal to?

df for the model = _____________ and df for error = ______________

II Use this with questions 2 to 4

A limousine company wishes to predict the daily operating cost, y, of its cars using the number of miles driven X1 and the make of the car (Chevy, Ford, or Dodge) X2. Which means we need 2 indicator variables.

and

The director of operations has proposed the following model;

III:

The ability to estimate the volume of a tree based on some simple measurements is important to the lumber industry. Data was collected for the following variables:

y= volume of a tree X1 = the diameter of a tree X2 = the height of a tree

5. Write down the first order linear model.

6. Write down a second order linear model with interaction.

Now using the SAS output for the second order linear model with interaction do problems.

7. Write down the prediction equation.

8. What is the prediction of y (tree volume) when X1 = 15.9 and X2 = 99?

9. What is the residual in problem 35. residual = _____

10. Refer to problem 35. What is the 95% CI for E (Y)?

11. Refer to problem 35. What is the 95% PI for Y.

12. SSE = ____________________

13. S2 = _____________________

14. S = _________________________

15. Write down a 95% confidence interval for β₂.
(__________________, ________________)

14. In testing if the diameter of a tree is significant, state the null and alternative hypothesis.

15. Refer to problem 43. What is the test statistic?

16. Refer to problems 43 and 44. What is the correct decision?

17. Refer to problems 43 through 45. What is the correct conclusion?

18. What is the value for R2? R² = _____

19. Interpret R2.

20. In testing if the model is useful, state the null hypothesis.

21. Refer to problem 20. What is the test statistic? ______?

22. Refer to problems 20 and 21, what is the correct decision?

23. Refer to problems 20 and 21, is there enough evidence to say the model is useful?

24. In testing if the squared terms and the interaction term are significant to the model when taken together, state the null hypothesis.

25. Refer to problem 24, T=6.57509. What is the correct decision?

26. Refer to problems 24  and 25. In conclusion there ________ enough evidence to say the squared terms and the interaction term are significant to the model when taken together?

Attachment:- bsas.rar