Chapter A, Problem 1FDA

Recall from Chapter 1 (page 34 of your text) that the Focus database and Focus sample contain information on the University of Wisconsin-Eau Claire (UWEC). Now would be a good time to review the discussion about these data sets. Among the your choice to solve the following problems regarding the relationship between the response variable, cumulative GPA, and the three predictor variables, high school percentile. ACT math score, and ACT English score.

1. a. Obtain a scatterplot matrix of the data for these four variables. What do these scatterplots tell you about the relationships among the variables?
2. b. Does a multiple linear regression equation relating cumulative GPA to high school percentile, ACT math score, and ACT English score seem appropriate for these data? Explain your answer.
3. c. Determine the multiple linear regression equation relating the response variable of cumulative GPA to the three predictor variables.
4. d. Interpret the estimated regression coefficients.
5. e. Determine the proportion of variation in the observed cumulative GPAs that can be explained by the multiple linear regression.
6. f. Construct residual plots and assess the appropriateness of the multiple linear regression equation.
7. g. Construct residual plots and a normal probability plot to assess the appropriateness of the assumptions of constant conditional standard deviation and normality for multiple linear regression inferences.
8. h. Identify any potential outliers.

   Presuming now that the assumptions for multiple linear regression inferences hold for the four variables cumulative GPA, high school percentile, ACT math score, and ACT English score, solve the following problems.

9. i. Obtain the analysis of variance table for the regression of cumulative GPA on the three predictor variables.

   variables considered are cumulative GPA (GPA), high school percentile (HSP), ACT math score (MATH), and ACT English score (ENGLISH). For these database exercises, you should use the Focus sample worksheet (FocusSample). Use the technology of

10. j. At the 5% level of significance, do the data provide sufficient evidence to conclude that the three predictor variables taken together are useful for predicting the cumulative GPA of UWEC students?
11. k. At the 5% level of significance, do the data provide sufficient evidence to conclude that high school percentile is useful for predicting cumulative CPA when ACT math score and ACT English score are also in the regression equation?
12. l. Repeat part (k) to determine the usefulness of ACT math score in predicting cumulative GPA when the other two predictor variables are in the regression equation.
13. m. Repeat part (k) to determine the usefulness of ACT English score in predicting cumulative GPA when the other two predictor variables are in the regression equation.
14. n. Should all three predictor variables remain in the multiple linear regression equation?
15. o. Do you think the three predictor variables do a good job of predicting cumulative GPA?
16. p. Determine a point estimate for the mean cumulative GPA of UWEC students who have a high school percentile of 80, an ACT math score of 24, and an ACT English score of 23.
17. q. Find a 95% confidence interval for the mean cumulative GPA of UWEC students who have a high school percentile of 80, an ACT math score of 24, and an ACT English score of 23.
18. r. Determine the predicted cumulative GPA of a UWEC student who has a high school percentile of 80, an ACT math score of 24, and an ACT English score of 23.
19. s. Obtain a 95% prediction interval for the cumulative GPA of a UWEC student who has a high school percentile of 80, an ACT math score of 24, and an ACT English score of 23.
20. t. Suggest other possible variables that could be considered as predictors of cumulative GPA.