Chapter B.2, Problem 47E

Note: The data for the Using Technology exercises are on the WeirsStats website.

B.47 Slopping Distance. Refer to Exercise B 44. where the problem is to determine a polynomial regression model for the relationship between stopping distance and car speed. Use the technology of your choice to obtain computer output similar to Outputs B.33-B.35 on pages B-54-B-56.

1. a. Based on the scallcrplol of stopping distance versus speed, what degree polynomial would you use to fit the data?
2. b. Based on the regression analyses for polynomials of degrees one through live, apply the forward selection method to select a polynomial regression equation for these data. Use a 5% level of significance.
3. c. Based on the regression analyses for polynomials of degrees one through five, apply the backward elimination method to select a polynomial regression equation for these data. Use α = 0.05.
4. d. Do the forward selection and backward elimination methods yield the same result?
5. e. Interpret the plots of residuals versus fitted values for the linear, quadratic, and cubic polynomial fits with regard to the appropriateness of each of the three polynomial regression equations. Do these interpretations agree with the regression models obtained in parts (b) and (cl? Which regression model would you select?
6. f. Using the plot of residuals versus fitted values for the polynomial regression equation that you selected in part (e), assess the assumption of equal conditional standard deviations.
7. g. For the polynomial regression equation that you selected in part (e\ obtain a normal probability plot of the residuals, and assess the assumption of normality of the conditional distributions.
8. h. It appears that a polynomial regression model may not be completely appropriate here. Based on your results from the previous parts of this exercise, decide on a suitable transformation and perform regression and residual analyses for that model. Discuss your findings and compare, with regard to the assumptions for regression inferences, the model obtained using the method of transformations to the one selected in part (e).