Chapter B.1, Problem 31E

Hip Fracture Rates. Refer to Exercise B.25, where the problem is to determine a regression model for relating hip fracture rate to age for women in Beijing, China, Obtain output similar to that in Outputs B.20–B.24 on pages B-29–B-31.

1. a. Based on the scatterplots of hip fracture rate versus age, which transformations should be attempted on fracture rate? on age?
2. b. Based on the plots of powers of hip fracture rate versus powers of age, which pairs of transformed variables would you consider for further analysis? Explain your reasoning.
3. c. For each pair of a power of hip fracture rate and a power of age selected for further analysis in part (b): (i) perform a regression analysis, (ii) obtain a plot of residuals versus fitted values and a normal probability plot of the residuals, (iii) perform a residual analysis to assess the assumptions of linearity of the regression equation, constancy of the conditional standard deviations, and normality of the conditional distributions, and (iv) check for outliers and influential observations.
4. d. For each model considered in part (c), does your analysis in part (c) reveal any violations of the assumptions for regression inferences? Explain your answers.
5. e. For each model considered in part (c), obtain a plot of the regression equation on the scatterplot of the data, as seen in Output B.24 on page B-31. Based on these plots and the results of the residual analyses in parts (c) and (d), select a final model for predicting hip fracture rate based on age. Do you feel that your model fits the data well? Explain your answer.