10-4 Multiple Regression 561 Statistical Literacy and Critical Thinking 1.Response and Predictor Variables Using all of the Tour de France bicycle race results up to a recent year, we get this multiple regression equation: Speed = 29.2 - 0.00260 Distance + 0.540 Stages + 0.0570 Finishers, where Speed is the mean speed of the winner (km>h), Distance is the length of the race (km), Stages is the number of stages in the race, and Finishers is the number of bicyclists who finished the race. Identify the response and predictor variables. 2.Best Multiple Regression Equation For the multiple regression equation given in Exercise 1, the P-value is 0.000 and the adjusted R2 value is 0.894. If we were to include an additional predictor variable of the number of bicyclists who entered the race, the P-value is 0.000 and the adjusted R2 is again 0.894. Is it correct to reason that we should include the number of bicyclists who entered the race because the adjusted R2 remains the same but the multiple regression equation gives us more information because it includes another variable? Explain. 3.Adjusted Coefficient of Determination For Exercise 2, why is it better to use values of adjusted R2 instead of simply using values of R2? 4. InterpretingR2 For the multiple regression equation given in Exercise 1, we get R2 = 0.897. What does that value tell us? Interpreting a Computer Display. In Exercises 5–8, we want to consider the correlation between heights of fathers and mothers and the heights of their sons. Refer to the StatCrunch display and answer the given questions or identify the indicated items. The display is based on Data Set 10 “Family Heights” in Appendix B. (The response y variable represents heights of sons.) 5.Height of Son Identify the multiple regression equation that expresses the height of a son in terms of the height of his father and mother. 6.Height of Son Identify the following: a. The P-value corresponding to the overall significance of the multiple regression equation b. The value of the multiple coefficient of determination R2 c. The adjusted value of R2 7.Height of Son Should the multiple regression equation be used for predicting the height of a son based on the height of his father and mother? Why or why not? 10-4 Basic Skills and Concepts
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