562 CHAPTER 10 Correlation and Regression 8. Height of Son A son will be born to a father who is 70 in. tall and a mother who is 60 in. tall. Use the multiple regression equation to predict the height of the son. Is the result likely to be a good predicted value? Why or why not? Garbage: Finding the Best Multiple Regression Equation. In Exercises 9–12, refer to the accompanying table, which was obtained by using the data from 62 households listed in Data Set 42 “Garbage Weight” in Appendix B. The response (y) variable is PLAS (weight of discarded plastic in pounds). The predictor (x) variables are METAL (weight of discarded metals in pounds), PAPER (weight of discarded paper in pounds), and GLASS (weight of discarded glass in pounds). Predictor (x) Variables P-Value R2 Adjusted R2 Regression Equation METAL>PAPER>GLASS 0.000 0.563 0.540 PLAS = -0.170 + 0.290 METAL + 0.122 PAPER + 0.0777 GLASS METAL>PAPER 0.000 0.514 0.498 PLAS = 0.00394 + 0.344 METAL + 0.121 PAPER PAPER>GLASS 0.000 0.499 0.482 PLAS = 0.0647 + 0.157 PAPER + 0.0967 GLASS METAL>GLASS 0.000 0.392 0.371 PLAS = 0.469 + 0.519 METAL + 0.0774 GLASS METAL 0.000 0.344 0.333 PLAS = 0.641 + 0.573 METAL PAPER 0.000 0.421 0.411 PLAS = 0.348 + 0.166 PAPER GLASS 0.005 0.126 0.111 PLAS = 1.46 + 0.121 GLASS 9. If only one predictor 1x2 variable is used to predict the weight of discarded plastic, which single variable is best? Why? 10. If exactly two predictor 1x2 variables are to be used to predict the weight of discarded plastic, which two variables should be chosen? Why? 11. Which regression equation is best for predicting weight of discarded plastic? Why? 12. A household discards 3.00 lb of metal, 10.25 lb of paper, and 9.35 lb of glass. What is the best predicted value for the weight of discarded plastic? Is that predicted value likely to be a good estimate? Is that predicted value likely to be very accurate? Appendix B Data Sets. In Exercises 13–16, refer to the indicated data set in Appendix B and use technology to obtain results. 13. Predicting Car Fuel Consumption Refer to Data Set 35 “Car Data” in Appendix B and use the weight, engine displacement, and highway fuel consumption (HWY) of all 48 cars. Find the best regression equation for predicting the highway fuel consumption. Why is it best? Is the best regression equation a good regression equation for predicting the highway fuel consumption? Why or why not? 14. Predicting Height Refer to Data Set 3 “ANSUR II 2012” in Appendix B and use the variables of Height, Foot_Length, and ArmSpan for all 6068 subjects. Find the best regression equation for predicting Height. Why is it best? Is the best regression equation a good regression equation for predicting Height? Why or why not? 15. Predicting IQ Score Refer to Data Set 12 “IQ and Brain Size” in Appendix B and find the best regression equation with IQ score as the response 1y2 variable. Use predictor variables of brain volume and>or body weight. Why is this equation best? Based on these results, can we predict someone’s IQ score if we know their brain volume and body weight? Based on these results, does it appear that people with larger brains have higher IQ scores?
RkJQdWJsaXNoZXIy NjM5ODQ=