10-2 Regression 543 26.Cheese and Engineering Listed below are weights (pounds) of per capita consumption of mozzarella cheese and the numbers of civil engineering PhD degrees awarded in various years (based on data from the U.S. Department of Agriculture and the National Science Foundation). What is the best predicted number of civil engineering PhD degrees awarded in a year when per capita cheese consumption is 12.0 pounds? Is that prediction likely to be accurate? Cheese Consumption 9.3 9.7 9.7 9.7 9.9 10.2 10.5 11.0 10.6 10.6 Civil Engineering PhDs 480 501 540 552 547 622 655 701 712 708 27.Lemons and Car Crashes Listed below are annual data for weights (metric tons) of lemons imported from Mexico and U.S. car crash fatalities per 100,000 population. Using these data, find the best predicted crash fatality rate for a year in which there are 500 metric tons of lemon imports. Is the prediction worthwhile? Lemon Imports 230 265 358 480 530 Crash Fatality Rate 15.9 15.7 15.4 15.3 14.9 28.Weighing Seals with a Camera Listed below are the overhead widths (cm) of seals measured from photographs and weights (kg) of the seals. Using the listed data, find the best predicted weight of a seal if the overhead width measured from a photograph is 2 cm. Can the prediction be correct? If not, what is wrong? Overhead Width 7.2 7.4 9.8 9.4 8.8 8.4 Weight 116 154 245 202 200 191 Large Data Sets. Exercises 29–32 use the same Appendix B data sets as Exercises 29–32 in Section 10-1. In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted values following the prediction procedure summarized in Figure 10-5 on page 533. 29. Taxis Repeat Exercise 15 using all of the time>tip data from the 703 taxi rides listed in Data Set 32 “Taxis” from Appendix B. 30. Taxis Repeat Exercise 16 using all of the distance>tip data from the 703 taxi rides listed in Data Set 32 “Taxis” from Appendix B. 31. Taxis Repeat Exercise 17 using all of the distance>fare data from the 703 taxi rides listed in Data Set 32 “Taxis” from Appendix B. 32. Taxis Repeat Exercise 18 using all of the time>fare data from the 703 taxi rides listed in Data Set 32 “Taxis” from Appendix B. 33. Least-Squares Property According to the least-squares property, the regression line minimizes the sum of the squares of the residuals. Refer to the jackpot>tickets data in Table 10-1 on page 507 and use the regression equation yn = -10.9 + 0.174x that was found in Examples 1 and 2 of this section. a. Identify the nine residuals. b. Find the sum of the squares of the residuals. c. Show that the equation yn = -10.0 + 0.200x results in a larger sum of squares of residuals. 10-2 Beyond the Basics
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