518 CHAPTER 9 Correlation and Regression Section 9.3 In Exercises 13–16, use the value of the correlation coefficient r to calculate the coefficient of determination r2. What does this tell you about the explained variation of the data about the regression line? about the unexplained variation? 13. r = -0.450 14. r = -0.937 15. r = 0.642 16. r = 0.795 In Exercises 17 and 18, use the data to (a) find the coefficient of determination r2 and interpret the result, and (b) find the standard error of estimate se and interpret the result. 17. The table shows the times (in seconds) to accelerate from 0 to 60 miles per hour and the top speeds (in miles per hour) for eight electric cars. The regression equation is ny = -14.399x + 196.996. (Source: Car and Driver) Time to accelerate from 0 to 60 miles per hour, x 6.4 6.7 5.1 5.1 4.3 5.1 2.4 2.4 Top speed, y 110 93 114 125 128 141 163 162 18. The table shows the cooking areas (in square inches) of 18 gas grills and their prices (in dollars). The regression equation is ny = 1.501x - 341.501. (Source: Lowe’s) Area, x 645 529 650 450 844 395 669 725 620 Price, y 249 519 299 469 1199 229 829 549 599 Area, x 445 575 454 529 710 935 710 320 673 Price, y 349 449 149 649 799 1149 849 325 518 In Exercises 19–24, construct the indicated prediction interval and interpret the results. 19. Construct a 90% prediction interval for the amount of milk produced in Exercise 9 when there are an average of 9275 thousand milk cows. 20. Construct a 90% prediction interval for the average time adults ages 35 to 44 spend per day watching television in Exercise 10 when the average time adults ages 25 to 34 spend per day watching television is 2.25 hours. 21. Construct a 95% prediction interval for the number of hours of sleep for an adult in Exercise 11 who is 45 years old. 22. Construct a 95% prediction interval for the fuel efficiency of an automobile in Exercise 12 that has an engine displacement of 265 cubic inches. 23. Construct a 99% prediction interval for the top speed of an electric car in Exercise 17 that takes 5.9 seconds to accelerate from 0 to 60 miles per hour. 24. Construct a 99% prediction interval for the price of a gas grill in Exercise 18 with a usable cooking area of 900 square inches.
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