SECTION 9.3 Measures of Regression and Prediction Intervals 507 20. New Vehicle Sales The table shows the numbers of new vehicle sales (in thousands) in the United States for Toyota and Honda for 11 years. The equation of the regression line is ny = 0.584x + 169.227. (Source: NADA Industry Analysis Division) New vehicle sales (Toyota), x 2218 1770 1764 1645 2083 2236 New vehicle sales (Honda), y 1429 1151 1231 1147 1423 1525 New vehicle sales (Toyota), x 2374 2499 2500 2435 2113 New vehicle sales (Honda), y 1541 1587 1638 1641 1347 Constructing and Interpreting a Prediction Interval In Exercises 21–30, construct the indicated prediction interval and interpret the results. 21. Proceeds Construct a 95% prediction interval for the proceeds from initial public offerings in Exercise 11 when the number of offerings is 200. 22. Mean Hourly Wage Construct a 95% prediction interval for the mean hourly wage in Exercise 12 when the median hourly wage is $21.50. 23. Points Earned Construct a 90% prediction interval for total points earned in Exercise 13 when the number of goals allowed by the team is 140. 24. Trees Construct a 90% prediction interval for the trunk diameter of a tree in Exercise 14 when the height is 80 feet. 25. Mean Wage Construct a 99% prediction interval for the mean annual wage in Exercise 15 when the percentage of employment in STEM occupations is 13% in the industry. 26. Voter Turnout Construct a 99% prediction interval for number of ballots cast in Exercise 16 when the voting age population is 210 million. 27. Natural Gas Construct a 95% prediction interval for the export of natural gas from the United States in Exercise 17 when the marketed production of natural gas in the United States is 31 trillion cubic feet. 28. Total Assets Construct a 90% prediction interval for the total assets in federal defined benefit plans in Exercise 18 when the total assets in IRAs are $6400 billion. 29. New Vehicle Sales Construct a 95% prediction interval for new vehicle sales for General Motors in Exercise 19 when the number of new vehicles sold by Ford is 2028 thousand. 30. New Vehicle Sales Construct a 99% prediction interval for new vehicle sales for Honda in Exercise 20 when the number of new vehicles sold by Toyota is 2159 thousand. Old Vehicles In Exercises 31–34, use the figure shown at the left. 31. Scatter Plot Construct a scatter plot of the data. Show y and x on the graph. 32. Regression Line Find and draw the regression line. 33. Coefficient of Determination Find the coefficient of determination r2 and interpret the results. 34. Error of Estimate Find the standard error of estimate se and interpret the results. Average age (in years), y 2021 2019 2018 2017 2016 2015 2014 12.1 11.8 2020 11.9 11.7 11.7 11.6 11.5 11.4 Year, x Keeping vehicles longer The average age of vehicles on U.S. roads for eight different years: (Sources: Bureau o f Transportation Statistics, IHS Markit) FIGURE FOR EXERCISES 31–34
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