Review Exercises 519 Section 9.4 In Exercises 25 and 26, use technology to find (a) the multiple regression equation for the data shown in the table, (b) the standard error of estimate, and (c) the coefficient of determination. Interpret the results. 25. The table shows the carbon monoxide, tar, and nicotine contents, all in milligrams, of ten brands of cigarettes. (Source: Scientific Reports) Carbon monoxide, y Tar, x1 Nicotine, x2 12 9.4 0.73 7 6.0 0.50 7 6.0 0.50 7 7.0 0.60 10 10.0 0.80 1 1.0 0.10 10 10.0 0.80 10 10.0 0.80 10 10.0 0.80 10 10.0 0.80 26. The table shows the numbers of acres planted, the numbers of acres harvested, and the annual yields (in pounds per acre) of potatoes for five years. (Source: United States Department of Agriculture) Yield, y Acres planted, x1 Acres harvested, x2 43,400 1,056,700 1,037,700 43,200 1,052,600 1,044,500 44,300 1,026,500 1,014,800 45,300 963,300 937,300 45,300 921,000 914,100 In Exercises 27 and 28, use the multiple regression equation to predict the y-values for the values of the independent variables. 27. An equation that can be used to predict fuel economy (in miles per gallon) for automobiles is ny = 41.3 - 0.004x 1 - 0.0049x2 where x1 is the engine displacement (in cubic inches) and x2 is the vehicle weight (in pounds). (a) x1 = 305, x2 = 3750 (b) x1 = 225, x2 = 3100 (c) x1 = 105, x2 = 2200 (d) x1 = 185, x2 = 3000 28. Use the regression equation found in Exercise 25. (a) x1 = 9.0, x2 = 0.70 (b) x1 = 3.0, x2 = 0.25 (c) x1 = 8.0, x2 = 0.60 (d) x1 = 5.2, x2 = 0.46
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