Solution: In Exercises 1 4, (a) display the data in a scatter plot, (b) calculate the

In Exercises 1 4, (a) display the data in a scatter plot, (b) calculate the sample correlation coefficient r, and (c) describe the type of correlation and interpret the correlation in the context of the data.The numbers of pass attempts and passing yards for seven professional quarterbacks for a recent regular season (Source: National Football League) Pass attempts, x 449 565 528 197 670 351 218 Passing yards, y 3265 4018 3669 1141 5177 2362 1737

In Exercises 1 4, (a) display the data in a scatter plot, (b) calculate the sample correlation coefficient r, and (c) describe the type of correlation and interpret the correlation in the context of the data. The numbers of wildland fires (in thousands) and wildland acres burned (in millions) in the United States for eight years (Source: National Interagency Coordinate Center) Fires, x 84.1 73.5 63.6 65.5 66.8 96.4 85.7 79.0 Acres, y 3.6 7.2 4.0 8.1 8.7 9.9 9.3 5.3

In Exercises 1 4, (a) display the data in a scatter plot, (b) calculate the sample correlation coefficient r, and (c) describe the type of correlation and interpret the correlation in the context of the data.The intelligence quotients (IQs) and brain sizes, as measured by the total pixel count (in thousands) from an MRI scan, for nine female college students (Adapted from Intelligence) IQ, x 138 140 96 83 101 135 85 77 88 Pixel count, y 991 856 879 865 808 791 799 794 894

In Exercises 1 4, (a) display the data in a scatter plot, (b) calculate the sample correlation coefficient r, and (c) describe the type of correlation and interpret the correlation in the context of the data.The annual per capita sugar consumptions (in kilograms) and the average numbers of cavities of 11- and 12-year-old children in seven countries Sugar consumption, x 2.1 5.0 6.3 6.5 7.7 8.7 11.6 Cavities, y 0.59 1.51 1.55 1.70 2.18 2.10 2.73

In Exercises 58, use Table 11 in Appendix B, or perform a hypothesis test using Table 5 in Appendix B to make a conclusion about the correlation coefficient. If convenient, use technology Refer to the data in Exercise 1. At a = 0.05, is there enough evidence to conclude that there is a significant linear correlation between the data? (Use the value of r found in Exercise 1.)

In Exercises 58, use Table 11 in Appendix B, or perform a hypothesis test using Table 5 in Appendix B to make a conclusion about the correlation coefficient. If convenient, use technology Refer to the data in Exercise 2. At a = 0.05, is there enough evidence to conclude that there is a significant linear correlation between the data? (Use the value of r found in Exercise 2.)

In Exercises 58, use Table 11 in Appendix B, or perform a hypothesis test using Table 5 in Appendix B to make a conclusion about the correlation coefficient. If convenient, use technology Refer to the data in Exercise 3. At a = 0.01, is there enough evidence to conclude that there is a significant linear correlation between the data? (Use the value of r found in Exercise 3.)

Refer to the data in Exercise 4. At a = 0.01, is there enough evidence to conclude that there is a significant linear correlation between the data? (Use the value of r found in Exercise 4.)

In Exercises 912, find the equation of the regression line for the data. Then construct a scatter plot of the data and draw the regression line. (Each pair of variables has a significant correlation.) Then use the regression equation to predict the value of y for each of the x-values, if meaningful. If the x-value is not meaningful to predict the value of y, explain why not. If convenient, use technology.The amounts (in billions of pounds) of milk produced in the United States and the average prices (in dollars) per gallon of milk for nine years (Adapted from U.S. Department of Agriculture and U.S. Bureau of Labor Statistics) Milk produced, x 167.6 165.3 170.1 170.4 170.9 Price per gallon, y 2.79 2.90 2.68 2.95 3.23 Milk produced, x 177.0 181.8 185.7 190.0 Price per gallon, y 3.24 3.00 3.87 3.68 (a) x = 150 billion pounds (b) x = 175 billion pounds (c) x = 180 billion pounds (d) x = 210 billion pounds

In Exercises 912, find the equation of the regression line for the data. Then construct a scatter plot of the data and draw the regression line. (Each pair of variables has a significant correlation.) Then use the regression equation to predict the value of y for each of the x-values, if meaningful. If the x-value is not meaningful to predict the value of y, explain why not. If convenient, use technology.The average times (in hours) per day spent watching television for men and women for 10 years (Adapted from The Nielsen Company) Men, x 4.03 4.18 4.32 4.37 4.48 Women, y 4.67 4.77 4.85 4.97 5.08 Men, x 4.43 4.52 4.58 4.65 4.82 Women, y 5.12 5.28 5.28 5.32 5.42 (a) x = 4.2 hours (b) x = 4.5 hours (c) x = 4.75 hours (d) x = 6 hours

In Exercises 912, find the equation of the regression line for the data. Then construct a scatter plot of the data and draw the regression line. (Each pair of variables has a significant correlation.) Then use the regression equation to predict the value of y for each of the x-values, if meaningful. If the x-value is not meaningful to predict the value of y, explain why not. If convenient, use technology.The ages (in years) and the numbers of hours of sleep in one night for seven adults Age, x 35 20 59 42 68 38 75 Hours of sleep, y 7 9 5 6 5 8 4 (a) x = 16 years (b) x = 25 years (c) x = 85 years (d) x = 50 years

In Exercises 912, find the equation of the regression line for the data. Then construct a scatter plot of the data and draw the regression line. (Each pair of variables has a significant correlation.) Then use the regression equation to predict the value of y for each of the x-values, if meaningful. If the x-value is not meaningful to predict the value of y, explain why not. If convenient, use technology.The engine displacements (in cubic inches) and the fuel efficiencies (in miles per gallon) of seven automobiles Displacement, x 170 134 220 305 109 256 322 Fuel efficiency, y 29.5 34.5 23.0 17.0 33.5 23.0 15.5 (a) x = 86 cubic inches (b) x = 198 cubic inches (c) x = 289 cubic inches (d) x = 407 cubic inches

In Exercises 1316, use the value of the correlation coefficient r to calculate the coefficient of determination r 2 . What does this tell you about the explained variation of the data about the regression line? About the unexplained variation?r = -0.450

In Exercises 1316, use the value of the correlation coefficient r to calculate the coefficient of determination r 2 . What does this tell you about the explained variation of the data about the regression line? About the unexplained variation?r = -0.937

In Exercises 1316, use the value of the correlation coefficient r to calculate the coefficient of determination r 2 . What does this tell you about the explained variation of the data about the regression line? About the unexplained variation?r = 0.642

In Exercises 1316, use the value of the correlation coefficient r to calculate the coefficient of determination r 2 . What does this tell you about the explained variation of the data about the regression line? About the unexplained variation?r = 0.795

In Exercises 17 and 18, use the data to find (a) the coefficient of determination r 2 and interpret the result, and (b) the standard error of estimate se and interpret the result.The table shows the prices (in thousands of dollars) and fuel efficiencies (in miles per gallon) for nine compact sports sedans. The regression equation is yn = -0.414x + 37.147. (Adapted from Consumer Reports) Price, x 37.2 40.8 29.7 33.7 37.5 32.7 39.2 37.3 31.6 Fuel efficiency, y 21 19 25 24 22 24 23 21 23

In Exercises 17 and 18, use the data to find (a) the coefficient of determination r 2 and interpret the result, and (b) the standard error of estimate se and interpret the result.The table shows the cooking areas (in square inches) of 18 gas grills and their prices (in dollars). The regression equation is yn = 1.454x - 532.053. (Source: Lowes) Area, x 780 530 942 660 600 732 660 640 869 Price, y 359 98 547 299 449 799 699 199 1049 Area, x 860 700 942 890 733 732 464 869 600 Price, y 499 248 597 999 428 849 99 999 399

In Exercises 1924, construct the indicated prediction interval and interpret the results.Construct a 90% prediction interval for the price per gallon of milk in Exercise 9 when 185 billion pounds of milk is produced

In Exercises 1924, construct the indicated prediction interval and interpret the results.Construct a 90% prediction interval for the average time women spend per day watching television in Exercise 10 when the average time men spend per day watching television is 4.25 hours.

In Exercises 1924, construct the indicated prediction interval and interpret the results.Construct a 95% prediction interval for the number of hours of sleep for an adult in Exercise 11 who is 45 years old.

In Exercises 1924, construct the indicated prediction interval and interpret the results.Construct a 95% prediction interval for the fuel efficiency of an automobile in Exercise 12 that has an engine displacement of 265 cubic inches.

In Exercises 1924, construct the indicated prediction interval and interpret the results.Construct a 99% prediction interval for the fuel efficiency of a compact sports sedan in Exercise 17 that costs $39,900.

Construct a 99% prediction interval for the price of a gas grill in Exercise 18 with a usable cooking area of 900 square inches.

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 interpret the result, and (c) the coefficient of determination and interpret the result.The table shows the carbon monoxide, tar, and nicotine content, all in milligrams, of 14 brands of U.S. cigarettes. (Source: Federal Trade Commission) Carbon monoxide, y Tar, x1 Nicotine, x2 15 16 1.1 17 16 1.0 11 10 0.8 12 11 0.9 14 13 0.8 16 14 0.8 14 16 1.2 16 16 1.2 10 10 0.8 18 19 1.4 17 17 1.2 11 12 1.0 10 9 0.7 14 15 1.2

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 interpret the result, and (c) the coefficient of determination and interpret the result.The table shows the numbers of acres planted, the numbers of acres harvested, and the annual yields (in pounds) of spinach for five years. (Source: United States Department of Agriculture) Yield, y Acres planted, x1 Acres harvested, x2 15,200 36,400 35,000 18,600 35,400 32,900 17,900 34,400 32,300 18,600 38,500 36,600 16,000 36,400 35,680

In Exercises 27 and 28, use the multiple regression equation to predict the y-values for the values of the independent variables.An equation that can be used to predict fuel economy (in miles per gallon) for automobiles is yn = 41.3 - 0.004x1 - 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

In Exercises 27 and 28, use the multiple regression equation to predict the y-values for the values of the independent variables.Use the regression equation found in Exercise 25. (a) x1 = 10, x2 = 0.7 (b) x1 = 15, x2 = 1.1 (c) x1 = 13, x2 = 0.8 (d) x1 = 9, x2 = 0.8