An airline designs a study to evaluate fuel usage by a certain type of aircraft. From a random sample of 50 flights, the flight length in hundreds of miles and the fuel usage in gallons are recorded.

a. Plot the data on a scatter plot. Is the assumption of linearity satisfied?

b. What is the correlation between fuel usage and flight length? Interpret your answer. Give a 99% confidence interval for the true correlation.

c. Fit a least-squares regression line.

i. What is the interpretation of the slope?

ii. What is the interpretation of the intercept? Is it meaningful?

iii. What is the coefficient of determination? Interpret your answer.

d. Estimate the mean fuel usage for a 1000-mile flight, and provide a 95% confidence interval for your estimate.

e. Predict the fuel usage for a 1000-mile flight, and provide a 95% prediction interval. Would a fuel usage of 700 gallons be considered excessive? f. Predict the fuel usage for a 3,500-mile flight, and provide a 95% prediction interval. Is this a reasonable prediction? Why or why not?

'Mileage' 'FuelUse'

530 382

533 257

536 376

569 290

580 416

603 362

655 361

667 347

707 498

712 449

735 482

784 452

814 426

839 441

844 524

885 488

890 551

913 570

957 556

976 522

979 542

1050 640

1055 598

1069 502

1070 639

1114 679

1116 630

1129 659

1308 695

1348 767

1356 632

1363 641

1395 740

1474 737

1504 783

1528 802

1613 861

1615 874

1632 847

1657 748

1674 872

1698 802

1730 925

1769 912

1775 936

1789 846

1804 883

1820 902

1851 925

1983 908