The chief of automobile maintenance for the city of Normal feels that maintenance costs on high- mileage cars are much higher than those costs for low-mileage cars. The maintenance chief regresses yearly maintenance costs for a sample of 200 cars on each car’s total mileage for the year. She finds the following:
= $50 + .030X Sy|x = 150 sb = .005 r2 = .90
= 50,000 sx = 10,000
where Y is maintenance cost (in dollars) for the year and X is the mileage on a car.
(a) Is there a relationship between maintenance costs and mileage?
(b) What are the predicted maintenance costs of a car with 50,000 miles? Place a 95% confidence limit around this estimate.
(c) The maintenance chief considers $ 1,000 in maintenance a year excessive. For this criterion, how many miles will generate maintenance costs of $ 1,000?