The chief of automobile maintenance for the city of Stillwater 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:

Yhat= $50 +.030X, Sy|x = $150, s_b= .0005, r²=.90. Xbar=50,000. s_x= 10,000

where Y is maintenance cost (in dollars) for the year and X is the mileage on a car.

a. Is there arelationshipbetween maintenance costs and mileage?

b. What are the predicted maintenance costs of a car with 50,000 miles?