The maintenance manager at a trucking company wants to build a regression model to forecast the time (in years) until the first engine overhaul based on four explanatory variables: (1) annual miles driven (in 1,000s of miles), (2) average load weight (in tons), (3) average driving speed (in mph), and (4) oil change interval (in 1,000s of miles). Based on driver logs and onboard computers, data have been obtained for a sample of 25 trucks. A portion of the data is shown in the accompanying table.

Time until First Engine Overhaul	Annual Miles Driven	Average Load Weight	Average Driving Speed	Oil Change Interval
7.9	43.1	21.0	47.0	13.0
0.8	98.6	25.0	49.0	30.0
6.3	61.2	24.0	62.0	23.0

Click here for the Excel Data File a. For each explanatory variable, discuss whether it is likely to have a positive or negative influence on time until the first engine overhaul.

Explanatory Variable Effect on Time

Annual Miles Driven

Average Load Weight

Average Driving Speed

Oil Change Interval

b. Estimate the regression model. (Negative values should be indicated by a minus sign. Round your answers to 4 decimal places.)

Time = ____ + ______Miles + ______Load+ ____Speed + ______ Oil

c. Based on part (a), are the signs of the regression coefficients logical?

Regression Coefficients Signs

Annual Miles Driven

Average Load Weight

Average Driving Speed

Oil Change Interval