The maintenance manager at a trucking company wants to build a regression model to forecast the time until the first engine overhaul based on four independent variables: (1) annual miles driven, (2) average load weight, (3) average driving speed, (4) oil change interval. 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.

a. For each explanatory variable, discuss whether it is likely to have a positive or negative causal effect on time until the first engine overhaul.
b. Use Excel to estimate the regression model (use all four explanatory variables).
c. Based on part (a), are the signs of the regression coefficients logical?
d. Predict the time before the first engine overhaul for a particular truck driven 60(000) miles per year with an average load of 22 tons, an average driving speed of 57 mph, and 18(000) miles between oil changes.

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Time until First Engine Annual Driven miles) Miles Average Average oil Change Load Driving Interval (1,000 miles) 15 29 1,000 Weight Speed (Years) 79 0.9 (tons) mph) 46 46 42.8 98.5 25 6.1 61.2 24 58 19