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 explanatory variables: (1) annual miles driven, (2) average load weight, (3) average driving speed, and (4) oil change interval. Based on driver logs and onboard computers, data have been obtained for a sample of 25 trucks.
a. Estimate the time until the first engine overhaul as a function of all four explanatory variables.
b. At the 10% significance level, are the explanatory variables jointly significant? Show the relevant steps of the test.
c. Are the explanatory variables individually significant at the 10% significance level? Show the relevant steps of the test.