The maintenance manager at a trucking company wants to build a regression model to forecast the time until the first engine overhaul (Time in years) based on four predictor variables: (1) annual miles driven (Miles in 1,000s), (2) average load weight (Load in tons), (3) average driving speed (Speed in mph), and (4) oil change interval (Oil in 1,000s miles). Based on driver logs and onboard computers, data have been obtained for a sample of 15 trucks as follows.

a.Estimate the time until the first engine overhaul as a function of all four predictor variables. Pleaseinterpreteach slope coefficient (Round your answers to the second decimal places).

b. At the 5% significance level, are the predictor variable jointly significant? Please write down the null and alternative hypotheses and explain your conclusion.

c. Are the predictor variables individually significant at the 5% significance level? Please explain your conclusion for each predictor variable.

Time Miles Load Speed Oil 7.8 42.4 28 51 17 0.6 98.5 39 49 26 9 43 18 78 13 1.1 110.5 38 72 28 1.2 101.9 35 47 18 2.3 97.2 37 69 24 2.5 93.1 25 54 11 7.1 54 35 71 8 8.6 51.1 21 64 15 4.6 84.8 30 65 34 0.6 120.5 35 65 35 4.9 77.6 29 46 28 4.9 68.2 18 58 38 5.3 54.8 33 55 19 5.4 66.8 24 70 24