The maintenance manager at a trucking company wants to build a regression model to forecast the time (in years) until th

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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 Tine until first Average Driving Oil Change Engine Overhaul Annual Files Driven Average Load 7.7 0.2 43. 15.0 20. Speed 45.0 51.0 Interval 18.0 33.0 98.2 1 60.8 6.1 28.0 56.0 22.0 Click here for the Excel Data File 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 Effect on time Explanatory variable Annual Miles Driven Average Load Weight Average Driving Speed Ol Change Interval

b. Estimate the regression model (Negative values should be indicated by a minus sign. Round your answers to 4 decimal places.) 011 Time Miles Lood I speed c. Based on part (2), are the signs of the regression coefficients logical? Signs Regression coellicients Annual Mes Delven Average Load Weight Average Driving Speed Ou Change Interval

d. What is the predicted time before the first engine overhaul for a particular truck driven 55,000 mies per year with an average load of 22 tons, an average driving speed of 55 mph, and 15,000 miles between oil changes. (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal placen.) Timo year

A B E F Annual Time Until First Miles 1 Engine Overhaul ]Driven 7.7 43 Average Average Oil Change Load Weight Driving Speed Interval 15 46 18 N 3 0.7 98.2 20 51 33 4 8.8 43.1 22 67 11 Сл 5 1.3 110.6 29 65 21 6 1.5 102.5 27 47 14 2 97.2 24 58 21 00 8 2.5 92.6 24 60 20 7.2 53.7 21 63 8 10 8.2 51.7 27 52 21 11 4.2 84.8 21 52 25 12 0.3 120.8 27 54 20 13 5.1 78 24 53 28 14 5 68.8 17 48 22 15 5 54.7 24 59 24 16 5.4 66.7 15 55 25

17 8.7 39 16 54 12 18 5.7 52.9 17 55 27 19 5.7 54.5 21 44 14 20 4.1 74.6 25 64 21 21 6.5 58.5 24 59 12 22 6.4 52.5 17 49 24 23 6.8 68.4 20 47 17 24 4.3 94.3 27 54 20 25 7.4 46.2 12 56 19 26 6.1 60.8 28 56 22