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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. Time until First Engine Overhaul 7.7 0.8 Annual Miles Driven 42.9 98.3 : 61.1 Average Load Weight 22.0 20.0 : 22.0 Average Driving Speed 44.0 47.0 : 62.0 Oil Change Interval 16.0 34.0 6.3 15.0 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 Oil Change Interval

Time Until First Engine Overhaul 7.7 Annual Miles Average Load Average Oil Change Driven Weight Driving Speed Interval 42.9 22 44 16 0.8 98.3 20 47 34 8.4 43.7 25 66 13 1.1 110.7 30 62 25 1.4 101.9 32 53 22 2.2 96.8 19 58 19 2.2 93.3 27 52 13 7.8 54.1 24 66 17 8.1 51.4 25 48 14 4.4 84.7 27 51 29 0.7 120.4 32 47 26 5.3 77 22 52 26 5.5 68.8 26 47 24 5.2 55.1 25 61 18 5.8 66.3 16 55 29 8.8 38.9 19 51 20 5.6 52.4 17 54 20 5.7 54.6 24 47 20 4.1 75 26 65 26 6 58.7 22 54 20 6.5 52.5 21 54 22 7 68.3 17 55 17 4.2 94.1 26 59 26 7.3 45.8 19 58 14 6.3 61.1 22 62 15