In: Statistics and Probability
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 | Annual Miles Driven | Average Load Weight | Average Driving Speed | Oil Change Interval |
7.9 | 42.7 | 18.0 | 43.0 | 14.0 |
0.9 | 98.4 | 29.0 | 48.0 | 24.0 |
⋮ | ⋮ | ⋮ | ⋮ | ⋮ |
6.3 | 61.6 | 25.0 | 59.0 | 20.0 |
Excel Data File:
Time Until First Engine Overhaul | Annual Miles Driven | Average Load Weight | Average Driving Speed | Oil Change Interval |
7.9 | 42.7 | 18 | 43 | 14 |
0.9 | 98.4 | 29 | 48 | 24 |
8.6 | 43.3 | 17 | 64 | 17 |
1.4 | 110.6 | 32 | 55 | 25 |
1.2 | 102.3 | 26 | 56 | 21 |
1.8 | 97.3 | 28 | 64 | 23 |
2.4 | 93.1 | 26 | 53 | 19 |
7.5 | 54.4 | 21 | 65 | 11 |
8 | 51.6 | 18 | 56 | 12 |
4.2 | 84.8 | 27 | 52 | 31 |
0.3 | 120.5 | 27 | 56 | 25 |
5.3 | 77.3 | 20 | 49 | 25 |
4.9 | 69 | 23 | 49 | 29 |
5.4 | 55.2 | 26 | 59 | 25 |
5.7 | 67.1 | 23 | 59 | 29 |
8.8 | 39.4 | 23 | 53 | 18 |
5.3 | 52.4 | 21 | 55 | 30 |
6.1 | 54.3 | 17 | 53 | 12 |
4.5 | 74.3 | 26 | 67 | 23 |
6.2 | 58.6 | 21 | 54 | 16 |
6.9 | 52 | 17 | 56 | 20 |
7.3 | 68.9 | 18 | 49 | 14 |
3.9 | 94.4 | 28 | 58 | 20 |
7.3 | 45.4 | 16 | 55 | 19 |
6.3 | 61.6 | 25 | 59 | 20 |
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. Estimate the regression model.
(Negative values should be indicated by a minus sign. Round
your answers to 4 decimal places.)
TimeˆTime^ = + Miles + Load + Speed + Oil |
c. Based on part (a), are the signs of
the regression coefficients logical?