The maintenance manager at a trucking company wants to build aregression model to forecast the time (in years) until the firstengine overhaul based on four explanatory variables: (1) annualmiles driven (in 1,000s of miles), (2) average load weight (intons), (3) average driving speed (in mph), and (4) oil changeinterval (in 1,000s of miles). Based on driver logs and onboardcomputers, data have been obtained for a sample of 25 trucks. Aportion 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 |
8.1 | 42.8 | 22.0 | 50.0 | 10.0 |
0.9 | 98.7 | 26.0 | 49.0 | 25.0 |
â‹® | â‹® | â‹® | â‹® | â‹® |
6.1 | 61.6 | 28.0 | 54.0 | 16.0 |
|
a. For each explanatory variable, discuss whetherit is likely to have a positive or negative causal effect on timeuntil the first engine overhaul.
The effect on time is either Positive or Negative! Fill them inbelow.
| |
| Explanatory variable | Effect on time | Annual Miles Driven | | Average Load Weight | | Average Driving Speed | | Oil Change Interval | |
|
b. Estimate the regression model.(Negative values should be indicated by a minus sign. Roundyour answers to 4 decimal places.)
TimeˆTime^  = ________+_______ Miles +_______ Load +________ Speed + _______ Oil
c. Based on part (a), are the signs ofthe regression coefficients logical?
The below signs will be filled with the word logical or notlogical!
| |
| Regression coefficients | Signs | Annual Miles Driven | | Average Load Weight | | Average Driving Speed | | Oil Change Interval | |
|
d. What is the predicted time before the firstengine overhaul for a particular truck driven 57,000 miles per yearwith an average load of 18 tons, an average driving speed of 57mph, and 18,000 miles between oil changes. (Roundcoefficient estimates to at least 4 decimal places and final answerto 2 decimal places.)
Excel data:
Time Until First Engine Overhaul | Annual Miles Driven | Average Load Weight | Average Driving Speed | Oil Change Interval |
8.1 | 42.8 | 22 | 50 | 10 |
0.9 | 98.7 | 26 | 49 | 25 |
8.7 | 43.2 | 18 | 67 | 19 |
1.4 | 111 | 27 | 60 | 24 |
1.4 | 102.2 | 31 | 46 | 19 |
2 | 97.3 | 27 | 67 | 22 |
2.5 | 93.3 | 19 | 59 | 17 |
7.6 | 54.1 | 18 | 70 | 12 |
8.1 | 51.2 | 24 | 47 | 20 |
3.9 | 84.9 | 29 | 51 | 26 |
0.6 | 120.3 | 30 | 50 | 20 |
5.3 | 77.6 | 24 | 49 | 25 |
5 | 68.2 | 25 | 49 | 21 |
5.2 | 55.4 | 28 | 53 | 21 |
5.3 | 66.4 | 19 | 62 | 24 |
8.5 | 39.8 | 15 | 45 | 16 |
5.8 | 52.4 | 19 | 58 | 27 |
6.2 | 54.5 | 24 | 47 | 14 |
4.2 | 75.1 | 23 | 60 | 20 |
6.1 | 58.4 | 19 | 50 | 13 |
6.7 | 52.2 | 24 | 49 | 23 |
6.8 | 68.3 | 21 | 56 | 24 |
4 | 94.3 | 19 | 55 | 21 |
7.6 | 45.2 | 22 | 56 | 17 |
6.1 | 61.6 | 28 | 54 | 16 |
Don't care how you solve as long as answers are correct. I willlike for it being correct!
