Question 2
Frasers Logistics operates a large fleet of trucks thattransport goods on behalf of their clients. The trucks undergoregular scheduled maintenance as well as unscheduled maintenancewhen a problem occurs. Data about the maintenanceexpense is collected continuously and recorded by the admin staffof Frasers. Frasers do believe in updating their fleetof trucks on a continuous basis and hence has trucks in operationof various ages. They suspect that both the age of thetruck as well as the distance covered in km in a particular yearwill have an impact on the maintenance costs of the trucks. Thedata for a particular size truck has been collected and is shown inthe table below.
Truck | Expense (E) | Distance in km (K) | Age in years (A) | Truck | Expense (E) | Distance in km (K) | Age in years (A) |
1 | 3529.80 | 16800 | 2 | 13 | 12201.75 | 47040 | 8 |
2 | 4563.75 | 17280 | 1 | 14 | 6409.80 | 43560 | 1 |
3 | 8137.95 | 37840 | 4 | 15 | 10899.75 | 20320 | 10 |
4 | 9294.15 | 39840 | 9 | 16 | 2695.20 | 14880 | 3 |
5 | 12588.15 | 49440 | 6 | 17 | 3402.15 | 12000 | 3 |
6 | 11903.25 | 44160 | 8 | 18 | 6540.60 | 31680 | 5 |
7 | 3471.90 | 12480 | 1 | 19 | 3844.50 | 36785 | 2 |
8 | 11993.70 | 47040 | 7 | 20 | 12056.70 | 47520 | 7 |
9 | 12157.95 | 26560 | 9 | 21 | 11266.80 | 46560 | 7 |
10 | 13732.95 | 48000 | 11 | 22 | 5701.65 | 31200 | 5 |
11 | 2623.95 | 10560 | 3 | 23 | 13628.40 | 50400 | 10 |
12 | 5530.80 | 21600 | 2 | | | | |
The Expense column reflects the full maintenance expense forthat particular truck during the past financial year, the Distancecolumn reflects the distance in km that the truck covered in thepast financial year and the Age column reflects the age of thetruck.
Use the data in the sheet named “Frasers” anduse Excel and the Data Analysis add-in to perform linear regressionanalysis on the data to determine whether direct distance travelled(K) or age (A) or both should be used for estimating futuremaintenance expenditure. Specifically answer the followingquestions:
- Decide which linear regression model (with distance travelled(K) or age (A) or both as independent variable) is the better modeland motivate your selection.
The remaining answers must be based onthe model that you have selected.
- What is the total variation in “Expense” that is explained bythe independent variable(s) that you have selected.
- Is the overall regression model statistically significant? Testat the 5% level of significance using the model that you haveselected in a. For this test formulate the appropriate null andalternative hypothesis, determine the region of acceptance, use theappropriate test statistic and draw the statistical and managementconclusions.
- Is the distance travelled (K) variable significant at the 5%level of significance? For this test use the model that you haveselected in a. and formulate the appropriate null and alternativehypothesis, determine the region of acceptance, use the appropriatetest statistic and draw the statistical and managementconclusions.
- Interpret the intercept of the regression equation.
- Write down the linear regression equation in algebraic formatusing E for expense, K for the distance travelled and A for the ageof the truck.
