Question

Question 2

Frasers Logistics operates a large fleet of trucks that transport goods on behalf of their clients. The trucks undergo regular scheduled maintenance as well as unscheduled maintenance when a problem occurs.   Data about the maintenance expense is collected continuously and recorded by the admin staff of Frasers.   Frasers do believe in updating their fleet of trucks on a continuous basis and hence has trucks in operation of various ages.   They suspect that both the age of the truck as well as the distance covered in km in a particular year will have an impact on the maintenance costs of the trucks. The data for a particular size truck has been collected and is shown in the 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 for that particular truck during the past financial year, the Distance column reflects the distance in km that the truck covered in the past financial year and the Age column reflects the age of the truck.

Use the data in the sheet named “Frasers” and use Excel and the Data Analysis add-in to perform linear regression analysis on the data to determine whether direct distance travelled (K) or age (A) or both should be used for estimating future maintenance expenditure. Specifically answer the following questions:

1. Decide which linear regression model (with distance travelled (K) or age (A) or both as independent variable) is the better model and motivate your selection.

The remaining answers must be based on the model that you have selected.

2. What is the total variation in “Expense” that is explained by the independent variable(s) that you have selected.
3. Is the overall regression model statistically significant? Test at the 5% level of significance using the model that you have selected in a. For this test formulate the appropriate null and alternative hypothesis, determine the region of acceptance, use the appropriate test statistic and draw the statistical and management conclusions.
4. Is the distance travelled (K) variable significant at the 5% level of significance? For this test use the model that you have selected in a. and formulate the appropriate null and alternative hypothesis, determine the region of acceptance, use the appropriate test statistic and draw the statistical and management conclusions.
5. Interpret the intercept of the regression equation.
6. Write down the linear regression equation in algebraic format using E for expense, K for the distance travelled and A for the age of the truck.

Answer 1

Using excel we run the given three model:

(i) "Distance" as the predictor variable:

The output is given below:

(ii) Now we take "age" as the predictor:

The output is given below:

(iii) Taking both "Distance" and "Age" as the predictor:

The output is given below: