MBA60: ADVANCED QUANTITATIVE METHODS FOR MANAGERS

Assignment 3

2008/9

HELLENIC OPEN UNIVERSITY

MBA PROGRAMM

MBA60: ADVANCED QUANTITATIVE METHODS FOR MANAGERS

Advanced Quantitative Analysis – 3rd Assignment

A mail-order catalog business that sells personal computer supplies, software, and hardware maintains a centralized warehouse for the distribution of products ordered. Management is currently examining the process of distribution from the warehouse and is interesting in studying the factors that affect warehouse distribution costs. Data have been collected over the past 24 months indicating the warehouse distribution costs and the number of orders received. The results are as follows:

Month	Number of Orders (thousands)	Distribution Cost (thousands of €)
1	4.015	52.951
2	3.806	71.664
3	5.309	85.582
4	4.262	63.694
5	4.296	72.813
6	4.097	68.442
7	3.213	52.468
8	4.809	70.772
9	5.237	82.036
10	4.732	74.396
11	4.413	70.847
12	2.921	54.088
13	3.977	62.983
14	4.428	72.309
15	3.964	58.994
16	4.582	79.383
17	5.582	94.449
18	3.450	59.741
19	5.079	90.502
20	5.735	93.245
21	4.269	69.336
22	3.708	53.714
23	5.387	89.187
24	4.161	66.804

Assume that you want to develop a model to predict distribution cost based on the number of orders received.

1. Construct a scatter diagram.

2. Use the least squares method to estimate the regression coefficients b₀ and b₁.

3. State the regression equation.

4. Plot on the same graph, the scatter diagram and the regression line.

5. Give the interpretation of the regression coefficients b₀ and b₁.

6. Determine the coefficient of correlation and explain its meaning in this problem.

7. Determine the coefficient of determination and explain its meaning in this problem.

8. Determine the standard error of the estimate and explain its meaning in this problem.

9. Perform a residual analysis [i.e. plot the residuals versus time (month)]. Is there any evidence of a pattern in the residuals? Explain.

10. At the 0.01 level of significance, is there any evidence of a linear relationship between distribution cost and the number of orders?

11. Would it be appropriate to use the model to predict the monthly distribution cost for 10 thousands received orders? Explain.

12. Predict the average distribution cost for 6,000 received orders.

13. Set up a 95% confidence interval estimate of the average distribution cost for 6,000 orders.

14. Construct a ±2*Se band about the regression line and determine the percentage of the points of the scatter diagram that lie inside this band.

15. Set up a 95% confidence interval estimate of the population slope.

16. Explain how the results obtained above can help the company to budget distribution costs.

[Adapted from: Berenson, Levine and Krehbiel, Basic Business Statistics, Prentice Hall, 2004]