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 has the business objective of determining the factors that affect warehouse distribution costs. Currently, a handling fee is added to the order, regardless of the amount of the order. Data that indicate the warehouse distribution costs and the number of orders received have been collected over the past 24 months and can be seen below: Months Distribution Cost ($thousands) Number of Orders 1 52.95 4015 2 71.66 3806 3 85.58 5309 4 63.69 4262 5 72.81 4296 6 68.44 4097 7 52.46 3213 8 70.77 4809 9 82.03 5237 10 74.39 4732 11 70.84 4413 12 54.08 2921 13 62.98 3977 14 72.30 4428 15 58.99 3964 16 79.38 4582 17 94.44 5582 18 59.74 3450 19 90.50 5079 20 93.24 5735 21 69.33 4269 22 53.71 3708 23 89.18 5387 24 66.81 4161 (a) Assuming a linear relationship, use the least-squares method to develop a simple regression equation. (b) Predict the monthly warehouse distribution costs when the number of orders is 4,500. (c) Plot the residuals versus the time period. (d) Compute the Durbin-Watson statistic. At the 0.05 level of significance, is there evidence of positive autocorrelation among the residuals? (e) Based on the results of (c) and (d), is there reason to question the validity of the model?
A mail-order catalog business that sells personal computer supplies, software, and hardware maintains a centralized warehouse for the distribution of products ordered. Management is currently examining the process of distribution from the warehouse and has the business objective of determining the factors that affect warehouse distribution costs. Currently, a handling fee is added to the order, regardless of the amount of the order. Data that indicate the warehouse distribution costs and the number of orders received have been collected over the past 24 months and can be seen below:
|
Months |
Distribution Cost ($thousands) |
Number of Orders |
|
1 |
52.95 |
4015 |
|
2 |
71.66 |
3806 |
|
3 |
85.58 |
5309 |
|
4 |
63.69 |
4262 |
|
5 |
72.81 |
4296 |
|
6 |
68.44 |
4097 |
|
7 |
52.46 |
3213 |
|
8 |
70.77 |
4809 |
|
9 |
82.03 |
5237 |
|
10 |
74.39 |
4732 |
|
11 |
70.84 |
4413 |
|
12 |
54.08 |
2921 |
|
13 |
62.98 |
3977 |
|
14 |
72.30 |
4428 |
|
15 |
58.99 |
3964 |
|
16 |
79.38 |
4582 |
|
17 |
94.44 |
5582 |
|
18 |
59.74 |
3450 |
|
19 |
90.50 |
5079 |
|
20 |
93.24 |
5735 |
|
21 |
69.33 |
4269 |
|
22 |
53.71 |
3708 |
|
23 |
89.18 |
5387 |
|
24 |
66.81 |
4161 |
(a) Assuming a linear relationship, use the least-squares method to develop a simple regression equation.
(b) Predict the monthly warehouse distribution costs when the number of orders is 4,500.
(c) Plot the residuals versus the time period.
(d) Compute the Durbin-Watson statistic. At the 0.05 level of significance, is there evidence of positive autocorrelation among the residuals?
(e) Based on the results of (c) and (d), is there reason to question the validity of the model?
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