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# BEASTBUY Data Analysis

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Problem Set 4

You work in the shipping and logistics department for Beast Buy, an American mail order company that specializes in pet food for VERY exotic pets. Beast Buy has four warehouses/distribution centers that provide product to each of four different regions in the US; Atlanta services the southeast, Boston services the northeast, Cleveland services the midwest, and Denver services the west. Your manager has recently asked you to analyze the efficiency of these distribution centers.

The data tab contains data from each of the last 26 weeks for each of the four distribution centers. The first column simply denotes the week in which the data were collected. The second column indicates which warehouse the data are from (1=Atlanta, 2=Boston, 3=Cleveland, 4=Denver). The third column contains the distribution cost (in thousands of US dollars) associated with the particular warehouse in each week, and the final column contains data on the number of orders routed through each warehouse each week. Use this data to answer the following questions. Problem 4.1 comes from week 9 material, 4.2 comes from week 10 material, and 4.3 relates to week 11 material. Because this is due before week 11, question 4.3 is extra credit. Should you encounter any difficulties with these problems, the optional problems below are very similar to the questions in this problem set, and the answers to the optional questions can be found in the back of the textbook. You can also request that the tutor work extensively with you on the optional problems.

Problem 4.1

The first issue your boss has asked you to address is whether or not there are differences in distribution cost between each of the four warehouses. Use the 0.05 level of significance to:

a) Perform a one-way ANOVA to look for differences in distribution costs between warehouses.

b) If the results in (a) indicate that it is appropriate, use the Tukey-Kramer procedure to determine which distribution centres differ in mean distribution costs.

c) Briefly summarize (in plain English) your procedures and the results of (a) and (b) for your manager.

Problem 4.2

In addition to looking at differences between distribution centres, your manager also wants to know the relationship between the number of orders routed through each centre and the distribution cost. Thus, the number of orders is your independent variable and the cost is your dependent variable.

a) Construct a scatter plot of the two variables.

b) Estimate a simple linear regression between these two variables.

c) Interpret the meaning of ?0 and ?1.

d) Predict the mean distribution costs of 500 orders, 1000 orders, and 1500 orders. Are these appropriate predictions?
e) Comment briefly on the predictive power/statistical significance of your estimates.

Problem 4.3

EXTRA CREDIT. To answer this question, you will need to read the materials for week 11 of the class. Here, your task is to combine 4.1 and 4.2 into a single multiple regression model using dummy variables. To put the data in an Excel-friendly format, you will first need to create dummy variables for each of the different processing centres.

a) Estimate a multiple regression model, again using cost as the dependent variable, however for your independent variables you will want to use orders AND your set of dummy variables (see technical note below).

b) Comment on the results from (a) in light of your results in 4.1 and 4.2. Does the coefficient on orders here match your results from 4.2? Do the coefficients on your dummy variables, and differences between the coefficients on your dummy variables, match up with your results from 4.1?

The data set is given below:

Week Warehouse Cost Orders
1 1 96.40 1285
1 2 32.37 432
1 3 105.76 1366
1 4 91.68 1037
2 1 57.90 889
2 2 28.72 442
2 3 109.99 1466
2 4 98.33 762
3 1 58.65 827
3 2 50.87 842
3 3 63.26 938
3 4 62.43 518
4 1 106.28 1220
4 2 98.65 1326
4 3 44.30 795
4 4 143.62 892
5 1 34.08 553
5 2 57.54 817
5 3 51.74 611
5 4 99.78 1138
6 1 94.71 1340
6 2 75.03 1061
6 3 88.43 1261
6 4 105.58 796
7 1 101.74 1198
7 2 113.49 1336
7 3 34.72 402
7 4 150.34 1234
8 1 32.15 447
8 2 128.25 1358
8 3 41.43 489
8 4 118.36 908
9 1 25.54 428
9 2 97.43 1259
9 3 57.50 844
9 4 182.18 1259
10 1 65.22 957
10 2 35.74 490
10 3 67.83 984
10 4 73.76 585
11 1 30.94 393
11 2 77.66 826
11 3 65.10 697
11 4 79.66 1155
12 1 130.68 1301
12 2 76.60 1061
12 3 79.00 1022
12 4 88.93 816
13 1 59.56 843
13 2 69.96 855
13 3 81.63 1203
13 4 117.69 1450
14 1 61.79 644
14 2 41.62 485
14 3 80.25 976
14 4 82.21 733
15 1 41.75 539
15 2 58.73 601
15 3 71.79 1002
15 4 60.34 776
16 1 51.70 571
16 2 36.41 595
16 3 83.02 859
16 4 159.00 1355
17 1 38.68 453
17 2 70.74 1056
17 3 33.73 430
17 4 80.77 561
18 1 100.92 1124
18 2 81.44 886
18 3 42.55 597
18 4 82.48 726
19 1 82.78 901
19 2 80.02 947
19 3 60.69 667
19 4 70.91 991
20 1 56.34 800
20 2 27.71 461
20 3 51.33 650
20 4 125.94 901
21 1 32.15 481
21 2 42.12 461
21 3 52.69 663
21 4 65.18 421
22 1 108.26 1216
22 2 50.07 522
22 3 32.78 445
22 4 48.60 420
23 1 61.72 1020
23 2 42.33 522
23 3 98.49 1275
23 4 64.26 707
24 1 54.12 555
24 2 30.81 516
24 3 84.06 1201
24 4 55.44 606
25 1 70.39 828
25 2 69.07 1160
25 3 69.31 1107
25 4 105.83 1134
26 1 52.87 596
26 2 104.18 1155
26 3 35.25 396
26 4 42.11 484

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