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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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    https://brainmass.com/statistics/regression-analysis/beastbuy-data-analysis-438193

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    Solution Summary

    The solution provides step by step method for the calculation of ANOVA and multiple regression analysis. Formula for the calculation and Interpretations of the results are also included.

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