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# Statistics: factors in the process of distribution

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Problem 13.5 A mail-order catalog business selling personal computer supplies, software, and hardware maintains a centralized warehouse. Management is currently examining the process of distribution from the warehouse and wants to study the factors that affect warehouse distribution costs. Currently, a small handling fee is added to each order, regardless of the amount of the order. Data collected over the past 24 months indicate that the warehouse distribution costs (in thousands of dollars), the sales (in thousands of dollars), and the number of orders. (WARECOST.xls)
Cost Sales Orders
52.95 386 4015
71.66 446 3806
85.58 512 5309
63.69 401 4262
72.81 457 4296
68.44 458 4097
52.46 301 3213
70.77 484 4809
82.03 517 5237
74.39 503 4732
70.84 535 4413
54.08 353 2921
62.98 372 3977
72.3 328 4428
58.99 408 3964
79.38 491 4582
94.44 527 5582
59.74 444 3450
90.5 623 5079
93.24 596 5735
69.33 463 4269
53.71 389 3708
89.18 547 5387
66.8 415 4161

a. State the multiple regression equation.

b. Interpret the meaning of the slopes B1 & B2 in this problem..

c. Explain why the regression coefficient B0 has no practical meaning in the context of this problem.

d. Predict the average monthly warehouse distribution cost when sales are \$400,000 and the number of orders is 4,500.

e. Set up a 95% confidence interval estimate for the average monthly distribution cost when sales are \$400,000 and the number of orders is 4,500.

f. Set up a 95% prediction interval estimate for the average monthly distribution cost at a particular warehouse when sales are \$400,000 and the number of orders is 4,500

g. Determine the coefficient of multiple determination r2 (y12) and interpret its meaning

Problem 13.9 In problem 13.5 (above), sales and number of orders were used to predict distribution costs at a mail order catalog business. Using the computer output you obtained to solve that problem.

a. Perform a residual analysis on your results and determine the adequacy of fit of the model.

b. Plot the residuals against the months. Is there any evidence of a pattern in the residuals. Explain.

c. Determine the Durbin Watson statistic.

d. At the .05 level of significance, is there evidence of positive autocorrelation in the residuals?

Problem 13.16 In problem 13.5 (above), sales and number of orders were used to predict distribution costs at a mail order catalog business. Using the computer output you obtained to solve that problem:

a. Determine whether there sis a significant relationship between distribution costs and the two explanatory variables (sales and number of orders) at the .05 level of significance .

b. Interpret the meaning of the p-value.

Problem 13.23 In problem 13.5 (above), sales and number of orders were used to predict distribution costs at a mail order catalog business. Using the computer output you obtained to solve that problem:

a. Set up a 95% confidence interval estimate of the population slope between distribution costs and sales.

b. At the .05 level of significance, determine whether each explanatory variables make a significant contribution to the regression model. On the basis of these results, indicate the independent variables that should be included in this model.

Problem 13.29 In problem 13.5 (above), sales and number of orders were used to predict distribution costs at a mail order catalog business. Using the computer output you obtained to solve that problem:

a. At the .05 level of significance, determine whether each explanatory variable makes a significant contribution to the regression model. On the basis of these results, indicate the regression model that should be used in the problem.

b. Compute the coefficients of partial determination r2 (y1.2) and r2 (y2.1) and interpret the meaning.