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If I could please see how you work through this problem, it would be greatly appreciated! (6+7+5+5 = 23 points) Consider the “GroceryRetailer” dataset. A large, national grocery retailer tracks productivity and costs of its facilities closely. Data were obtained from a single distribution center for a one-year period. Each data point for each variable represents one week of activity. The variables included are the number of cases shipped (X1), the indirect costs of the total labor hours as a percentage (X2), a qualitative predictor called holiday that is coded 1 if the week has a holiday and 0 otherwise (X3), and the total labor hours (Y). a) Obtain the ANOVA table that decomposes the regression sum of squares into sequential sums of squares associated with X1; X3 given X1; and with X2 given X1 and X3. Give their values along with the associated degrees of freedom. b) Test whether X2 can be dropped from the regression model given that X1 and X3 are retained. Use the F test statistic and α = 0.05. State the alternatives, decision rule, and conclusion. What is the p-value of the test? c) Now test H0: β2 = 0 vs. Ha: β2 ≠ 0 in the model E(Y) = β0 + β1 X1 + β3 X3 + β2 X2 using a t-test. Give the value of the test statistic, the p-value and conclusion. d) Using the ANOVA table from part (a), use sequential sums of squares to test H0: β2 = β3 = 0 in the model E(Y) = β0 + β1 X1 + β3 X3 + β2 X2. Give the test statistic, p-value and conclusion.

If I could please see how you work through this problem, it would be greatly appreciated!

 

(6+7+5+5 = 23 points) Consider the “GroceryRetailer” dataset. A large, national grocery retailer tracks productivity and costs of its facilities closely. Data were obtained from a single distribution center for a one-year period. Each data point for each variable represents one week of activity. The variables included are the number of cases shipped (X1), the indirect costs of the total labor hours as a percentage (X2), a qualitative predictor called holiday that is coded 1 if the week has a holiday and 0 otherwise (X3), and the total labor hours (Y).

  1. Obtain the ANOVA table that decomposes the regression sum of squares into sequential sums of squares associated with X1; X3 given X1; and with X2 given X1 and X3. Give their values along with the associated degrees of freedom.
  2. Test whether X2 can be dropped from the regression model given that X1 and X3 are retained. Use the F test statistic and α = 0.05. State the alternatives, decision rule, and conclusion. What is the p-value of the test?
  3. Now test H0: β2 = 0 vs. Ha: β2 ≠ 0 in the model E(Y) = β0 + β1 X1 + β3 X3 + β2 X2 using a t-test. Give the value of the test statistic, the p-value and conclusion.
  4. Using the ANOVA table from part (a), use sequential sums of squares to test H0: β2 = β3 = 0 in the model E(Y) = β0 + β1 X1 + β3 X3 + β2 X2. Give the test statistic, p-value and conclusion.

 

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