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

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**(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 (X_{1}), the indirect costs of the total labor hours as a percentage (X_{2}), a qualitative predictor called holiday that is coded 1 if the week has a holiday and 0 otherwise (X_{3}), and the total labor hours (Y).

- Obtain the ANOVA table that decomposes the regression sum of squares into sequential sums of squares associated with X
_{1}; X_{3}given X_{1}; and with X_{2}given X_{1}and X_{3}. Give their values along with the associated degrees of freedom. - Test whether X
_{2}can be dropped from the regression model given that X_{1}and X_{3}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? - Now test H
_{0}: β_{2}= 0 vs. H_{a}: β_{2}≠ 0 in the model E(Y) = β_{0}+ β_{1 }X_{1}+ β_{3}X_{3}+ β_{2}X_{2}using a t-test. Give the value of the test statistic, the p-value and conclusion. - Using the ANOVA table from part (a), use sequential sums of squares to test H
_{0}: β_{2}= β_{3 }= 0 in the model E(Y) = β_{0}+ β_{1 }X_{1}+ β_{3}X_{3}+ β_{2}X_{2}. Give the test statistic, p-value and conclusion.