1. (4x5 = 20 points) Consider the "Grocery Retailer" 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 (Xi), the indirect costs of the total labor hours as a percentage (X), a qualitative predictor called holiday that is coded 1 if the week has a holiday and 0 otherwise (X,), and the total labor hours (Y). [We'll cover qualitative predictors formally in Lesson 8, but this question does not require knowledge of Lesson 8 to answer.] a) Obtain the ANOVA table that decomposes the regression sum of squares into sequential sums of squares associated with Xi; with Xs given Xi; and with X2 given X, and Xs. State their values along with the associated degrees of freedom. [Hint: Click "Options" to switch between adjusted and sequential sums of squares and click "Model" to change the order the predictors enter the model.] b) Test whether X, can be dropped from the regression model given that X, and X, are retained in the model. Derive the appropriate F test statistic from values in the ANOVA table from part (a) and use a = 0.05. Remember to state the hypotheses, decision rule, p-value, and conclusion. c) Test Ho: B2 = 0 vs. H.: B2 = 0 in the model E(Y) = Bo + BIX, + B3 Xs + Bz X2 using a t-test and o = 0.05. Use the regression output from part (a) to state the value of the test statistic, decision rule, p-value, and conclusion. d) Test Ho: B2 = B3 = 0 in the model E(Y) = Bo + B1X1 + B3 X3 + Bz X2. Derive the appropriate F test statistic from values in the ANOVA table from part (a) and use a = 0.05. Remember to state the hypotheses, decision rule, p-value, and conclusion