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2. A large, national grocery retailer tracks productivity and costs of its facilities closely. 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 O otherwise (X3), and the total labor hours (Y). We were told to analyze the relationship between the total labor hours and the number of cases shipped, the indirect costs of the total labor hours, while controlling for whether the week has a holiday, using an ordinary multiple regression model with interaction terms between the number of cases shipped, the indirect costs of the total labor hours and the qualitative predictor and with independent normally distributed error terms with zero mean and constant variance. The partial data for a total 52 weeks from a single distribution center are shown as follows. Each data point for each variable represents one week of activity. Y X1 X2 X3 4496 328476 6.2 o 317164 4.61 4945 265518 8.61 4499 290455 7.99 0 Here are some of the summary statistics and computer output. SSTO= 3162136, SSR(X1,X2,X3,x1x3,X2X3)= 2211006 and SSE(X1,X2,X3)= 985530. Parameter Estimates Variable DF Parameter Standard Estimate Error Intercept 1 4270.89343 231.92264 x1 1 0.00079278 0.00041797 x2 1 -29.89748 26.68872 X3 1 164.18381 448.62207 X1X3 1 -0.00024700 0.00088132 X2X3 70.77517 54.87108 a) Write down the first 3 rows of the design matrix (10 points); b) Write down the estimated regression equations/models for the total labor hours in a week without a holiday (10 points); c) Is the relationship between the total labor hours and the indirect costs of the total labor hours depends on whether the weeks has a holiday, while controlling for number of cases shipped. Conduct a hypothesis testing. Use a = .10 (15 points); d) Is there a significant difference in the total labor hours between a week with a holiday and a week without a holiday when there is no cases shipped and no indirect cost? Conduct a hypothesis testing. Use a = .05 (15 points)