A large, national grocery retailer tracks productivity and costs of its facilities closely. Data in the le HW'3-4.txt 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). Fit a regression model to predict Y using only predictors X1 and X2. a) State the estimated equation and interpret the values of 391 and 52. b) Plot the residuals vs. X1X2 to check if the interaction effect is needed. 'What is your conclusion? c) Perform the DW test for autocorrelation among the residuals. What is your conclusion: is the independence assumption violated? (1) Test the overall signicance of the regression model. State the hypotheses, p-value, and conclusion. e) Report and interpret the value of R2. f} Obtain a point estimate, a 95% condence interval for the average labor hours lr' and a 95% prediction interval for Y, when X1 : 302,000 and X; : 7.2