R problem. Grocery Retailer A large, national grocery retailer tracks productivity and costs of its facilities closely. Data below 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 ( otherwise (X3), and the total labor hours (Y). Assume the following regression model Yi = Bo+ BIXa+ B2X2 + B3Xate, i=1,...,52 where So, B1, 82 and 83 are unknown constants and e; ~ N(0, o'), a > 0 holds true. a. Obtain the scatter plot matrix and the correlation matrix. b. Plot the residuals against fitted values, X], X2, and X3 on separate graphs. In- terpret the plots and summarize your findings. c. Test whether there is a regression relation, using level of significance 0.05. State the null and alternative hypotheses, decision rule, and conclusion. What does your test result imply about 81, 82, and ; What is the P-value of the test? d. Compute R2, adjusted R', Cp, AIC and BIC for the following models: Model 1: Y = BotE Model 2: Y = Bo + BIXIte Model 3: Y = Bo + PIXI+ B2X2 +E Model 4: Y = Bo+ BIX1 + BzX2 + B3X3 + E Model 5: Y = Bo + BIX1+ BzX2 + B3X3 + PIXI * X2 + e Model 6: Y = Bo+ BIX1+ B2X2 + ByX3 + B,X] * X3 + E Model 7: Y = Bo + BIXi+ 82X2 + 83X3 + 86.X2 * X3 + e On the basis of the analyses above, identify the most appropriate model