Refer to Grocery retailer Problem 6.9.

a. Fit regression model (6.5) to the data for three predictor variables. State the estimated regression function. How are b_l ,b₂ , and b₃ interpreted here?

b. Obtain the residuals and prepare a, box plot of the residuals. What information does this plot provide?

c. Plot the residuals against , X _I, X₂ , X₃, and X _I X₂ on separate graphs. Also prepare a normal probability plot. Interpret the plots and summarize your findings.

d. Prepare a time plot of the residuals. Is there any indication.o1:hat the error terms are correlated? Discuss.

e. Divide the 52 cases into two groups, placing the 26 cases with the smallest fitted values ; into group I and the other 26 cases into group 2. Conduct the Brown-Forsythe test for constancy of the error variance, using α = .01. State the decision rule and conclusion.

Problem 6.9

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 (X_I)' 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).

a. Prepare separate stem-and-leaf plots for the number of cases shipped X_it and the indirect cost of the total hours X_i2. Are there any outlying cases present? Are there any gaps in the data?

b. The cases are given in consecutive weeks. Prepare a time plot for each predictor variable. - What do the plots show?

c. Obtain the scatter plot matrix and the correlation matrix. What information do these diagnostic aids provide here?