A supermarket chain is interested in exploring the relationship between the sales of its store-brand canned vegetables (y), the amount spent on promotion of the vegetables in local newspapers (*1), and the arnount of shelf space allocated to the brand (x2). One of the chain's supermarkets was randomly selected, and over a 20-week period x1 and 42 were varied, as reported in the table. These data are saved in the CANVEG file. Week Sales ($) Advertising Shelf Expenditures ($) Space (sq. ft.) 2,010 1,850 2,400 1,575 3,550 2,015 3,908 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1,870 4,877 2,190 5,005 2,500 3,005 3,480 5,500 1,995 2,390 4,390 2,785 2,989 201 205 355 208 590 397 820 400 997 515 996 625 860 1,012 1,135 635 837 1,200 990 1,205 75 50 75 30 75 50 75 30 75 30 75 50 50 50 75 30 30 SO 30 30 a. Fit the following model to the data: y = Bo to Bix1 + B2.X2 + B3X1X2 + 8 b. Conduct an F-test to investigate the overall useful- ness of this model. Use a = .05. c. Test for the presence of interaction between advertising expenditures and shelf space. Use a = .05. d. Explain what it means to say that advertising expen- ditures and shelf space interact. e. Explain how you could be misled by using a first-or- der model instead of an interaction model to explain how advertising expenditures and shelf cnce sales. £. Based on the type of data collected, comment on the assumption of independent errors. space influ-