12.158Promotion of supermarket vegetables. 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(x1),and the amount of shelf space allocated to the brand(x2).One of the chain's supermarkets was randomly selected, and over a 20-week periodx1andx2were varied, as reported in the table.

1. Fit the following model to the data:

y=0+1x1+2x2+3x1x2+

1. Conduct anF-test to investigate the overall usefulness of this model. Use =.05.
2. Test for the presence of interaction between advertising expenditures and shelf space. Use =.05.
3. Explain what it means to say that advertising expenditures and shelf space interact.
4. Explain how you could be misled by using a first-order model instead of an interaction model to explain how advertising expenditures and shelf space influence sales.
5. Based on the type of data collected, comment on the assumption of independent errors.