13.7 You have been asked to develop a multiple regression model to predict per capita sales of cold cereal in cities with populations over 100,000. As a first step you hold a meeting with the key marketing managers that have experience with cereal sales. From this meeting you discover that per capita sales are expected to be influenced by the cereal price, price of competing cereals, mean per capita income, percentage of college graduates, mean annual temperature, and mean annual rainfall. You also learn that the linear relationship between price and per capita sales is expected to have a different slope for cities east of the Mississippi River.

Per capita sales are expected to be higher in cities with high and low per capita income compared to cities with intermediate per capita income. Per capita sales are also expected to be different in the following four sectors of the country: Northwest, Southwest, Northeast, Southeast.
Prepare a model specification whose coefficients can be estimated using multiple regression. Define each variable completely and indicate the mathematical form of the model. Discuss your specification, indicate which variables you expect to be statistically significant, and explain the rationale for your expectation.