13.5 Sharon Parsons, president of Gourmet Box Mini Pizza, has asked for your assistance in developing a model that predicts the demand for the new snack lunch pizza named Pizza1. This product competes in a market with three other brands that are named B2, B3, and B4 for identification. At present the products are sold by three major distribution chains, identified as 1, 2, and 3. These three chains have different market sizes, and, thus, sales for each distributor are likely to be different. The data file Market contains weekly data collected over the past 52 weeks from the three distribution chains. The variables in the data file are defined next.

Use multiple regression to develop a model that predicts the quantity of Pizza1 sold per week by each distributor. The model should contain only important predictor variables.

Distributor Numerical identifier of the distributor 1, 2, or 3 Weeknum Sequential number of the week in which data were collected Sales Pizza1 Number of units of Pizza1 sold by the distributor during the week Price Pizza1 Retail price for Pizza1 charged by the distributor during that week Promotion Level of promotion for the week, designated as 0, no promotion; 1, television ad; 2, store display; 3, both television and store display Sales B2 Number of units of brand 2 sold by the distributor during the week Price B2 Retail price for brand 2 charged by the distributor during that week Sales B3 Number of units of brand 3 sold by the distributor during the week Price B3 Retail price for brand 3 charged by the distributor during that week Sales B4 Number of units of brand 4 sold by the distributor during the week Price B4 Retail price of brand 4 charged by the distributor during that week