A company wants to compare three different point-of-sale promotions for its snack foods. The three promotions are

Question:

A company wants to compare three different point-of-sale promotions for its snack foods. The three promotions are
Promotion 1: Buy two items, get a third free.
Promotion 2: Mail in a rebate for $1.00 with any $2.00 purchase.
Promotion 3: Buy reduced-price multipacks of each snack food.
The company is interested in the average increase in sales volume due to the promotions. Fifteen grocery stores were selected in a targeted market, and each store was randomly assigned one of the promotion types. During the month-long run of the promotions, the company collected data on increase in sales volume (Y, in hundreds of units) at each store, to be gauged against average monthly sales volume (X, in hundreds of units) prior to the promotions. Let Z1 = 1 if promotion type 1, or 0 otherwise. Let Z2 = 1 if promotion type 2, or 0 otherwise. The sample data are shown in the following table.

a. State an ANACOVA regression model for comparing the three promotion types, controlling for average pre-promotion monthly sales.
b. Identify the model that should be used to check whether the ANACOVA model in part (a) is appropriate. Carry out the appropriate test.
c. Using ANACOVA, determine adjusted mean increases in sales volume for the three promotions, and test whether they differ significantly from one another. (Mean pre-promotional average sales volume = 33.6667; unadjusted mean increases in sales volume were 13.4 for promotion 1, 12.4 for promotion 2, and 17.6 for promotion 3.)
Regression of Y on X, Z1, Z2, XZ1, and XZ2