Question: Modeling product sales. A company wants to model the total weekly sales, y, of its product as a function of the variables packaging and location. Two types of packaging, P₁ and P₂, are used in each of four locations, L₁, L₂, L₃, and L₄.

(a) Write a main effects model to relate E(y) to packaging and location. What implicit assumption are we making about the interrelationships between sales, packaging, and location when we use this model?

(b) Now write a model for E(y) that includes interaction between packaging and location. How many parameters are in this model (remember to include β0)? Compare this number to the number of packaging-location combinations being modeled.

(c) Suppose the main effects and interaction models are fit for 40 observations on weekly sales. The values of SSE are

SSE for main effects model = 422.36

SSE for interaction model = 346.65

Determine whether the data indicate that the interaction between location and packaging is important in estimating mean weekly sales. Use α = .05. What implications does your conclusion have for the company's marketing strategy?