A manufacturer of breakfast cereal was interested in assessing the

impact of price and display type on sales of their most popular brand. They decided to conduct a factorial experiment using three levels of price: high, medium and low, and three levels of display: top, middle, bottom. The response was the sales during a week in each supermarket. The manufacturer selected 27 supermarkets and randomly assigned the stores so that each of the nine treatment combinations was repeated 3 times. The investigators used a factorial model of the form = + + + where ~ (0, 2), i=high, medium, low; j=top, middle, bottom; k=1,2,3 for the replication and ∑ = 0 and ∑ = 0.