A fast-food restaurant chain whose menu features hamburgers and chicken sandwiches is about to add a fish sandwich to its menu. There was considerable debate among the executives about the likely demand and what the appropriate price should be. A recently hired economics graduate observed that the demand curve would reveal a great deal about the relationship between price and demand. She convinced the executives to conduct an experiment. A random sample of 20 restaurants was drawn. The restaurants were almost identical in terms of sales and in the demographics of the surrounding area. At each restaurant, the fish sandwich was sold at a different price. The number of sandwiches sold over a 7-day period and the price were recorded. A first-order model and a second-order model were proposed.

a. Write the equation for each model.

b. Use regression analysis to estimate the coefficients and other statistics for each model.

c. Which model seems to fit better? Explain.

d. Use the better model to calculate the point prediction for weekly sales when the price is $2.95.