Assignment: Demand Estimation for the San Francisco Bread Company

Consider the hypothetical example of the San Francisco Bread Company, a chain of bakery/cafes.  SF Bread Co. has initiated an empirical estimation of customer traffic at 35 regional locations to help the firm formulate pricing and promotional plans for the coming year.  Annual operating data for the 35 outlets appear in the attached Table 1.

The following regression equation was fit to these data:

Q_i = b₀ + b₁P_i + b₂P_xi + b₃Ad_i + b₄I_i + u_it.

Where: Q is the number of meals served,

P is the average price per meal (customer ticket amount, in dollars),

P_x is the average price charged by competitors (in dollars),

Ad is the local advertising budget for each outlet (in dollars),

I is the average income per household in each outlet's service area,

u_i is a residual (or disturbance) term. 

The subscript indicates the regional market (i = 1,..., 35) from which the observation was taken.  Least squares estimation of the regression equation on the basis of the 35 data cross sectional observations resulted in the estimated regression coefficients and other statistics as shown in Table 2.

A. Describe the economic meaning for the individual independent variables included in the San Francisco Bread Company demand equation.  Interpret each estimated coefficient and its impact on the dependent variable (number of meals served)?

B. Using the estimates from the regression analysis, compute the expected (average) unit sales and average sales revenue for a typical market? 

C. From the regression estimates develop a demand equation for SF Bread Co.  Use the coefficient averages (bottom on Table 1) for the non-price variables to develop the demand equation.

D. Develop the null and alternative hypothesis for each of the 4 independent variables. Briefly describe when is appropriate to use a one-tail test relative to a two-tailed t-test?

E. Use a t-test to determine the level statistical significance for each individual independent variable included at the 95 and 99 percent confidence levels. 

F. Briefly explain the terminology of the coefficient of determination (R²).

G. Develop the null and alternative hypothesis and conduct an F-test for the complete set of coefficients in the equation to determine the significance at the 95 and 99 percent levels.