CASE Study Demand Estimation for The San Francisco Bread Co.

Given the highly competitive nature of the restaurant industry, individual companies cautiously guard operating information for individual outlets. As a result, there are no publicly available data that can be used to estimate important operating relationships. To see the process that might be undertaken to develop a better understanding of store location decisions, consider the hypothetical example of The San Francisco Bread Co., a San Francisco-based chain of bakery-cafes. San Francisco has initiated an empirical estimation of customer traffic at 30 regional locations to help the firm formulate pricing and promotional plans for the coming year. Annual operating data for the 30 outlets appear in Table 3.5.

Table 3.5 The San Francisco Bread

Market Demand (Q) Price (P) Competitor Price (Px) Advertising (Ad) Income (I)
1 596,611 7.62 6.54 200,259 54,880
2 596,453 7.29 5.01 204,559 51,755
3 599,201 6.66 5.96 206,647 52,955
4 572,258 8.01 5.30 207,025 54,391
5 558,142 7.53 6.16 207,422 48,491
6 627,973 6.51 7.56 216,224 51,219
7 593,024 6.20 7.15 217,954 48,685
8 565,004 7.28 6.97 220,139 47,219
9 596,254 5.95 5.52 220,215 49,775
10 652,880 6.42 6.27 220,728 54,932
11 596,784 5.94 5.66 226,603 48,092
12 657,468 6.47 7.68 228,620 54,929
13 519,866 6.99 5.10 230,241 46,057
14 612,941 7.72 5.38 232,777 55,239
15 621,707 6.46 6.20 237,300 53,976
16 597,215 7.31 7.43 238,765 49,576
17 617,427 7.36 5.28 241,957 55,454
18 572,320 6.19 6.12 251,317 48,480
19 602,400 7.95 6.38 254,393 53,249
20 575,004 6.34 5.67 255,699 49,696
21 667,581 5.54 7.08 262,270 52,600
22 569,880 7.89 5.10 275,588 50,472
23 644,684 6.76 7.22 277,667 53,409
24 605,468 6.39 5.21 277,816 52,660
25 599,213 6.42 6.00 279,031 50,464

26 610,735 6.82 6.97 279,934 49,525
27 603,830 7.10 5.30 287,921 49,489
28 617,803 7.77 6.96 289,358 49,375
29 529,009 8.07 5.76 294,787 48,254
30 573,211 6.91 5.96 296,246 46,017
Average 598,412 6.93 6.16 244,649 51,044
The following regression equation was fit to these data:

Q is the number of meals served, P is the average price per meal (customer ticket amount, in dollars), Px 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 immediate service area, and is a residual (or disturbance) term. The subscript iindicates the regional market from which the observation was taken. Least squares estimation of the regression equation on the basis of the 30 data observations resulted in the estimated regression coefficients and other statistics shown in Table 3.6.

A. Describe the economic meaning and statistical significance of each individual independent variable included in the San Francisco demand equation.
B. Interpret the coefficient of determination (R2) for the San Francisco demand equation.
C. What are expected unit sales and sales revenue in a typical market?
D. To illustrate use of the standard error of the estimate statistic, derive the 95 percent confidence interval for expected unit sales and total sales revenue in a typical market.
Table 3.6 Estimated Demand Function for The San Francisco Bread

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