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Demand Estimation for The San Francisco Bread Company Consider the hypothetical example of The San Francisco Bread Company, a San Francisco-based chain of bakery/cafes.  San Francisco Bread Company 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 the attached Table 1. The following regression equation was fit to these data:                     Qi = b0 + b1Pi + b2Pxi + b3Adi + b4Ii + uit. Where:            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 service area,                         ui is a residual (or disturbance) term.  The subscript indicates the regional market (i = 1,…, 30) from which the observation was taken.  Least squares estimation of the regression equation on the basis of the 30 data cross sectional observations resulted in the estimated regression coefficients and other statistics as shown in Table 2. A. Describe the economic meaning for 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 (average) unit sales and sales revenue in a typical market? D. Describe the level statistical significance for each individual independent variable included in the San Francisco demand equation. E. Interpret each coefficient and its impact on the dependent variable. F. Conduct a F-test for the set of coefficients in the equation to determine if they are significant at the 95 and 99 percent levels. (See Below for Data)  Table 1 - San Francisco Bread Company (30 Markets) Market   Demand    Price    Competitor    Advertising    Income Market        (Q)          (P)        Price(Px)            (Ad)              (I) 1              596,611     7.62         6.52             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     5.96         5.52             220,215        49,755 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            519,886     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             238,756        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 Mean       598,412     6.93         6.16             244,649        51,044

Demand Estimation for The San Francisco Bread Company Consider the hypothetical example of The San Francisco Bread Company, a San Francisco-based chain of bakery/cafes.  San Francisco Bread Company 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 the attached Table 1. The following regression equation was fit to these data:                     Qi = b0 + b1Pi + b2Pxi + b3Adi + b4Ii + uit. Where:            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 service area,                         ui is a residual (or disturbance) term.  The subscript indicates the regional market (i = 1,…, 30) from which the observation was taken.  Least squares estimation of the regression equation on the basis of the 30 data cross sectional observations resulted in the estimated regression coefficients and other statistics as shown in Table 2. A. Describe the economic meaning for 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 (average) unit sales and sales revenue in a typical market? D. Describe the level statistical significance for each individual independent variable included in the San Francisco demand equation. E. Interpret each coefficient and its impact on the dependent variable. F. Conduct a F-test for the set of coefficients in the equation to determine if they are significant at the 95 and 99 percent levels. (See Below for Data)  Table 1 - San Francisco Bread Company (30 Markets) Market   Demand    Price    Competitor    Advertising    Income Market        (Q)          (P)        Price(Px)            (Ad)              (I) 1              596,611     7.62         6.52             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     5.96         5.52             220,215        49,755 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            519,886     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             238,756        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 Mean       598,412     6.93         6.16             244,649        51,044

EBK HEALTH ECONOMICS AND POLICY
EBK HEALTH ECONOMICS AND POLICY
7th Edition
ISBN:9781337668279
Author:Henderson
Publisher:Henderson
Chapter6: Population Health
Section: Chapter Questions
Problem 9QAP
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Demand Estimation for The San Francisco Bread Company

Consider the hypothetical example of The San Francisco Bread Company, a San Francisco-based chain of bakery/cafes.  San Francisco Bread Company 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 the attached Table 1.

The following regression equation was fit to these data:

                    Qi = b0 + b1Pi + b2Pxi + b3Adi + b4Ii + uit.

Where:            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 service area,

                        ui is a residual (or disturbance) term. 

The subscript indicates the regional market (i = 1,…, 30) from which the observation was taken.  Least squares estimation of the regression equation on the basis of the 30 data cross sectional observations resulted in the estimated regression coefficients and other statistics as shown in Table 2.

A. Describe the economic meaning for 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 (average) unit sales and sales revenue in a typical market?

D. Describe the level statistical significance for each individual independent variable included in the San Francisco demand equation.

E. Interpret each coefficient and its impact on the dependent variable.

F. Conduct a F-test for the set of coefficients in the equation to determine if they are significant at the 95 and 99 percent levels.

(See Below for Data) 

Table 1 - San Francisco Bread Company (30 Markets)

Market   Demand    Price    Competitor    Advertising    Income

Market        (Q)          (P)        Price(Px)            (Ad)              (I)

1              596,611     7.62         6.52             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     5.96         5.52             220,215        49,755

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            519,886     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             238,756        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

Mean       598,412     6.93         6.16             244,649        51,044

Table of critical values for the F distribution (for use with ANOVA): How to use this table: There are two tables here. The first one gives critical values of F at the p = 0.05 level of significance. The second table gives critical values of F at the p = 0.01 level of significance. 1. Obtain your F-ratio. This has (x,y) degrees of freedom associated with it. 2. Go along x columns, and down y rows. The point of intersection is your critical F-ratio. 3. If your obtained value of F is equal to or larger than this critical F-value, then your result is significant at that level of probability. An example: I obtain an F ratio of 3.96 with (2, 24) degrees of freedom. I go along 2 columns and down 24 rows. The critical value of Fis 3.40. My obtained F-ratio is larger than this, and so I conclude that my obtained F-ratio is likely to occur by chance with a pc.05. Critical values of F for the 0.05 significance level: 1 2 3 4 5 6 7 8 10 1 161.45 199.50 215.71 224.58 230.16 233.99 236.77 238.88 240.54 241.88 18.51 19.00 19.16 19.25 19.30 19.33 19.35 19.37 19.39 19.40 3 10.13 9.55 9.28 9.12 9.01 8.94 8.89 8.85 8.81 8.79 7.71 6.94 6.59 6.39 6.26 6.16 6.09 6.04 6.00 5.96 6.61 5.79 5.41 5.19 5.05 4.95 4.88 4.82 4.77 4.74 6 5.99 5.14 4.76 4.53 4.39 4.28 4.21 4.15 3.73 4.10 4.06 7 5.59 4.74 4.35 4.12 3.97 3.87 3.79 3.68 3.64 8 5.32 4.46 4.07 3.84 3.69 3.48 3.33 3.20 3.11 3.58 3.50 3.44 3.39 4.26 4.10 3.63 3.48 3.35 3.14 2.98 5.12 3.86 3.37 3.29 3.23 3.18 10 4.97 3.71 3.22 3.14 3.07 3.02 11 4.84 3.98 3.59 3.36 3.10 3.01 2.95 2.90 2.85 12 4.75 3.89 3.49 3.26 3.00 2.91 2.85 2.80 2.75 13 4.67 3.81 3.41 3.18 3.03 2.92 2.83 2.77 2.71 2.67 14 4.60 3.74 3.34 3.11 2.96 2.85 2.76 2.70 2.65 2.60 15 4.54 3.68 3.29 3.06 2.90 2.79 2.71 2.64 2.59 2.54 16 4.49 3.63 3.24 3.01 2.85 2.74 2.66 2.59 2.54 2.49 2.45 17 4.45 3.59 3.20 2.97 2.81 2.70 2.61 2.55 2.49 18 4.41 3.56 3.16 2.93 2.77 2.66 2.58 2.51 2.46 2.41 19 4.38 3.52 3.13 2.90 2.74 2.63 2.54 2.48 2.42 2.38 20 4.35 3.49 3.10 2.87 2.71 2.60 2.51 2.45 2.39 2.35 21 4.33 3.47 3.07 2.84 2.69 2.57 2.49 2.42 2.37 2.34 2.32 22 4.30 3.44 3.05 2.82 2.66 2.55 2.46 2.40 2.30 23 4.28 3.42 3.03 3.01 2.80 2.64 2.53 2.44 2.38 2.32 2.30 2.28 2.28 2.26 24 4.26 3.40 2.78 2.62 2.51 2.42 2.36 25 4.24 3.39 2.99 2.76 2.60 2.49 2.41 2.34 2.24 26 4.23 3.37 2.98 2.74 2.59 2.47 2.39 2.32 2.27 2.22 27 4.21 3.35 2.96 2.73 2.57 2.46 2.37 2.31 2.25 2.20 28 4.20 3.34 2.95 2.71 2.56 2.45 2.36 2.29 2.24 2.19 29 4.18 3.33 2.93 2.70 2.55 2.43 2.35 2.28 2.22 2.18 30 4.17 3.32 2.92 2.69 2.53 2.42 2.33 2.32 2.27 2.21 2.17 31 4.16 3.31 2.91 2.68 2.52 2.41 2.26 2.20 2.15 32 4.15 3.30 2.90 2.67 2.51 2.40 2.31 2.24 2.19 2.14 33 4.14 3.29 2.89 2.66 2.50 2.39 2.30 2.24 2.18 2.13 34 4.13 3.28 2.88 2.65 2.49 2.38 2.29 2.23 2.17 2.12 35 4.12 3.27 2.87 2.64 2.49 2.37 2.29 2.22 2.16 2.11
Transcribed Image Text:Table of critical values for the F distribution (for use with ANOVA): How to use this table: There are two tables here. The first one gives critical values of F at the p = 0.05 level of significance. The second table gives critical values of F at the p = 0.01 level of significance. 1. Obtain your F-ratio. This has (x,y) degrees of freedom associated with it. 2. Go along x columns, and down y rows. The point of intersection is your critical F-ratio. 3. If your obtained value of F is equal to or larger than this critical F-value, then your result is significant at that level of probability. An example: I obtain an F ratio of 3.96 with (2, 24) degrees of freedom. I go along 2 columns and down 24 rows. The critical value of Fis 3.40. My obtained F-ratio is larger than this, and so I conclude that my obtained F-ratio is likely to occur by chance with a pc.05. Critical values of F for the 0.05 significance level: 1 2 3 4 5 6 7 8 10 1 161.45 199.50 215.71 224.58 230.16 233.99 236.77 238.88 240.54 241.88 18.51 19.00 19.16 19.25 19.30 19.33 19.35 19.37 19.39 19.40 3 10.13 9.55 9.28 9.12 9.01 8.94 8.89 8.85 8.81 8.79 7.71 6.94 6.59 6.39 6.26 6.16 6.09 6.04 6.00 5.96 6.61 5.79 5.41 5.19 5.05 4.95 4.88 4.82 4.77 4.74 6 5.99 5.14 4.76 4.53 4.39 4.28 4.21 4.15 3.73 4.10 4.06 7 5.59 4.74 4.35 4.12 3.97 3.87 3.79 3.68 3.64 8 5.32 4.46 4.07 3.84 3.69 3.48 3.33 3.20 3.11 3.58 3.50 3.44 3.39 4.26 4.10 3.63 3.48 3.35 3.14 2.98 5.12 3.86 3.37 3.29 3.23 3.18 10 4.97 3.71 3.22 3.14 3.07 3.02 11 4.84 3.98 3.59 3.36 3.10 3.01 2.95 2.90 2.85 12 4.75 3.89 3.49 3.26 3.00 2.91 2.85 2.80 2.75 13 4.67 3.81 3.41 3.18 3.03 2.92 2.83 2.77 2.71 2.67 14 4.60 3.74 3.34 3.11 2.96 2.85 2.76 2.70 2.65 2.60 15 4.54 3.68 3.29 3.06 2.90 2.79 2.71 2.64 2.59 2.54 16 4.49 3.63 3.24 3.01 2.85 2.74 2.66 2.59 2.54 2.49 2.45 17 4.45 3.59 3.20 2.97 2.81 2.70 2.61 2.55 2.49 18 4.41 3.56 3.16 2.93 2.77 2.66 2.58 2.51 2.46 2.41 19 4.38 3.52 3.13 2.90 2.74 2.63 2.54 2.48 2.42 2.38 20 4.35 3.49 3.10 2.87 2.71 2.60 2.51 2.45 2.39 2.35 21 4.33 3.47 3.07 2.84 2.69 2.57 2.49 2.42 2.37 2.34 2.32 22 4.30 3.44 3.05 2.82 2.66 2.55 2.46 2.40 2.30 23 4.28 3.42 3.03 3.01 2.80 2.64 2.53 2.44 2.38 2.32 2.30 2.28 2.28 2.26 24 4.26 3.40 2.78 2.62 2.51 2.42 2.36 25 4.24 3.39 2.99 2.76 2.60 2.49 2.41 2.34 2.24 26 4.23 3.37 2.98 2.74 2.59 2.47 2.39 2.32 2.27 2.22 27 4.21 3.35 2.96 2.73 2.57 2.46 2.37 2.31 2.25 2.20 28 4.20 3.34 2.95 2.71 2.56 2.45 2.36 2.29 2.24 2.19 29 4.18 3.33 2.93 2.70 2.55 2.43 2.35 2.28 2.22 2.18 30 4.17 3.32 2.92 2.69 2.53 2.42 2.33 2.32 2.27 2.21 2.17 31 4.16 3.31 2.91 2.68 2.52 2.41 2.26 2.20 2.15 32 4.15 3.30 2.90 2.67 2.51 2.40 2.31 2.24 2.19 2.14 33 4.14 3.29 2.89 2.66 2.50 2.39 2.30 2.24 2.18 2.13 34 4.13 3.28 2.88 2.65 2.49 2.38 2.29 2.23 2.17 2.12 35 4.12 3.27 2.87 2.64 2.49 2.37 2.29 2.22 2.16 2.11
SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square 0.91280128 0.83320617 0.80651916 Standard Error 14865.8981 Observations 30 ANOVA df MS F Significance F Regression 4 27599092617 6.9E+09 31.22141 2.16137E-09 Residual 25 5524873170 2.21E+08 Total 29 33123965787 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% 272840.0973 Intercept X Variable 1 X Variable 2 X Variable 3 X Variable 4 128740.913 69966.78194 1.840029 0.077667 -15358.27043 272840.1 -15358.27043 -19864.901 15484.5544 4102.111195 -4.8426 5.6E-05 -28313.35155 -11416.451 -28313.35155 -11416.45108 3459.193122 4.476349 0.000145 8360.217835 22608.891 8360.217835 22608.89104 0.26006502 0.093982856 2.767154 0.010486 0.066503838 0.4536262 0.066503838 0.453626199 8.78206805 1.016513087 8.639405 5.62E-09 6.688521625 10.875614 6.688521625 10.87561448
Transcribed Image Text:SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square 0.91280128 0.83320617 0.80651916 Standard Error 14865.8981 Observations 30 ANOVA df MS F Significance F Regression 4 27599092617 6.9E+09 31.22141 2.16137E-09 Residual 25 5524873170 2.21E+08 Total 29 33123965787 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% 272840.0973 Intercept X Variable 1 X Variable 2 X Variable 3 X Variable 4 128740.913 69966.78194 1.840029 0.077667 -15358.27043 272840.1 -15358.27043 -19864.901 15484.5544 4102.111195 -4.8426 5.6E-05 -28313.35155 -11416.451 -28313.35155 -11416.45108 3459.193122 4.476349 0.000145 8360.217835 22608.891 8360.217835 22608.89104 0.26006502 0.093982856 2.767154 0.010486 0.066503838 0.4536262 0.066503838 0.453626199 8.78206805 1.016513087 8.639405 5.62E-09 6.688521625 10.875614 6.688521625 10.87561448
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