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. 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. 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

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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:

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,…, 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.

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

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

Critical values of F for the 0.01 significance level:
1
2
1 4052.19 4999.52 5403.34
4
5
6
7
10
5624.62 5763.65
5858.97 5928.33 5981.10 6022.50 6055.85
98.50
99.17
29.46
16.69
99.00
99.25
99.30
99.33
99.36
99.37
99.39
99.40
34.12
30.82
28.71
28.24
27.91
27.67
27.49
27.35
27.23
18.00
13.27
4
14.80
10.29
21.20
15.98
15.52
15.21
14.98
14.66
14.55
5
16.26
12.06
9.78
8.45
11.39
10.97
10.67
10.46
10.16
10.05
13.75
10.93
9.15
8.75
8.47
8.26
8.10
7.98
7.87
7
12.25
9.55
7.85
7.46
7.19
6.99
6.84
6.72
6.62
8.
11.26
8.65
7.59
5.81
7.01
6.42
6.63
6.37
6.18
6.03
5.91
9
10.56
8.02
6.99
6.06
5.80
5.61
5.47
5.35
5.26
10
10.04
7.56
6.55
5.99
5.64
5.39
5.20
5.06
4.94
4.85
9.65
9.33
11
7.21
6.22
5.67
5.32
5.07
4.89
4.74
4.63
4.54
12
6.93
5.95
5.41
5.06
4.82
4.64
4.50
4.39
4.30
13
9.07
6.70
5.74
5.21
4.86
4.62
4.44
4.30
4.19
4.10
14
8.86
6.52
5.56
5.04
4.70
4.46
4.28
4.14
4.03
3.94
15
8.68
6.36
5.42
4.56
3.81
4.89
4.77
4.67
4.58
4.32
4.14
4.00
3.90
16
8.53
6.23
5.29
4.44
4.20
4.03
3.89
3.78
3.69
17
8.40
6.11
5.19
4.34
4.10
3.93
3.79
3.68
3.59
18
8.29
8.19
4.25
4.17
3.84
3.77
6.01
5.09
4.02
3.71
3.60
3.51
5.01
3.63
3,56
19
5.93
4.50
3.94
3.52
3.43
20
8.10
8.02
5.85
4.94
4.43
4.10
3.87
3.70
3.46
3.37
21
5.78
4.87
4.37
4.04
3.81
3.64
3.51
3.40
3.31
22
7.95
4.31
4.26
5.72
4.82
3.99
3.76
3.59
3.45
3.35
3.26
23
7.88
5.66
4.77
3.94
3.71
3.54
3.41
3.30
3.21
4.22
4.18
24
7.82
5.61
4.72
4.68
3.90
3.67
3.50
3.36
3.26
3.17
25
7.77
5.57
3.86
3.63
3.46
3.32
3.22
3.13
26
7.72
5.53
4.64
3.82
3.59
3.56
4.14
3.42
3.29
3.18
3.09
27
7.68
5.49
4.60
4.11
3.79
3.39
3.26
3.15
3.06
28
7.64
5.45
4.57
4.07
3.75
3.53
3.36
3.23
3.12
3.03
29
7.60
5.42
4.54
4.05
3.73
3.50
3.33
3.20
3.09
3.01
30
7.56
5.39
4.51
3.70
3.31
4.02
3.99
3.47
3.17
3.07
2.98
31
7.53
5.36
4.48
3.68
3.45
3.28
3.15
3.04
2.96
32
7.50
5.34
4.46
3.97
3.65
3.43
3.26
3.13
3.02
2.93
123

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