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
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
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.
C. What are expected (average) unit sales and sales revenue in a typical market?
(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
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