Chez Henri is a restaurant chain that operates in 40 different cities. It hired an economist to estimate the factors affecting the demand for its sales. The following equation was estimated using cross sectional data from each of its 40 restaurants.
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Y
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Annual restaurant sales (in thousands)
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X1
|
Disposable per capital income (in thousands) of the residents living within 5 miles of a restaurant
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X2
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Population (in thousands) within a 5-mile radius of a restaurant
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X3
|
Number of competing restaurants within a 5-mile radius
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The following information was obtained from the regression analysis:
Multiple R: 0.92
R-Square: 0.85
Std. Error of Est.: 0.40
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Analysis of Variance
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|
|
|
|
|
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DF
|
Sum Squares
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Mean Sqr.
|
F-Stat
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|
Regression
|
3
|
220
|
73.3
|
18.2
|
|
Residual
|
36
|
60
|
1.7
|
|
|
|
|
|
|
|
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Variable
|
Coefficient
|
Std. Error
|
T-Value
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|
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Constant
|
0.4
|
0.2
|
2.0
|
|
|
X1
|
0.01
|
0.004
|
2.5
|
|
|
X2
|
0.02
|
0.015
|
1.3
|
|
|
X3
|
-20.2
|
4.50
|
-4.6
|
|
Answer the following questions:
a. Give the estimated demand equation for predicting restaurant sales
b. Provide an interpretation for each of the regression coefficients
c. Which of the coefficients are statistically significant and which are not? Explain
d. What percent of variation are restaurant sales explained by this equation?