# Question

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.

Y Annual restaurant sales (in thousands)

X1 Disposable per capital income (in thousands) of the residents living within 5 miles of a restaurant

X2 Population (in thousands) within a 5-mile radius of a restaurant

X3 Number of competing restaurants within a 5-mile radius

The following information was obtained from the regression analysis:

Multiple R: 0.92

R-Square: 0.85

Std. Error of Est.: 0.40

Analysis of Variance

DF Sum Squares Mean Sqr. F-Stat

Regression 3 220 73.3 18.2

Residual 36 60 1.7

Variable Coefficient Std. Error T-Value

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?

Y Annual restaurant sales (in thousands)

X1 Disposable per capital income (in thousands) of the residents living within 5 miles of a restaurant

X2 Population (in thousands) within a 5-mile radius of a restaurant

X3 Number of competing restaurants within a 5-mile radius

The following information was obtained from the regression analysis:

Multiple R: 0.92

R-Square: 0.85

Std. Error of Est.: 0.40

Analysis of Variance

DF Sum Squares Mean Sqr. F-Stat

Regression 3 220 73.3 18.2

Residual 36 60 1.7

Variable Coefficient Std. Error T-Value

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?

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