# Interpreting the given regression results

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 of Squares Mean Square 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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#### Solution Preview

a. Give the estimated demand equation for predicting restaurant sales.

Y=0.4+0.01*X1+0.02*X2-20.2*X3

b. Provide an interpretation for each of the regression coefficients.

Coefficient of X1 is a positive value. It shows that Y and X1 has direct relationship which shows that Y will increase for any increase in X1 and Y will decrease for any decrease in X1. Its value is 0.01. It means that for every one thousand increase in per disposable capita income of the ...

#### Solution Summary

Solution determines the estimated demand equation and interprets the obtained regression coefficients and parameters.

Interpreting the Given Regression Results.

A multiplicative demand function of the form: Qd = a*P^b1*Y^b2*Po^b3 is estimated using cross-sectional data and 224 observations. The regression results were as follows:

Constant (a) Price(P) Income(Y) Price of other good (Po)

Coefficient 0.02248 -0.2243 1.3458 0.1034

Standard Error 0.01885 0.0563 0.5012 0.8145

a. How should the coefficients be interpreted in this equation?

b. What is the quantity demanded if price is $10, income is $9000, and price of the other good is $15?

c. Is demand elastic or inelastic? How can you tell? What impact would a price increase have on total revenue and on total profit?

d. How are these two goods related? Should the firm be concerned about a change in the price of the other good?

e. Is this product a luxury, necessity, or inferior good?