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Interpreting the Given Regression Results.

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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?

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a. In case of multiplicative demand function, coefficients represent the percent change in demand due to 1% change in value of independent variable.

In the given model, the coefficient of P is -0.2243. Negative value of coefficient indicates that price and quantity demanded have inverse relationship. It means that, keeping the other factors unchanged, a 1% increase in price would cause 0.2243% decrease in quantity demanded and 1% fall in price would cause 0.2243% increase in quantity demanded .

In the given model, the coefficient of Y is 1.3458. The positive value of the coefficient indicates that income and demand have a direct relationship. It means that, keeping the other factors unchanged, a 1% increase in income would cause a 1.3458% increase in demand and a 1% fall in income would cause a 0.2243% fall in demand.

In the given model, the coefficient of Po is 0.1304. A positive ...

Solution Summary

Solution analyzes the given regression results. It discusses about the price elasticity of demand, relationship between the two goods in consideration and nature of given good based upon the information provided.

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Analyze and interpret the given 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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