# Interpreting Regression and Elasticity Coefficients

We believe that the quantity of hamburger (Qh) purchased within a market is a function of its own price (Ph), the price of chicken (Pc), advertising expenditures (A) and household disposable income (I). Using data available to the research team, we have estimated the following linear regression relationship:

Qh = 205.2 - 200*Ph + 100*Pc + 0.023*A + 0.0005*I

(a) How might we interpret the coefficients in the estimated regression?

(b) What is the forecasted demand for hamburger when Ph is $1.00, Pc is $1.20, A is $5,000 and I is $20,000?

(c) Calculate the own price elasticity for hamburger. If price were to decrease by 1% would the total revenue for hamburger increase or decrease? Explain.

(d) Calculate the cross price elasticity with respect to chicken price, the advertising elasticity and the income elasticity using the information listed and calculated in (b). Interpret the economic meaning of these measures.

(e) Which of the explanatory variable has the greatest impact on hamburger demand? Explain.

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#### Solution Preview

In the example, we believe that the quantity of hamburger (Qh) purchased within a market is a function of its own price (Ph), the price of chicken (Pc), advertising expenditures (A) and household disposable income (I). Using data available to the research team, we have estimated the following linear regression relationship:

Qh = 205.2 - 200*Ph + 100*Pc + 0.023*A + 0.0005*I

(a) How might we interpret the coefficients in the estimated regression?

Coefficient of Ph is negative. It indicates that price and quantity demanded for hamburger has inverse relationship. Quantity demanded will increase in case price falls and quantity demanded will decrease in case price rises. For an increase of one unit in own price, quantity demanded for hamburger will decrease by 200 units. For a decrease of 1 unit in own price, quantity demanded for hamburgers will increase by 200 units.

Coefficient of A is positive. It indicates that advertising expenditure and quantity demanded for hamburger has direct relationship in the given case. Quantity demanded will increase in case their advertising expense increases and quantity demanded will decrease in case advertising expense decreases. For an increase of 1 unit in advertising expenditure, quantity demanded will increase by 0.023 units. For a decrease of 1 unit in advertising expenditure, quantity demanded will decrease by 0.023 units.

Coefficient of I is positive. It indicates that disposable income level of consumers and ...

#### Solution Summary

Solution interprets the coefficients in the given regression equation. It also calculates elasticity of demand with respect to each variable and discusses its implications.

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?