The following question refers to this regression equation. (Standard errors in p

Question

The following question refers to this regression equation. (Standard errors in parentheses)

Qd= 15 - 10 P + 1.5 Adv + 0.4 Px + 2 I

(5.23) (2.29) (0.525) (1.75) (1.5)

R^2 = 0.65

N = 120

F = 35.25

Standard error of Y estimate = 0.565

Qd = Quantity demanded

Consider the case when:

P = Price = 7

Adv = Advertising expense = 54

Px = price of competitor's good = 8

I = average monthly income = 4

a. Calculate the elasticity for each variable at that point and briefly comment on what information this gives you for each variable.

b. Should this firm be concerned if macroeconomic forecasters predict a recession? Explain your answer.

Explanation / Answer

R^2 = 0.65. This signifies that the 65% variation in the dependent variable which is the quantity demanded is explained by the independent variables which are price, adv, px and I. Now using the F table if you look at the p-value for a given level of significance you will see that this p<0.05 and thus the overall model is significant.

now to check the individual significance of the varibles use the t statistic (t -table)

Again for all the variables p<0.05 so all are significant.

So this can answer you question 1

the elasticity or inelasticity will depend on the sign of the coefficient of that particular variable

Accordingly to calculate the value

One by one keep one variable constant and substitute the value of others

This way you can estimate the change in demand due to a unit change in a particular value. which is called the elasticity.

for your second question

Yes a recession would be a concern for the firm

Due to a recession the prices will go up. From the equation it is clear that demand is inversly related to price so demand will decrease with an increase in price

Also the average monthly income will decrease due to recession and accordingly the demand will decrease

The decrease in demand is definately a concern for the firm

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