Question

How might a manager use the information included in the regression equation shown below?

Check all that apply.

Standard errors are in parentheses. Q = 8,400 - 10 P + 5 A + 4 Px + 0.05 I

(1,750) (2.25) (1.36) (2.15) (0.01) R2 = 0.75, N = 120

where Q=Quantity demanded; P=Price; A=Advertising expenditures, in thousands; Px=Price of competitor's good; I=Average monthly income

A. The R2 can be used to determine if consumers are very responsive to price changes.

B.The coefficient on advertising can be used to approximate the impact of a change in advertising expenditure on quantity demanded.

C.The constant term "8400" can be used to determine the minimum quantity needed to make entry into this industry sustainable.

D.The coefficient on income can be used to approximate the impact of a recession on quantity demanded.

Answer 1

Let's first discuss what is a regression analysis. In simple terms, regression analysis is where we predict a particular datapoint (called dependent variable, in our case Q, quantity demanded) based on other datapoints (called independednt variables, in our case these are P, A, Px, I etc.)

What our equation

Q = 8,400 - 10 P + 5 A + 4 Px + 0.05 I

is doing is that it is predicting Q based on price, expendcitures etc.

Next, lets discuss what are standard errors. Standard error represents the accurac with which any sample represent the population. For example, a standard error of .01 in our average monthly income case means that when we say the actual income impact is somewhere between .05.01. Same goes for all other coefficients.

A. Can R2 be used to determine if customers are very responsive to price changes (Note: I am assuming it is R² )- Our R² is .75, which means our model explains 75% of the variability around its mean. But R² is for whole equation and not price changes only. Hence, it cant be used.

B. Yes, the coefficient on advertising can be used to approximate the impact of a change in advertising expenditure on quantity demanded. Keeping all other variables constant, moving only advertising expenditure will give us the movement in quantity demanded. And that movement is dependent on the cofficient of advertising.

C. Our entry would be sustainable when costs=income. While we are only given advertising costs, even if we take only those into account, we need more information on income etc. to find where costs would be equal to income. The number 8400 alone will not be able to tell us that.

D. Yes. Same as part B, the quantity demanded is directly proportional to the income. Keeping all other things constant, we would know the impact of recession (where income reduces) on the quantity demanded. Its pretty straightforward that for every 1 reduction in income, quantity demanded is reduced by .05.