Answered: Suppose the Sherwin-Williams Company…

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter4: Estimating Demand

Section: Chapter Questions

Problem 8E

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Question

Suppose the Sherwin-Williams Company has developed the following multiple regression model, with paint sales Y (x 1,000 gallons) as the dependent variable and promotional expenditures A (x $1,000) and selling price P (dollars per gallon) as the independent variables.

Y=α+βaA+βpP+εY=α+βaA+βpP+ε

Now suppose that the estimate of the model produces following results: α=344.585α=344.585, ba=0.102ba=0.102, bp=−11.192bp=−11.192, sba=0.173sba=0.173, sbp=4.487sbp=4.487, R2=0.813R2=0.813, and F-statistic=11.361F-statistic=11.361. Note that the sample consists of 10 observations.

1.) According to the estimated model, holding all else constant, a $1,000 increase in promotional expenditures decrease or increase sales by approximately 102,813 or 11,192 gallons. Similarly, a $1 increase in the selling price decrease or increase sales by approximately 813,11,192 or 102 gallons.

2.)Which of the independent variables (if any) appears to be statistically significant (at the 0.05 level) in explaining paint sales? Check all that apply.

a.)Selling price (P)

b.)Promotional expenditures (A)

What proportion of the total variation in sales is explained by the regression equation?

a.) 0.813

b.)0.102

c.)0.173

Expert Solution

Step 1

Consider the following regression equation:

Y = α + βaA + βpP + ε

Here, Y is the dependent variable that represents paint sales in 1000 gallons. A and P are the independent variables that represent promotional expenditure (in $1000) and selling price ($ per gallon) respectively.

In reference to the given regression results, the regression equation becomes:

Y = 344.585 + 0.11A - 11.192P + ε

The standard errors of the regression coefficient of the variables A and P are:

sba = 0.155

sbp = 4.312

R2 = 0.722

F-statistic = 11.361

n (number of observations) = 10

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