Answered: Suppose the Sherwin-Williams Company…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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.)The given F-value shows that you cannot or can reject the null hypothesis that neither one of the independent variables explain a significant (at the 0.05 level) proportion of the variation in income.

2.)Based on the regression model, what is the best estimate of paint sales (x 1,000 gallons) in a sales region where promotional expenditures are $110,000and the selling price is $12.50?

a.)213.792

b.)215.905

c.)193.465

3.) When promotional expenditures are $80,000 and the selling price is $12.50, the point price elasticity is -0.654, -0.648 or -0.723, and the point promotional price elasticity is 0.052 or 0.058.

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