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+ε�=�+��+��+�

Now suppose that the estimate of the model produces following results: α=344.585�=344.585, ba=0.106��=0.106, bp=−12.112��=−12.112, sba=0.155�ba=0.155, sbp=4.312�bp=4.312, R2=0.764�2=0.764, and F-statistic=12.593F-statistic=12.593. Note that the sample consists of 10 observations.

According to the estimated model, holding all else constant, a $1,000 increase in promotional expenditures sales by approximately gallons. Similarly, a $1 increase in the selling price sales by approximately gallons.

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.

Selling price (P)

Promotional expenditures (A)

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

0.155

0.106

0.764

The given F-value shows that you 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.

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 $120,000and the selling price is $11.50?

212.485

192.577

218.017

When promotional expenditures are $80,000 and the selling price is $11.50, the point price elasticity is , and the point promotional price elasticity is .

Expert Solution

Step 1

It is given that 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.

The fitted multiple regression model is given by:

$\hat{y} = 344.585 + 0.106 A - 12.112 P$