1. Suppose that you have following data: Variable Description CEO salary measured in thousands of $ Firm's sale measure in millions of $ Return on equity in percent Salary sales roe *Return on equity is a measure of financial performance calculated by dividing net income by shareholders' equity. Your estimated regression is given by log (salary) = 4.322 + 0.276 log(sale) + 0.0215roe-0.0008roe", R = 282, n = 209. (324) (0.033) (0.0129) (0.00026) a) Is the effect of all independent variables statistically equal to 0? b) Interpret the coefficient on log(sale). c) Interpret the effect of roe on log(salary).

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
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Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
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Chapter4A: Problems In Applying The Linear Regression Model
Section: Chapter Questions
Problem 2E
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1. Suppose that you have following data:
Variable
Description
CEO salary measured in thousands of $
Firm's sale measure in millions ofS
Return on equity in percent
Salary
sales
roe
*Return on equity is a measure of financial performance calculated by dividing net
income by shareholders' equity.
Your estimated regression is given by
log (salary) = 4.322 + 0.276 log(sale) + 0.0215roe - 0.0008roe?, R = 282, n = 209.
(324) (0.033)
(0.0129)
(0.00026)
a) Is the effect of all independent variables statistically equal to 0?
b) Interpret the coefficient on log(sale).
c) Interpret the effect of roe on log(salary).
• Without more information, your interpretation of the effect of roe on
log(salary) should include answers to these sub-question.
Should the roe be included in this model?
il.
Comment on relationship between roe and log(salary): is it U-shaped or inverse
U-shaped?
What is the turning point? How would you interpret this point?
Plot log(salary) vs roe.
v.
ii.
iv.
Compute predicted value of log(salary) for roe-10, roe-11, roe-20, roe-21,
roe-30, and roe-31 while holding other factors constant
d) Find the differences in predicted log(salary) when roe increases by 1% going from 10
to 11; when roe increase by 1% going from 20 to 21; and when roe increases by 1%
going from 30 to 31.
e) Suppose that you have F-statistics for the following F-tests
1. Ho:B+21B2 = 0; F = 6.71
ii. Ho: B, + 41Bz = 0; F = 19.31
il. Ho:B + 61ßz = 0; F = 22.54.
Use this information to calculate the 95% CI for the differences in predicted value of
log(salary) from part d. Where is the Cl widest. What does this tell you about the effects
of roe on log(salary)?
Transcribed Image Text:1. Suppose that you have following data: Variable Description CEO salary measured in thousands of $ Firm's sale measure in millions ofS Return on equity in percent Salary sales roe *Return on equity is a measure of financial performance calculated by dividing net income by shareholders' equity. Your estimated regression is given by log (salary) = 4.322 + 0.276 log(sale) + 0.0215roe - 0.0008roe?, R = 282, n = 209. (324) (0.033) (0.0129) (0.00026) a) Is the effect of all independent variables statistically equal to 0? b) Interpret the coefficient on log(sale). c) Interpret the effect of roe on log(salary). • Without more information, your interpretation of the effect of roe on log(salary) should include answers to these sub-question. Should the roe be included in this model? il. Comment on relationship between roe and log(salary): is it U-shaped or inverse U-shaped? What is the turning point? How would you interpret this point? Plot log(salary) vs roe. v. ii. iv. Compute predicted value of log(salary) for roe-10, roe-11, roe-20, roe-21, roe-30, and roe-31 while holding other factors constant d) Find the differences in predicted log(salary) when roe increases by 1% going from 10 to 11; when roe increase by 1% going from 20 to 21; and when roe increases by 1% going from 30 to 31. e) Suppose that you have F-statistics for the following F-tests 1. Ho:B+21B2 = 0; F = 6.71 ii. Ho: B, + 41Bz = 0; F = 19.31 il. Ho:B + 61ßz = 0; F = 22.54. Use this information to calculate the 95% CI for the differences in predicted value of log(salary) from part d. Where is the Cl widest. What does this tell you about the effects of roe on log(salary)?
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