Problem 1 Hypotheses Testtly InsignificantroblemsLAIM 1 Which of the following can cause the usual OLS t statistics to be invalid (that is, not to have t distribu-tions under Ho)?(i)(ii) A sample correlation coefficient of .95 between two independent variables that are in the model.(iii) Omitting an important explanatory variable.2 Consider an equation to explain salaries of CEOs in terms of annual firm sales, return on equity (roe.ipercentage form), and return on the firm's stock (ros, in percentage form):log(salary)= Bo + Blog(sales) + B₂roe + Bros + u.(i)In terms of the model parameters, state the null hypothesis that, after controlling for sales androe, ros has no effect on CEO salary. State the alternative that better stock market performanceincreases a CEO's salary.(ii) Using the data in CEOSAL1, the following equation was obtained by OLS:p-Value(Heteroskedasticity.log(salary) = 4.32 + .280 log(sales) + .0174 roe +.00024 ros(.32) (.035)(.0041)(.00054)n = 209, R² = .283.By what percentage is salary predicted to increase if ros increases by 50 points? Does ros havea practically large effect on salary?(iii)Test the null hypothesis that ros has no effect on salary against the alternative that ros has apositive effect. Carry out the test at the 10% significance level.(iv)Would you include ros in a final model explaining CEO compensation in terms of firm perfor-mance? Explain.renovee3 The variable rdintens is expenditures on research and development (R&D) as a percentage of sale=Sales are measured in millions of dollars. The variable profmarg is profits as a percentage of sales.Using the data in RDCHEM for 32 firms in the chemical industry, the following equatiois estimated:(i)rdintens = .472 + .321 log(sales) + .050 profmarg(.046)(1.369) (216)n = 32, R2 = .099.Interpret the coefficient on log(sales). In particular, if sales increases by 10%, what is the esti-mated percentage point change in rdintens? Is this an economically large effect?

The ordinary least square (OLS) estimation refers to the establishment of a linear relationship…

ems 1 Which of the following can cause the usual OLS t statistics to be invalid (that is, not to have t distribu tions under Ho)? (i) Heteroskedasticity. (ii) A sample correlation coefficient of .95 between two independent variables that are in the model_ (iii) Omitting an important explanatory variable. CEOs in terms of annual firm sales, return on equity (roe,

ems 1 Which of the following can cause the usual OLS t statistics to be invalid (that is, not to have t distribu tions under Ho)? (i) Heteroskedasticity. (ii) A sample correlation coefficient of .95 between two independent variables that are in the model_ (iii) Omitting an important explanatory variable. CEOs in terms of annual firm sales, return on equity (roe,

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Chapter1: Making Economics Decisions

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Question

Problem 1

Hypotheses Test
tly Insignificant
roblems
LAIM 1 Which of the following can cause the usual OLS t statistics to be invalid (that is, not to have t distribu-
tions under Ho)?
(i)
(ii) A sample correlation coefficient of .95 between two independent variables that are in the model.
(iii) Omitting an important explanatory variable.
2 Consider an equation to explain salaries of CEOs in terms of annual firm sales, return on equity (roe.i
percentage form), and return on the firm's stock (ros, in percentage form):
log(salary)= Bo + Blog(sales) + B₂roe + Bros + u.
(i)
In terms of the model parameters, state the null hypothesis that, after controlling for sales and
roe, ros has no effect on CEO salary. State the alternative that better stock market performance
increases a CEO's salary.
(ii) Using the data in CEOSAL1, the following equation was obtained by OLS:
p-Value
(
Heteroskedasticity.
log(salary) = 4.32 + .280 log(sales) + .0174 roe +.00024 ros
(.32) (.035)
(.0041)
(.00054)
n = 209, R² = .283.
By what percentage is salary predicted to increase if ros increases by 50 points? Does ros have
a practically large effect on salary?
(iii)
Test the null hypothesis that ros has no effect on salary against the alternative that ros has a
positive effect. Carry out the test at the 10% significance level.
(iv)
Would you include ros in a final model explaining CEO compensation in terms of firm perfor-
mance? Explain.
renovee
3 The variable rdintens is expenditures on research and development (R&D) as a percentage of sale=
Sales are measured in millions of dollars. The variable profmarg is profits as a percentage of sales.
Using the data in RDCHEM for 32 firms in the chemical industry, the following equatio
is estimated:
(i)
rdintens = .472 + .321 log(sales) + .050 profmarg
(.046)
(1.369) (216)
n = 32, R2 = .099.
Interpret the coefficient on log(sales). In particular, if sales increases by 10%, what is the esti-
mated percentage point change in rdintens? Is this an economically large effect?

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