1. We are interested in estimating the factors that affect CEO's salary. We con- struct the following model, log(salary) = Bo + B1 log(sales) + B2roe + Baroe? (1) Using the data in RDCHEM.RAW, the following equation was obtained by OLS: log(salary) = 4.322 +0.276 log(sales) + 0.0215roe - 0.00008roe, (0.324) (0.033) (0.0129) (0.00026) n = 32, R = 0.1484

Linear Algebra: A Modern Introduction
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Chapter6: Vector Spaces
Section6.7: Applications
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1. We are interested in estimating the factors that affect CEO's salary. We con-
struct the following model,
log(salary) = Bo + Bị log(sales) + Baroe + Baroe?
(1)
Using the data in RDCHEM.RAW, the following equation was obtained by
OLS:
log(salary) = 4.322 + 0.276 log(sales) + 0.0215roe – 0.00008roe?,
%3D
(0.324) (0.033)
(0.0129)
(0.00026)
n = 32,
R = 0.1484
(a) At what point does the marginal effect of roe on log(salary) become neg-
ative?
(b) Suppose we want to test the null hypothesis that roe is linearly related to
log(salary) against the alternative that the relationship is quadratic at 5%
level, state the null hypothesis and alternative hypothesis in terms of the
parameter in equation (1).
(c) Test the null hypothesis in part (b). Be sure to specify the null and al-
ternative hypothesis, the test statistics, the degree of freedom, and the
critical value.
(d) Based on your answer in part (c), do you think including the quadratic
term in equation (1) is necessary? Explain why or why not.
Transcribed Image Text:1. We are interested in estimating the factors that affect CEO's salary. We con- struct the following model, log(salary) = Bo + Bị log(sales) + Baroe + Baroe? (1) Using the data in RDCHEM.RAW, the following equation was obtained by OLS: log(salary) = 4.322 + 0.276 log(sales) + 0.0215roe – 0.00008roe?, %3D (0.324) (0.033) (0.0129) (0.00026) n = 32, R = 0.1484 (a) At what point does the marginal effect of roe on log(salary) become neg- ative? (b) Suppose we want to test the null hypothesis that roe is linearly related to log(salary) against the alternative that the relationship is quadratic at 5% level, state the null hypothesis and alternative hypothesis in terms of the parameter in equation (1). (c) Test the null hypothesis in part (b). Be sure to specify the null and al- ternative hypothesis, the test statistics, the degree of freedom, and the critical value. (d) Based on your answer in part (c), do you think including the quadratic term in equation (1) is necessary? Explain why or why not.
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