1. Determine whether the following ones are linear or non-linear regression models and
give the reason why.
a) y = a + b x + c x2 + d z + e
b) y = a + b xc + d z + e
2. Explain the pros and cons of using R2 as a measure of goodness-of-fit for the linear
regression models.
3. In the following regression model, if price increase by 1%, what would be the change
in y?
log(y) = -6.63 + … + 0.3274 log(price) + ehat
4. In the following regression model, if age increases from 35 to 36, what would be the
change in wage, which is measured in thousand dollars?
wage = 3258 + … + 3.246 age – 0.275 age2 + … + ehat
5. What is the problem with the following regression model?
log(wage) = b0 + b1log(age) + b2log(age2) + e
6. In the following regression model, is age statistically significant? Is it economically
significant? Be sure to give your reason. Note that what in the parenthesis is the standard
error.
log(wage) = … + 0.000584 age + … + ehat
(0.000211)
7. What is de-seasonalization and why is de-seasonalized data useful?
8. The following result is obtained from regressing consumption measured in thousand of
dollars on income measured in dollars and other variables. For the ease of presentation, it
is better to have the coefficient of income without so many zeros after the decimal point.
What kind of transformation should we make to consumption and income, then? What
would then the standard error become?
consumption = … + 0.000746 income + … + ehat
(0.000248)
9. Why do researchers prefer over-parameterization to under-parameterization?
10. What are the so-called heteroskedastic-robust standard errors and why are they
useful? How to get them in SAS?
11. What can we say about the linear regression model if the calculated p-value for the
White test is 0.0856?
12. What can we say about the linear regression model if the calculated Durbin-Watson
test statistic is 0.8746?
13. What can we say about the linear regression model if the calculated p-value of the
normality test is 0.0248?
14. What can we say about the linear regression model if the calculated p-value of the
Ramsey’s RESET test is 0.0748?
15. What is the common feature of the linear probability, probit, and logit models? What
is the major deficiency of the linear probability model?
16. What is the biggest difference between the probit and logit models?
17. What do p, d, and q mean in the ARIMA(p,d,q) and why is this model useful?
18. What is the difference between the fixed-effects and random effects models?
19. What is the difference between the reduced form and structural form?
20. What is simultaneity bias and why can the use of IV eliminate it?
21. What can we do if an equation in the simultaneous equation models is not identified?
22. What can we conclude if the p-value of the Hausman test for random effect is 0.0148?
23. What can we conclude if the p-value of the Bassman test for overidentification
restriction is 0.2485?
24. Let female be a dummy variable whose value is 1 for females and 0 for males. What
is the effect of education on wage in the following regression model? What is the
difference of impacts of education on wage for males and that for females?
wage = … + b1 female + b2 education + b3 (female*education) + …
25. Let female be a dummy variable whose value is 1 for females and 0 for males. What
is the gender difference?
wage = … + b1 female + b2 education + b3 (female*education) + …
26. True or False: GLS is preferred to OLS, when an important variable has been omitted
from the model. Explain your answer.
27. Is FGLS BLUE when the error terms are heteroskedastic?
28. You have estimated a linear regression model relating Y to X. Your professor says,
“I think that the relationship between Y and X is nonlinear.” Explain how you would test
the adequacy of your linear regression.
29. A researcher estimates the effect on crime rates of spending on police using city-level
data. Explain how simultaneous bias might occur.
30. True or False: heteroskedasticity in the errors leads to biased estimates of the
regression coefficients and their standard errors. Explain your answer.