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Question 4: Given the following two linear regression models: log Y = ?1 + ?2 log X + u (1) log (Y / X) = ?1 + v (2) where Y is the dependent variable, and X is the independent variable. Both u and v are random variables, and ?1, ?2, ?1 and ?2 are model parameters. Conduct OLS regression with the above two models, respectively. 1) What is the economic meaning of ?1? 2) At what circumstance Equation (1) is the same as Equation (2), how to do a hypothesis test on this? 3) Are the R² of the two models identical, if not, which one is bigger? 4) In equation (1), given an observation X0, how to calculate the expected Y0, E[Y0]? 5) In equation (1), if one variable log Z is omitted, at what circumstance the estimation of ?2 is still unbiased?

          Question 4:
Given the following two linear regression models:
log Y = ?1 + ?2 log X + u    (1)
log (Y / X) = ?1 + v         (2)
where Y is the dependent variable, and X is the independent variable. Both u and v are random variables, and ?1, ?2, ?1 and ?2 are model parameters. Conduct OLS regression with the above two models, respectively.
1) What is the economic meaning of ?1?
2) At what circumstance Equation (1) is the same as Equation (2), how to do a hypothesis test on this?
3) Are the R² of the two models identical, if not, which one is bigger?
4) In equation (1), given an observation X0, how to calculate the expected Y0, E[Y0]?
5) In equation (1), if one variable log Z is omitted, at what circumstance the estimation of ?2 is still unbiased?

Question 4:
Given the following two linear regression models:
log Y = ?1 + ?2 log X + u (1)
log (Y / X) = ?1 + v (2)
where Y is the dependent variable, and X is the independent variable. Both u and v are random variables, and ?1, ?2, ?1 and ?2 are model parameters. Conduct OLS regression with the above two models, respectively.
1) What is the economic meaning of ?1?
2) At what circumstance Equation (1) is the same as Equation (2), how to do a hypothesis test on this?
3) Are the R² of the two models identical, if not, which one is bigger?
4) In equation (1), given an observation X0, how to calculate the expected Y0, E[Y0]?
5) In equation (1), if one variable log Z is omitted, at what circumstance the estimation of ?2 is still unbiased?

Added by Taylor A.

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