Given the following two linear regression models: = 1+ 2+ (1) = 1 + (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 0, how to calculate the expected 0, E[0]? 5) In equation (1), if one variable is omitted, at what circumstance the estimation of 2 is still unbiased?

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Given the following two linear regression models:= 1 + 2 + (1) = 1 + (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 0, how to
calculate the expected 0, E[0]? 5) In equation (1), if one variable is omitted, at
what circumstance the estimation of 2 is still unbiased?
Transcribed Image Text:Given the following two linear regression models:= 1 + 2 + (1) = 1 + (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 0, how to calculate the expected 0, E[0]? 5) In equation (1), if one variable is omitted, at what circumstance the estimation of 2 is still unbiased?
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