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AIM 5: Explain the application of the Gauss-Markov and Central Limit Theorem in OLS estimates.

1、The Gauss-Markov theorem says that if the classical linear regression model assumptions are true, then the OLS estimators have all of the following properties except the:

A) OLS estimated coefficients are based upon linear functions.

B) OLS estimated coefficients are unbiased, which means E(b0) = B0 and E(b1) = B1.

C) OLS estimate of the variance of the errors is unbiased, i.e., E()= σ2.

D) OLS estimated coefficients have the minimum absolute error when compared to other methods of estimating the coefficients, i.e., they are the most precise.

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The correct answer is D

They have the minimum variance, which is not the same as the minimum absolute error.

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AIM 3: Define, calculate and interpret the standard errors of the coefficients in an OLS model.

In a two-variable regression of the dependent variable Y on the independent variable X, the standard error of the slope coefficient is:

 

A )

 

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B)

 

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C)

 

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D)

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The correct answer is C

The correct formulas for the standard errors uses X and not Y. The other formula among the choices using X is the standard error of the intercept.

 

aianjie

 

The correct answer is A

There is no requirement that the variance of the error term should be equal to one.

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AIM 2: Define and distinguish homoskedasticity and heteroskedasticity.

Which expression best represents the condition homoskedasticity? (In the expressions assume σ2 > 0)

A) V(εi|Xi) = σ2. 

B) E(εi|Xi) = σ2.

C) corr(Xi, εi) = 0.

D) corr(εi, εi + j) = 0. 

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The correct answer is A

Homoskedasticity means the variance of εi is constant and unrelated to the value of the independent variable.

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5、The assumptions underlying linear regression include all of the following EXCEPT the:

A) disturbance term is normally distributed with an expected value of 0.

B) independent variable is linearly related to the residuals (or disturbance term).

C) disturbance term is homoskedastic and is independently distributed.

D) dependent variable and independent variable are linearly related. 

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The correct answer is B

The independent variable is uncorrelated with the residuals (or disturbance term).

The other statements are true. The disturbance term is homoskedastic because it has a constant variance. It is independently distributed because the residual for one observation is not correlated with that of another observation. Note: The opposite of homoskedastic is heteroskedastic. For the examination, memorize the assumptions underlying linear regression!

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6、Linear regression is based on a number of assumptions. Which of the following is least likely an assumption of linear regression?

A) Values of the independent variable are not correlated with the error term.

B) A linear relationship exists between the dependent and independent variables.

C) There is at least some correlation between the error terms from one observation to the next.

D) The variance of the error terms each period remains the same.