Question 1

E  (1n−2∑i=1nu^i2) \left(\frac { 1 } { n - 2 } \sum _ { i = 1 } ^ { n } \hat { u } _ { i } ^ { 2 }\right ) (n−21​∑i=1n​u^i2​)

Accepted Answer

A)  is the expected value of the homoskedasticity only standard errors.
B)  =  σu2\sigma _ { u } ^ { 2 }σu2​ 
C)  exists only asymptotically.
D)  =  σu2\sigma _ { u } ^ { 2 }σu2​  /(n-2) . E) B) and C)
F) C) and D)

Question 2

You need to adjust  Su^2S _ {\hat{ u }} ^ { 2 }Su^2​  by the degrees of freedom to ensure that  Su^2S _ {\hat{ u }} ^ { 2 }Su^2​  is

Accepted Answer

A)  an unbiased estimator of  σu2\sigma _ { u } ^ { 2 }σu2​ 
B)  a consistent estimator of  σu2\sigma _ { u } ^ { 2 }σu2​ 
C)  efficient in small samples.
D)  F-distributed. E) B) and C)
F) None of the above

Question 3

The OLS estimator is a linear estimator,  β^\hat { \beta }β^​  1 =  ∑i=1na^iYi\sum _ { i = 1 } ^ { n } \hat { a } _ { i } Y _ { i }∑i=1n​a^i​Yi​  , where  a^\hat aa^  i =

Accepted Answer

A)    Xi−Xˉ∑j=1n(Xj−Xˉ) 2\frac { X _ { i } - \bar { X } } { \sum _ { j = 1 } ^ { n } \left( X _ { j } - \bar { X } \right)  ^ { 2 } }∑j=1n​(Xj​−Xˉ) 2Xi​−Xˉ​ 
B)    1n\frac { 1 } { n }n1​ 
C)    Xi−Xˉ∑j=1n(Xj−Xˉ) \frac { X _ { i } - \bar { X } } { \sum _ { j = 1 } ^ { n } \left( X _ { j } - \bar { X } \right)  }∑j=1n​(Xj​−Xˉ) Xi​−Xˉ​ 
D)    Xi∑j=1n(Xj−Xˉ) 2\frac { X _ { i } } { \sum _ { j = 1 } ^ { n } \left( X _ { j } - \bar { X } \right)  ^ { 2 } }∑j=1n​(Xj​−Xˉ) 2Xi​​  E) C) and D)
F) A) and D)

Question 4

Finite-sample distributions of the OLS estimator and t-statistics are complicated, unless

Accepted Answer

A)  the regressors are all normally distributed.
B)  the regression errors are homoskedastic and normally distributed, conditional on X1,... Xn.
C)  the Gauss-Markov Theorem applies.
D)  the regressor is also endogenous.E) B) and C)
F) A) and D)

Question 5

Slutsky's theorem combines the Law of Large Numbers

Accepted Answer

A)  with continuous functions.
B)  and the normal distribution.
C)  and the Central Limit Theorem.
D)  with conditions for the unbiasedness of an estimator.E) None of the above
F) A) and B)

Question 6

Under the five extended least squares assumptions, the homoskedasticity-only t-distribution in this chapter

Accepted Answer

A)  has a Student t distribution with n-2 degrees of freedom.
B)  has a normal distribution.
C)  converges in distribution to a  xn−22x _ { n - 2 } ^ { 2 }xn−22​  distribution.
D)  has a Student t distribution with n degrees of freedom. E) C) and D)
F) A) and C)

Question 7

(Requires Appendix material)If the Gauss-Markov conditions hold, then OLS is BLUE. In addition, assume here that X is nonrandom. Your textbook proves the Gauss-Markov theorem by using the simple regression model Yi = β0 + β1Xi + ui and assuming a linear estimator $\widetilde { \beta } _ { 1 } = \sum _ { i = 1 } ^ { n } a _ { i } Y _ { i }$ Substitution of the simple regression model into this expression then results in two conditions for the unbiasedness of the estimator: $\sum _ { i = 1 } ^ { n } a _ { i }$ = 0 and $\sum _ { i = 1 } ^ { n } a _ { i } X _ { i }$ = 1.
The variance of the estimator is var( $\tilde { \beta } _ { 1 }$  
  | X1,…, Xn)= $\sigma _ { u } ^ { 2 }$ $\sum _ { i = 1 } ^ { n } a _ { i } ^ { 2 }$ Different from your textbook, use the Lagrangian method to minimize the variance subject to the two constraints. Show that the resulting weights correspond to the OLS weights.

Accepted Answer

Define the Lagrangian as follows:
L =

_T...

Question 8

Estimation by WLS

Accepted Answer

A)  although harder than OLS, will always produce a smaller variance.
B)  does not mean that you should use homoskedasticity-only standard errors on the transformed equation.
C)  requires quite a bit of knowledge about the conditional variance function.
D)  makes it very hard to interpret the coefficients, since the data is now weighted and not any longer in its original form.E) None of the above
F) A) and B)

Question 9

Besides the Central Limit Theorem, the other cornerstone of asymptotic distribution theory is the

Accepted Answer

A)  normal distribution.
B)  OLS estimator.
C)  Law of Large Numbers.
D)  Slutsky's theorem.E) B) and C)
F) A) and C)

Exam 17: The Theory of Linear Regression With One Regressor

Under the five extended least squares assumptions, the homoskedasticity-only t-distribution in this chapter

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Finite-sample distributions of the OLS estimator and t-statistics are complicated, unless

Correct Answer
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Estimation by WLS

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You need to adjust $S _ {\hat{ u }} ^ { 2 }$ by the degrees of freedom to ensure that $S _ {\hat{ u }} ^ { 2 }$ is

Correct Answer
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Slutsky's theorem combines the Law of Large Numbers

Correct Answer
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Define the Lagrangian as follows:
L = _T...
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Besides the Central Limit Theorem, the other cornerstone of asymptotic distribution theory is the

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E $\left(\frac { 1 } { n - 2 } \sum _ { i = 1 } ^ { n } \hat { u } _ { i } ^ { 2 }\right )$

Correct Answer
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The OLS estimator is a linear estimator, $\hat { \beta }$ ₁ = $\sum _ { i = 1 } ^ { n } \hat { a } _ { i } Y _ { i }$ , where $\hat a$ _i =

Correct Answer
verified

Exam 17: The Theory of Linear Regression With One Regressor

Under the five extended least squares assumptions, the homoskedasticity-only t-distribution in this chapter

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Finite-sample distributions of the OLS estimator and t-statistics are complicated, unless

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Estimation by WLS

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You need to adjust Su^2S _ {\hat{ u }} ^ { 2 }Su^2​ by the degrees of freedom to ensure that Su^2S _ {\hat{ u }} ^ { 2 }Su^2​ is

Correct AnswerverifiedShow Answer

Slutsky's theorem combines the Law of Large Numbers

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Correct AnswerverifiedDefine the Lagrangian as follows:L = _T...View AnswerShow Answer

Besides the Central Limit Theorem, the other cornerstone of asymptotic distribution theory is the

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E (1n−2∑i=1nu^i2) \left(\frac { 1 } { n - 2 } \sum _ { i = 1 } ^ { n } \hat { u } _ { i } ^ { 2 }\right ) (n−21​∑i=1n​u^i2​)

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The OLS estimator is a linear estimator, β^\hat { \beta }β^​ 1 = ∑i=1na^iYi\sum _ { i = 1 } ^ { n } \hat { a } _ { i } Y _ { i }∑i=1n​a^i​Yi​ , where a^\hat aa^ i =

Correct AnswerverifiedShow Answer

Correct Answer
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Correct Answer
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Correct Answer
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You need to adjust $S _ {\hat{ u }} ^ { 2 }$ by the degrees of freedom to ensure that $S _ {\hat{ u }} ^ { 2 }$ is

Correct Answer
verified

Correct Answer
verified

Correct Answer
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Define the Lagrangian as follows:
L = _T...
View Answer

Correct Answer
verified

E $\left(\frac { 1 } { n - 2 } \sum _ { i = 1 } ^ { n } \hat { u } _ { i } ^ { 2 }\right )$

Correct Answer
verified

The OLS estimator is a linear estimator, $\hat { \beta }$ ₁ = $\sum _ { i = 1 } ^ { n } \hat { a } _ { i } Y _ { i }$ , where $\hat a$ _i =

Correct Answer
verified