Question 1

Explain how this: $$\begin{array} { l } 
E \left[ w _ { 1 } { } ^ { 2 } u _ { 1 } { } ^ { 2 } + w _ { 2 } { } ^ { 2 } u _ { 2 } { } ^ { 2 } + \ldots + w _ { n } { } ^ { 2 } u _ { n } ^ { 2 } + 2 w _ { 1 } u _ { 1 } w _ { 2 } u _ { 2 } + 2 w _ { 1 } u _ { 1 } w _ { 3 } u _ { 3 } + \ldots \right. \
\left. + 2 w _ { 2 } u _ { 2 } w _ { 3 } u _ { 3 } + 2 w _ { 2 } u _ { 2 } w _ { 4 } u _ { 4 } + \ldots + 2 w _ { n - 1 } u _ { n - 1 } w _ { n } u _ { n } \right]
\end{array}$$

Accepted Answer

The answer of Explain how this: \[\begin{array} { l }...

Question 2

A violation of assumption 2 of the CLRM carries more severe consequences than a violation of assumption 4.

Accepted Answer

A) True 
 B)False

Question 3

Assumption 4 of the CLRM is necessary but not sufficient to prove that $\hat { \beta } _ { 1 }$ is unbiased.

Accepted Answer

A) True 
 B)False

Question 4

Assumption 3 of the CLRM is necessary but not sufficient to prove that $\hat { \beta } _ { 1 }$ is linear.

Accepted Answer

A) True 
 B)False

Question 5

If the ui's are more likely to be positive when one of the explanatory variables is at higher values, then all of the estimators will be biased.

Accepted Answer

A) True 
 B)False

Exam 4: Hypothesis Testing

A violation of assumption 2 of the CLRM carries more severe consequences than a violation of assumption 4.

Assumption 4 of the CLRM is necessary but not sufficient to prove that $\hat { \beta } _ { 1 }$ is unbiased.

Assumption 3 of the CLRM is necessary but not sufficient to prove that $\hat { \beta } _ { 1 }$ is linear.

If the u_i's are more likely to be positive when one of the explanatory variables is at higher values, then all of the estimators will be biased.

Exam 4: Hypothesis Testing

A violation of assumption 2 of the CLRM carries more severe consequences than a violation of assumption 4.

Assumption 4 of the CLRM is necessary but not sufficient to prove that β^1\hat { \beta } _ { 1 }β^​1​ is unbiased.

Assumption 3 of the CLRM is necessary but not sufficient to prove that β^1\hat { \beta } _ { 1 }β^​1​ is linear.

If the ui's are more likely to be positive when one of the explanatory variables is at higher values, then all of the estimators will be biased.

Assumption 4 of the CLRM is necessary but not sufficient to prove that $\hat { \beta } _ { 1 }$ is unbiased.

Assumption 3 of the CLRM is necessary but not sufficient to prove that $\hat { \beta } _ { 1 }$ is linear.

If the u_i's are more likely to be positive when one of the explanatory variables is at higher values, then all of the estimators will be biased.