Question 1

If the ui's are binomially distributed, then $\hat { \beta } _ { 1 }$ will be biased.

Accepted Answer

A) True 
 B)False  False

Question 2

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

Accepted Answer

A) True 
 B)False  True

Question 3

What is a Monte Carlo study? In addition, give examples. Why are these studies useful?

Accepted Answer

A Monte Carlo study is a statistics study that draws repeated samples from a known population and then analyzes the characteristics of the samples. For example, one may draw repeated samples of 3 from a deck of 9 playing cards (all the hearts from 2 through 10). The average value of the 9 cards is 6. The mean value of a typical sample draw will approach 6 as well as the number of draws approaches infinity. This Monte Carlo experiment shows that the mean value of a sample of 3 cards is an unbiased estimator of the population mean. Another example would be a computer simulation where a sample of 40 observations on X and Y is considered the population. A regression is run to ascertain the values of $\hat { \beta } _ { 0 }$ and $\hat { \beta } _ { 1 }$ . Then 10,000 samples of n=20 can be obtained and $\hat { \beta } _ { 0 }$ and $\hat { \beta } _ { 1 }$ calculated for each. The average of these 10,000 $\hat { \beta } _ { 0 }$ s and $\hat { \beta } _ { 1 }$ s should equal the population values of $\beta _ { 0 }$ and $\beta _ { 1 }$ if the estimation technique is unbiased. Monte Carlo studies are useful because they can assess the properties of statistical estimators and tests.

Question 4

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

Accepted Answer

A) True 
 B)False

Question 5

Assumption 1 of the CLRM (Classical Linear Regression Model) is necessary but not sufficient to prove that $\hat { \beta } _ { 1 }$ is linear.

Accepted Answer

A) True 
 B)False

Question 6

Serial correlation results in inefficient estimates of the structural parameters.

Accepted Answer

A) True 
 B)False

Question 7

TYPE I errors will be more likely in the presence of multicollinearity.

Accepted Answer

A) True 
 B)False

Question 8

Multicollinearity can lead to unexpected signs on regression coefficients.

Accepted Answer

A) True 
 B)False

Question 9

Explain why calculating VIFs is a more thorough test for multicollinearity than considering correlation coefficients.

Accepted Answer

The answer of Explain why calculating VIFs is a more...

Question 10

If E[ $\hat { \beta } _ { 1 } - \beta _ { 1 }$ ] = 0, then $\hat { \beta } _ { 1 }$ is unbiased.

Accepted Answer

A) True 
 B)False

Question 11

$\hat { \beta } _ { 1 }$ is BLUE in the presence of perfect multicollinearity.

Accepted Answer

A) True 
 B)False

Question 12

Assumption 2 of the CLRM is necessary but not sufficient to prove that $\hat { \beta } _ { 1 }$ is unbiased.

Accepted Answer

A) True 
 B)False

Question 13

Assumption 2 of the CLRM is necessary but not sufficient to prove that $\hat { \beta } _ { 1 }$ is linear.

Accepted Answer

A) True 
 B)False

Question 14

Assumption 2 of the CLRM is necessary but not sufficient to prove that $\hat { \beta } _ { 1 }$ is best.

Accepted Answer

A) True 
 B)False

Question 15

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

Accepted Answer

A) True 
 B)False

Question 16

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

Accepted Answer

A) True 
 B)False

Question 17

Prove that the following equation is undefined in the presence of perfect multicollinearity.

Accepted Answer

The answer of Prove that the following equation is undefined...

Question 18

What is data mining? Explain why hypothesis tests, such as a test of significance, are invalid when data have been mined. Defend data mining as an econometric technique.

Accepted Answer

The answer of What is data mining? Explain why hypothesis...

Question 19

ui ~ N(0, $\sigma$2) indicates that the true error terms are normally distributed with an expected value of 0 and that each true error term has a variance equal to some constant, $\sigma$2.

Accepted Answer

A) True 
 B)False

Question 20

If a regression is in the incorrect functional form, explain why it is unlikely that E[u_i_│X_i] = 0.

Accepted Answer

The answer of If a regression is in the incorrect...

Exam 4: Hypothesis Testing

If the u_i's are binomially distributed, then $\hat { \beta } _ { 1 }$ will be biased.

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

What is a Monte Carlo study? In addition, give examples. Why are these studies useful?

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

Assumption 1 of the CLRM (Classical Linear Regression Model) is necessary but not sufficient to prove that $\hat { \beta } _ { 1 }$ is linear.

Serial correlation results in inefficient estimates of the structural parameters.

TYPE I errors will be more likely in the presence of multicollinearity.

Multicollinearity can lead to unexpected signs on regression coefficients.

Explain why calculating VIFs is a more thorough test for multicollinearity than considering correlation coefficients.

If E[ $\hat { \beta } _ { 1 } - \beta _ { 1 }$ ] = 0, then $\hat { \beta } _ { 1 }$ is unbiased.

$\hat { \beta } _ { 1 }$ is BLUE in the presence of perfect multicollinearity.

Assumption 2 of the CLRM is necessary but not sufficient to prove that $\hat { \beta } _ { 1 }$ is unbiased.

Assumption 2 of the CLRM is necessary but not sufficient to prove that $\hat { \beta } _ { 1 }$ is linear.

Assumption 2 of the CLRM is necessary but not sufficient to prove that $\hat { \beta } _ { 1 }$ is best.

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

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

Prove that the following equation is undefined in the presence of perfect multicollinearity.

What is data mining? Explain why hypothesis tests, such as a test of significance, are invalid when data have been mined. Defend data mining as an econometric technique.

u_i ~ N(0, $\sigma$ ²) indicates that the true error terms are normally distributed with an expected value of 0 and that each true error term has a variance equal to some constant, $\sigma$ ².

If a regression is in the incorrect functional form, explain why it is unlikely that E[u_i_│X_i] = 0.

Exam 4: Hypothesis Testing

If the ui's are binomially distributed, then β^1\hat { \beta } _ { 1 }β^​1​ will be biased.

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

What is a Monte Carlo study? In addition, give examples. Why are these studies useful?

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

Assumption 1 of the CLRM (Classical Linear Regression Model) is necessary but not sufficient to prove that β^1\hat { \beta } _ { 1 }β^​1​ is linear.

Serial correlation results in inefficient estimates of the structural parameters.

TYPE I errors will be more likely in the presence of multicollinearity.

Multicollinearity can lead to unexpected signs on regression coefficients.

Explain why calculating VIFs is a more thorough test for multicollinearity than considering correlation coefficients.

If E[ β^1−β1\hat { \beta } _ { 1 } - \beta _ { 1 }β^​1​−β1​ ] = 0, then β^1\hat { \beta } _ { 1 }β^​1​ is unbiased.

β^1\hat { \beta } _ { 1 }β^​1​ is BLUE in the presence of perfect multicollinearity.

Assumption 2 of the CLRM is necessary but not sufficient to prove that β^1\hat { \beta } _ { 1 }β^​1​ is unbiased.

Assumption 2 of the CLRM is necessary but not sufficient to prove that β^1\hat { \beta } _ { 1 }β^​1​ is linear.

Assumption 2 of the CLRM is necessary but not sufficient to prove that β^1\hat { \beta } _ { 1 }β^​1​ is best.

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

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

Prove that the following equation is undefined in the presence of perfect multicollinearity.

What is data mining? Explain why hypothesis tests, such as a test of significance, are invalid when data have been mined. Defend data mining as an econometric technique.

ui ~ N(0, σ\sigmaσ 2) indicates that the true error terms are normally distributed with an expected value of 0 and that each true error term has a variance equal to some constant, σ\sigmaσ 2.

If a regression is in the incorrect functional form, explain why it is unlikely that E[ui│Xi] = 0.

If the u_i's are binomially distributed, then $\hat { \beta } _ { 1 }$ will be biased.

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

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

Assumption 1 of the CLRM (Classical Linear Regression Model) is necessary but not sufficient to prove that $\hat { \beta } _ { 1 }$ is linear.

If E[ $\hat { \beta } _ { 1 } - \beta _ { 1 }$ ] = 0, then $\hat { \beta } _ { 1 }$ is unbiased.

$\hat { \beta } _ { 1 }$ is BLUE in the presence of perfect multicollinearity.

Assumption 2 of the CLRM is necessary but not sufficient to prove that $\hat { \beta } _ { 1 }$ is unbiased.

Assumption 2 of the CLRM is necessary but not sufficient to prove that $\hat { \beta } _ { 1 }$ is linear.

Assumption 2 of the CLRM is necessary but not sufficient to prove that $\hat { \beta } _ { 1 }$ is best.

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

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

u_i ~ N(0, $\sigma$ ²) indicates that the true error terms are normally distributed with an expected value of 0 and that each true error term has a variance equal to some constant, $\sigma$ ².

If a regression is in the incorrect functional form, explain why it is unlikely that E[u_i_│X_i] = 0.