Question 1

Inclusion of irrelevant variables is a potential problem because

Accepted Answer

A) results in biased estimated slope coefficients. 
B) might highlight spurious correlations. 
C) results in estimated standard errors that are too large. 
D) prevents accurately estimating true marginal effects. 
A) results in biased estimated slope coefficients. 
B) might highlight spurious correlations. 
C) results in estimated standard errors that are too large. 
D) prevents accurately estimating true marginal effects. C

Question 2

When would you use the RESET test? What is the null hypothesis for the test? What is the intuition for why it works? Explain.

Accepted Answer

The RESET test is used to test for the inclusion of higher order polynomials such as x² and x³.To perform the RESET test you first estimate the original regression model and then obtain the predicted values squared,predicted values cubed,and predicted values raised to the 4^th power.You then regress y on the original model and the three additional functions of the predicted values.The null hypothesis for the test is that the coefficients on the higher order polynomials are equal to 0 and the polynomials do not belong in the regression.Perform an F-test if all the new parameters are jointly equal to 0.The intuition behind this test is that higher order functions of the predicted values contain higher order functions of the independent variables and therefore if the predicted values raised to the 2,3,and 4 are statistically significant then higher order functions of the predicted values are needed.

Question 3

What is the potential shortcoming of using a strict cutoff to determine statistical significance? Explain.

Accepted Answer

A strict cutoff leads to potentially very different interpretations of which estimates are statistically significant,marginally significant,and statistically insignificant for variables for which the estimated p-values are actually very similar.For instance,if one variable has a p-value of .099 and another has a p-value of .101,we would conclude that the first is marginally significant while the second is statistically insignificant while in reality the difference between these two p-values is likely insignificant.

Question 4

Suppose you are a potential college student that is interested in determining whether it is worthwhile to declare a certain major.In an effort to find the answer,you collect data on 1,247 college who majored in HUMANITIES,SCIENCE,ENGINEERING,or ENGLISH and you estimate the sample regression function (standard errors in parentheses) $$\begin{array} { lllllll } 
log ~\widehat {Sal}ary  _ { i } =& 13.81 + &0.03 \text { GPA } _ { i } + &0.02 \log \text { StudyHours } _ { i } +& 0.01 \text { Science } _ { i } + &0.08 \text { Engineering } _ { i } +& 0.02 \text { English } _ { i } \
& (2.97)& (0.0005)& (0.00003)&( 0.02 ) & ( 0.025 ) & ( 0.001 )

\end{array}$$ 
a)Do you think omitted variable bias is a potential problem in this case? Why? Explain.
b)What is the problem associated with omitted variable bias? Explain.
c)How might you control for the potential omitted variable bias in this case? Explain.

Accepted Answer

a)Yes.There are likely several other fac

Question 5

Suppose you are interested in estimating how the test scores of elementary schools are related to average class size,parents education level (in years),and percent of English learners at the school.To do so,you collect a sample of 200 California public schools and specify the following model: $$\text { Score } = \beta _ { 0 } + \beta _ { 1 } \text { Class Size } + \beta _ { 2 } \text { Education Level } + \beta _ { 3 } \text { Percent English Learners } + \varepsilon$$ 
Suppose you are concerned that the proposed model needs higher order polynomials.
a)Initially you believe that class size is the only variable that should be entered as a higher order polynomial.Propose a new model and explain how you would test for this possibility.
b)After thinking about it,you believe that all of the independent variables may need to be entered in as a higher order polynomial.What type of test would you perform? Describe the steps you would take to implement this test.
c)Now instead you believe that the model estimated above is not appropriate and a better model would be $$\ln ( \text { Score } ) = \beta _ { 0 } + \beta _ { 1 } \text { Class Size } + \beta _ { 2 } \text { Education Level } + \beta _ { 3 } \text { Percent English Learners } + \varepsilon$$ 
How would you test between the initial model and this model? Be as specific as possible.

Accepted Answer

a)I would specify the following model an

Question 6

When would you use the Davidson-MacKinnon test? What is the null hypothesis for the test? What is the intuition for why it works? Explain.

Accepted Answer

The Davidson-MacKinnon test is used to c

Question 7

If you had to either include an irrelevant variable or omit a relevant variable,you would prefer

Accepted Answer

A) including an irrelevant variable over omitting a relevant variable because omitting a relevant variable leads to biased estimates. 
B) including an irrelevant variable over omitting a relevant variable because omitting a relevant variable leads to the standard errors to increase. 
C) omitting a relevant variable over including an irrelevant variable because omitting a variable does not affect the estimated coefficients. 
D) omitting a relevant variable over including an irrelevant variable because including an irrelevant variable does not lead to biased estimates. 
A) including an irrelevant variable over omitting a relevant variable because omitting a relevant variable leads to biased estimates. 
B) including an irrelevant variable over omitting a relevant variable because omitting a relevant variable leads to the standard errors to increase. 
C) omitting a relevant variable over including an irrelevant variable because omitting a variable does not affect the estimated coefficients. 
D) omitting a relevant variable over including an irrelevant variable because including an irrelevant variable does not lead to biased estimates.

Question 8

Why is missing data a potential problem? What are two ways to deal with it? Which approach do you prefer and why?

Accepted Answer

Missing data is a potential concern beca

Question 9

Potential omitted variable bias is best dealt with by

Accepted Answer

A) performing tests of individual significance. 
B) carefully considering economic theory. 
C) including all possible independent variables. 
D) performing tests of joint significance. 
A) performing tests of individual significance. 
B) carefully considering economic theory. 
C) including all possible independent variables. 
D) performing tests of joint significance.

Question 10

Suppose that you are performing the Davidson-MacKinnon test for choosing among non-nested alternatives and that in the second stage you estimate the sample regression function and find that the predicted values are not statistically significant.You decide that

Accepted Answer

A) the initial model is statistically preferred. 
B) the second model is statistically preferred. 
C) neither model is appropriate. 
D) the coefficient estimates from both models are biased. 
A) the initial model is statistically preferred. 
B) the second model is statistically preferred. 
C) neither model is appropriate. 
D) the coefficient estimates from both models are biased.

Question 11

The Eye test is used to

Accepted Answer

A) test for the inclusion of higher-order polynomials. 
B) test for choosing between non-nested models. 
C) critically assess the regression results instead of taking all results at face value. 
D) test for omitted variable bias. 
A) test for the inclusion of higher-order polynomials. 
B) test for choosing between non-nested models. 
C) critically assess the regression results instead of taking all results at face value. 
D) test for omitted variable bias.

Question 12

The Davidson-MacKinnon test is used to

Accepted Answer

A) test for the inclusion of higher-order polynomials. 
B) test for choosing between non-nested models. 
C) test for the individual significance of coefficients. 
D) test for omitted variable bias. 
A) test for the inclusion of higher-order polynomials. 
B) test for choosing between non-nested models. 
C) test for the individual significance of coefficients. 
D) test for omitted variable bias.

Question 13

Suppose that you estimate the sample regression function 
$\log \text { Salary } _ { i } = 6.84 + .062 \text { Experience } _ { i } + .038 \text { Education } _ { i } - 8.538 \text { Blue Eyes } _ { i } + .019 \text { GPA } _ { i }$
Employing the "eye test" you might suspect that the marginal effect of

Accepted Answer

A) experience is estimated incorrectly because it does not seem reasonable that each additional year of experience increases salary by 6.2 percent,holding all other independent constant. 
B) education is estimated incorrectly because it does not seem reasonable that each additional year of education increases salary by 3.8 percent,holding all other independent constant. 
C) having Blue Eyes is estimated incorrectly because it does not seem reasonable that the average salary of individuals with Blue Eyes is 853.8 percent less than the average salary of individuals with other eye colors,holding all other independent constant. 
D) GPA is estimated incorrectly because it does not seem reasonable that each one unit increase in GPA increases salary by 1.9 percent,holding all other independent constant. 
A) experience is estimated incorrectly because it does not seem reasonable that each additional year of experience increases salary by 6.2 percent,holding all other independent constant. 
B) education is estimated incorrectly because it does not seem reasonable that each additional year of education increases salary by 3.8 percent,holding all other independent constant. 
C) having Blue Eyes is estimated incorrectly because it does not seem reasonable that the average salary of individuals with Blue Eyes is 853.8 percent less than the average salary of individuals with other eye colors,holding all other independent constant. 
D) GPA is estimated incorrectly because it does not seem reasonable that each one unit increase in GPA increases salary by 1.9 percent,holding all other independent constant.

Question 14

What is an outlier? Why are they a potential problem? What can you do to deal with outliers? Why does this approach work? Explain.

Accepted Answer

Outliers are observations that differ si

Question 15

What is the inclusion of an irrelevant variable? Why is it a problem? How do you try to prevent it? Explain.

Accepted Answer

The inclusion of an irrelevant variable

Question 16

Outliers are potentially problematic because they

Accepted Answer

A) result in biased estimates. 
B) skew the data to the right. 
C) skew the data to the left. 
D) result in larger estimated standard errors. 
A) result in biased estimates. 
B) skew the data to the right. 
C) skew the data to the left. 
D) result in larger estimated standard errors.

Question 17

One can deal with potential outliers by

Accepted Answer

A) dropping them from the data set. 
B) including a dummy variable equal to 1 if the observation is an outlier. 
C) performing Weighted Least Squares. 
D) dividing the value of outlier by the sample mean. 
A) dropping them from the data set. 
B) including a dummy variable equal to 1 if the observation is an outlier. 
C) performing Weighted Least Squares. 
D) dividing the value of outlier by the sample mean.

Question 18

Suppose that you are performing the RESET test for the inclusion of higher-order polynomials and that in the second stage you estimate the sample regression function and the predicted value terms are statistically significant.You decide that

Accepted Answer

A) higher-order polynomials are not necessary for this regression. 
B) you should investigate the inclusion of higher-order polynomials in your regression model. 
C) neither regression model is appropriate. 
D) higher-order polynomials are never appropriate to include in regression models. 
A) higher-order polynomials are not necessary for this regression. 
B) you should investigate the inclusion of higher-order polynomials in your regression model. 
C) neither regression model is appropriate. 
D) higher-order polynomials are never appropriate to include in regression models.

Question 19

Suppose you are interested in the factors that explain GDP all over the world.You gather data for the most recent year on GDP,Education level,Household Consumption,and Number of People Employed for every country in the world and you specify the following model. $$\begin{array} { ll } 
\log ( G D P ) = &\beta _ { 0 } + \beta _ { 1 } \text { Education Level } + \beta _ { 2 } \text { Household Consumption } \
&+ \beta _ { 3 } \text { Num People Employed } + \varepsilon \
\end{array}$$ 
a)You are able to find data for GDP,Household Consumption,Number of People Employed for every country but Education Level is missing for 40% of the countries.What are your options when estimating this model?
b)What type of countries do you think have missing data for Education Level? Why?
c)If you ran a regression with only the 60% of countries that don't have missing values,do you think your results would be different than if you had been able to gather data on all countries? Why or why not?

Accepted Answer

a)There are two options:(1)drop the 40%

Question 20

Suppose that you estimate the sample regression function $$ swidehat { alar}y  = \hat { \beta } _ { 0 } + \hat { \beta } _ { 1 } \text { Experience } _ { i } + \hat { \beta } _ { 2 } \text { Male } _ { i } + \hat { \beta } _ { 3 } \text { Married } _ { i }$$
You might be concerned that $\hat { \beta } _ { 1 }$
Is a biased estimate of the marginal effect of experience on salary because

Accepted Answer

A) a person's sex is likely an irrelevant independent variable. 
B) marital status is likely an irrelevant independent variable. 
C) education is likely an omitted independent variable. 
D) the identity of the last NCAA basketball champion is likely an omitted independent variable. 
A) a person's sex is likely an irrelevant independent variable. 
B) marital status is likely an irrelevant independent variable. 
C) education is likely an omitted independent variable. 
D) the identity of the last NCAA basketball champion is likely an omitted independent variable.

Inclusion of irrelevant variables is a potential problem because

When would you use the RESET test? What is the null hypothesis for the test? What is the intuition for why it works? Explain.

What is the potential shortcoming of using a strict cutoff to determine statistical significance? Explain.

When would you use the Davidson-MacKinnon test? What is the null hypothesis for the test? What is the intuition for why it works? Explain.

If you had to either include an irrelevant variable or omit a relevant variable,you would prefer

Why is missing data a potential problem? What are two ways to deal with it? Which approach do you prefer and why?

Potential omitted variable bias is best dealt with by

Suppose that you are performing the Davidson-MacKinnon test for choosing among non-nested alternatives and that in the second stage you estimate the sample regression function and find that the predicted values are not statistically significant.You decide that

The Eye test is used to

The Davidson-MacKinnon test is used to

What is an outlier? Why are they a potential problem? What can you do to deal with outliers? Why does this approach work? Explain.

What is the inclusion of an irrelevant variable? Why is it a problem? How do you try to prevent it? Explain.

Outliers are potentially problematic because they

One can deal with potential outliers by

Suppose that you are performing the RESET test for the inclusion of higher-order polynomials and that in the second stage you estimate the sample regression function and the predicted value terms are statistically significant.You decide that

An Introduction to Econometrics and Statistical Inference

Collection and Management of Data

Summary Statistics

Simple Linear Regression

Hypothesis Testing in Linear Regression Analysis

Multiple Linear Regression Analysis

Qualitative Variables and Non-Linearities in Multiple Linear Regression Analysis

Heteroskedasticity

Time Series Analysis

Auto-Correlation

Limited Dependent Variables

Panel Data

Instrumental Variables for Simultaneous Equations, Endogenous Independent Variables, and Measurement Error

Quantile Regression, Count Data, Sample Selection Bias, and Quasi-Experimental Methods

Filters

Exam 8: Model Selection in Multiple Linear Regression Analysis

Inclusion of irrelevant variables is a potential problem because

When would you use the RESET test? What is the null hypothesis for the test? What is the intuition for why it works? Explain.

What is the potential shortcoming of using a strict cutoff to determine statistical significance? Explain.

When would you use the Davidson-MacKinnon test? What is the null hypothesis for the test? What is the intuition for why it works? Explain.

If you had to either include an irrelevant variable or omit a relevant variable,you would prefer

Why is missing data a potential problem? What are two ways to deal with it? Which approach do you prefer and why?

Potential omitted variable bias is best dealt with by

Suppose that you are performing the Davidson-MacKinnon test for choosing among non-nested alternatives and that in the second stage you estimate the sample regression function and find that the predicted values are not statistically significant.You decide that

The Eye test is used to

The Davidson-MacKinnon test is used to

What is an outlier? Why are they a potential problem? What can you do to deal with outliers? Why does this approach work? Explain.

What is the inclusion of an irrelevant variable? Why is it a problem? How do you try to prevent it? Explain.

Outliers are potentially problematic because they

One can deal with potential outliers by

Suppose that you are performing the RESET test for the inclusion of higher-order polynomials and that in the second stage you estimate the sample regression function and the predicted value terms are statistically significant.You decide that

An Introduction to Econometrics and Statistical Inference

Collection and Management of Data

Summary Statistics

Simple Linear Regression

Hypothesis Testing in Linear Regression Analysis

Multiple Linear Regression Analysis

Qualitative Variables and Non-Linearities in Multiple Linear Regression Analysis

Heteroskedasticity

Time Series Analysis

Auto-Correlation

Limited Dependent Variables

Panel Data

Instrumental Variables for Simultaneous Equations, Endogenous Independent Variables, and Measurement Error

Quantile Regression, Count Data, Sample Selection Bias, and Quasi-Experimental Methods

Filters