Question 1

Weighted Least Squares is performed by

Accepted Answer

A) re-weighting the estimated standard errors from the OLS regression. 
B) re-weighting the estimated slope coefficients from the OLS regression. 
C) including the command ",robust" in the estimation. 
D) re-weighting the original data so that OLS provides estimated standard errors with minimum variance. 
A) re-weighting the estimated standard errors from the OLS regression. 
B) re-weighting the estimated slope coefficients from the OLS regression. 
C) including the command ",robust" in the estimation. 
D) re-weighting the original data so that OLS provides estimated standard errors with minimum variance. D

Question 2

Suppose that while performing the Modified White's test,you estimate the model $e _ { i } ^ { 2 } = \delta _ { 0 } + \delta _ { 1 } \hat { y } _ { i } + \delta _ { 2 } \hat { y } _ { i } ^ { 2 } + u _ { i }$
The final step in the Modified White's test is to perform

Accepted Answer

A) an F-test of the overall significance of the squared residuals regression. 
B) an F-test of the joint significance of δ1 and δ2. 
C) a t-test of the individual significance of δ1. 
D) a t-test of the individual significance of δ2. 
A) an F-test of the overall significance of the squared residuals regression. 
B) an F-test of the joint significance of δ1 and δ2. 
C) a t-test of the individual significance of δ1. 
D) a t-test of the individual significance of δ2. B

Question 3

The Goldfeld-Quandt test statistic is

Accepted Answer

A)  $G Q = U S S _ { 2 } / U S S _ { 1 }$ 
B)  $G Q = U S S _ { 1 } / U S S _ { 2 }$ 
C)  $G Q = U S S _ { 1 } \cdot U S S _ { 2 }$ 
D)  $F _ { n _ { 1 } - k _ { 1 } , n _ { 2 } - k _ { 2 } , 05 }$ 
A)  $G Q = U S S _ { 2 } / U S S _ { 1 }$ 
B)  $G Q = U S S _ { 1 } / U S S _ { 2 }$ 
C)  $G Q = U S S _ { 1 } \cdot U S S _ { 2 }$ 
D)  $F _ { n _ { 1 } - k _ { 1 } , n _ { 2 } - k _ { 2 } , 05 }$ B

Question 4

Heteroskedasticity violates assumption

Accepted Answer

A) M3. 
B) M4. 
C) M5. 
D) M6. 
A) M3. 
B) M4. 
C) M5. 
D) M6.

Question 5

The first step in the Goldfeld-Quandt test is to

Accepted Answer

A) estimate the model and calculate the estimated residuals. 
B) estimate the model and calculate the estimated residuals squared. 
C) sort the data set from the lowest to the highest value of the dependent variable. 
D) sort the data set from the lowest to the highest value of the suspect independent variable. 
A) estimate the model and calculate the estimated residuals. 
B) estimate the model and calculate the estimated residuals squared. 
C) sort the data set from the lowest to the highest value of the dependent variable. 
D) sort the data set from the lowest to the highest value of the suspect independent variable.

Question 6

Suppose you are interested in explaining variation in Mile Run Time in a sample of 22,359 individuals over the age of 18 and that you estimate the sample regression function (standard errors in parentheses)

$\begin{array}{lllll}
 \text {Mile Run Time}  _ { i } =& 7.28 +& 0.09  \text {Weight}  _ { i } +& 0.13  \text {Age}   _ { i } -& 0.43  \text {Days Exercise per Week } _ { i }\  \

&(2.36) &(0.04)&(0.06)&( 0.13 )\
\end{array}$
 
a)Which variable do you suspect could be responsible for heteroskedasticity in this model? Why? Explain.
b)How would you use the modified White's test to determine whether heteroskedasticity is present? Explain.
c)What would be your most preferred method for correcting for the potential heteroskedasticity? Explain.

Accepted Answer

a.The variable that would be responsible

Question 7

The second step in the Breusch-Pagan test is to regress the

Accepted Answer

A) residuals on the independent variables from the original OLS regression. 
B) squared residuals on the residuals from the original OLS regression. 
C) squared residuals on the independent variables from the original OLS regression. 
D) residuals on the squared residuals from the original OLS regression. 
A) residuals on the independent variables from the original OLS regression. 
B) squared residuals on the residuals from the original OLS regression. 
C) squared residuals on the independent variables from the original OLS regression. 
D) residuals on the squared residuals from the original OLS regression.

Question 8

How do you perform the Goldfeld-Quandt test for heteroskedasticity? Explain.

Accepted Answer

You perform the Goldfeld-Quandt test for

Question 9

What is the intuition behind the modified White's test for heteroskedasticity? Explain.

Accepted Answer

The intuition behind the modified White'

Question 10

The null hypothesis for the Goldfeld-Quandt test is

Accepted Answer

A)  $H _ { 0 } : U S S _ { 2 } / U S S _ { 1 } = 0$ 
B)  $H _ { 0 } : U S S _ { 2 } / U S S _ { 1 } \neq 0$ 
C)  $H _ { 0 } : U S S _ { 2 } / U S S _ { 1 } = 1$ 
D)  $H _ { 0 } : U S S _ { 2 } / U S S _ { 1 } \neq 1$ 
A)  $H _ { 0 } : U S S _ { 2 } / U S S _ { 1 } = 0$ 
B)  $H _ { 0 } : U S S _ { 2 } / U S S _ { 1 } \neq 0$ 
C)  $H _ { 0 } : U S S _ { 2 } / U S S _ { 1 } = 1$ 
D)  $H _ { 0 } : U S S _ { 2 } / U S S _ { 1 } \neq 1$

Question 11

Suppose that you plot the residuals for your sample and get  
You should conclude that

Accepted Answer

A) definitely heteroskedastic. 
B) likely homoskedastic. 
C) possibly heteroskedastic and you would perform a formal test for heteroskedasticity. 
D) possibly homoskedastic and you would perform a correction for homoskedasticity. 
A) definitely heteroskedastic. 
B) likely homoskedastic. 
C) possibly heteroskedastic and you would perform a formal test for heteroskedasticity. 
D) possibly homoskedastic and you would perform a correction for homoskedasticity.

Question 12

The first step in the Modified White's test is to estimate the model and

Accepted Answer

A) calculate the predicted values of the dependent variable. 
B) calculate the estimated residuals. 
C) calculate the estimated residuals and the predicted values of the dependent variable. 
D) plot the estimated residuals. 
A) calculate the predicted values of the dependent variable. 
B) calculate the estimated residuals. 
C) calculate the estimated residuals and the predicted values of the dependent variable. 
D) plot the estimated residuals.

Question 13

Suppose you are interested in explaining variation in Vacation Spending in a sample of 12,486 men and women and that you estimate the sample regression function (standard errors in parentheses)

$\begin{array}{llcc}
 \text {Vacation Spending}_ { i } = &639.82 +& 0.22 \text {Income} { i } + &217.39 \text {College Graduate}_ { i }\

&( 134.62 ) &( 0.05 )&(91.43)
\end{array}$
 
a)Which variable do you suspect could be responsible for heteroskedasticity in this model? Why? Explain.
b)How would you use the Goldfeld-Quandt test to determine whether heteroskedasticity is present? Explain.
c)Suppose you know that heteroskedasticity takes the form $$h ( x ) = \operatorname { Income } _ { i } ^ { 2 } \cdot \sigma ^ { 2 }$$ 
.How would you use Weighted Least Squares to correct for the heteroskedasticity? Explain.

Accepted Answer

a.It seems most reasonable that Income i

Question 14

Suppose you wish to explain variation in body mass index (BMI)by variation in height (in inches)by estimating the model $B M I _ { i } = \beta _ { 0 } + \beta _ { 1 } \text { Height } _ { i }$
And you suspect heteroskedasticity of the form $\operatorname { Var } ( \varepsilon ) = \sigma ^ { 2 } \text { Height } _ { i } ^ { 4 }$
)You could perform Weighted Least Squares by estimating the model

Accepted Answer

A)  $B M I _ { i } = \beta _ { 0 } + \beta _ { 1 } \text { Height } _ { i }$ . 
B)  $\text { BMI } _ { i } / \text { Height } _ { i } = \beta _ { 0 } \left( 1 / \text { Height } _ { i } \right) + \beta _ { 1 }$ . 
C)  $B M I _ { i } / \text { Height } _ { i } ^ { 2 } = \beta _ { 0 } \left( 1 / \text { Height } _ { i } ^ { 2 } \right) + \beta _ { 1 } \left( 1 / \text { Height } _ { i } \right)$ . 
D)  $1 = \beta _ { 0 } \left( 1 / B M I _ { i } \right) + \beta _ { 1 } \text { Height } _ { i } / B M I _ { i }$ . 
A)  $B M I _ { i } = \beta _ { 0 } + \beta _ { 1 } \text { Height } _ { i }$ . 
B)  $\text { BMI } _ { i } / \text { Height } _ { i } = \beta _ { 0 } \left( 1 / \text { Height } _ { i } \right) + \beta _ { 1 }$ . 
C)  $B M I _ { i } / \text { Height } _ { i } ^ { 2 } = \beta _ { 0 } \left( 1 / \text { Height } _ { i } ^ { 2 } \right) + \beta _ { 1 } \left( 1 / \text { Height } _ { i } \right)$ . 
D)  $1 = \beta _ { 0 } \left( 1 / B M I _ { i } \right) + \beta _ { 1 } \text { Height } _ { i } / B M I _ { i }$ .

Question 15

The alternative hypothesis for the Goldfeld-Quandt test is

Accepted Answer

A)  $H _ { 0 } : U S S _ { 2 } / U S S _ { 1 } = 0$ 
B)  $H _ { 0 } : U S S _ { 2 } / U S S _ { 1 } \neq 0$ 
C)  $H _ { 0 } : U S S _ { 2 } / U S S _ { 1 } = 1$ 
D)  $H _ { 0 } : U S S _ { 2 } / U S S _ { 1 } \neq 1$ 
A)  $H _ { 0 } : U S S _ { 2 } / U S S _ { 1 } = 0$ 
B)  $H _ { 0 } : U S S _ { 2 } / U S S _ { 1 } \neq 0$ 
C)  $H _ { 0 } : U S S _ { 2 } / U S S _ { 1 } = 1$ 
D)  $H _ { 0 } : U S S _ { 2 } / U S S _ { 1 } \neq 1$

Question 16

What is the intuition behind the Breusch-Pagan test for heteroskedasticity? Explain.

Accepted Answer

The intuition behind the Breusch-Pagan t

Question 17

Suppose that you plot the residuals for your sample against independent variable x and get  
You should conclude that the data are

Accepted Answer

A) definitely heteroskedastic. 
B) likely homoskedastic. 
C) possibly heteroskedastic and you would perform a formal test for heteroskedasticity. 
D) possibly homoskedastic and you would perform a correction for homoskedasticity. 
A) definitely heteroskedastic. 
B) likely homoskedastic. 
C) possibly heteroskedastic and you would perform a formal test for heteroskedasticity. 
D) possibly homoskedastic and you would perform a correction for homoskedasticity.

Question 18

The rejection rule for the Goldfeld-Quandt test at the 95% level is reject H0 if

Accepted Answer

A)  $G Q > F _ { n _ { 1 } - k _ { 1 } , n _ { 2 } - k _ { 2,0 } 05 }$ 
B)  $G Q  F _ { n _ { 1 } - k _ { 1 } , n _ { 2 } - k _ { 2 } , 025 }$ 
D)  $G Q > 1$ 
A)  $G Q > F _ { n _ { 1 } - k _ { 1 } , n _ { 2 } - k _ { 2,0 } 05 }$ 
B)  $G Q  F _ { n _ { 1 } - k _ { 1 } , n _ { 2 } - k _ { 2 } , 025 }$ 
D)  $G Q > 1$

Question 19

How do you perform the modified White's test for heteroskedasticity? Explain.

Accepted Answer

You perform the modified White's test fo

Question 20

Homoskedasticity occurs when

Accepted Answer

A) the error variance is constant. 
B) the error variance is non-constant. 
C) the dependent variable variance is constant. 
D) the dependent variable variance is non-constant. 
A) the error variance is constant. 
B) the error variance is non-constant. 
C) the dependent variable variance is constant. 
D) the dependent variable variance is non-constant.

Weighted Least Squares is performed by

Suppose that while performing the Modified White's test,you estimate the model $e _ { i } ^ { 2 } = \delta _ { 0 } + \delta _ { 1 } \hat { y } _ { i } + \delta _ { 2 } \hat { y } _ { i } ^ { 2 } + u _ { i }$ The final step in the Modified White's test is to perform

The Goldfeld-Quandt test statistic is

Heteroskedasticity violates assumption

The first step in the Goldfeld-Quandt test is to

The second step in the Breusch-Pagan test is to regress the

How do you perform the Goldfeld-Quandt test for heteroskedasticity? Explain.

What is the intuition behind the modified White's test for heteroskedasticity? Explain.

The null hypothesis for the Goldfeld-Quandt test is

Suppose that you plot the residuals for your sample and get You should conclude that

The first step in the Modified White's test is to estimate the model and

The alternative hypothesis for the Goldfeld-Quandt test is

What is the intuition behind the Breusch-Pagan test for heteroskedasticity? Explain.

Suppose that you plot the residuals for your sample against independent variable x and get You should conclude that the data are

The rejection rule for the Goldfeld-Quandt test at the 95% level is reject H₀ if

How do you perform the modified White's test for heteroskedasticity? Explain.

Homoskedasticity occurs when

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

Model Selection in Multiple Linear Regression Analysis

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 9: Heteroskedasticity

Weighted Least Squares is performed by

The Goldfeld-Quandt test statistic is

Heteroskedasticity violates assumption

The first step in the Goldfeld-Quandt test is to

The second step in the Breusch-Pagan test is to regress the

How do you perform the Goldfeld-Quandt test for heteroskedasticity? Explain.

What is the intuition behind the modified White's test for heteroskedasticity? Explain.

The null hypothesis for the Goldfeld-Quandt test is

Suppose that you plot the residuals for your sample and get You should conclude that

The first step in the Modified White's test is to estimate the model and

The alternative hypothesis for the Goldfeld-Quandt test is

What is the intuition behind the Breusch-Pagan test for heteroskedasticity? Explain.

Suppose that you plot the residuals for your sample against independent variable x and get You should conclude that the data are

The rejection rule for the Goldfeld-Quandt test at the 95% level is reject H0 if

How do you perform the modified White's test for heteroskedasticity? Explain.

Homoskedasticity occurs when

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

Model Selection in Multiple Linear Regression Analysis

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

The rejection rule for the Goldfeld-Quandt test at the 95% level is reject H₀ if