Question 1

Use the following to answer questions
Assuming you have two regression models and .  
-What is the relevant encompassing model required to compare the two regression models?

Accepted Answer

A)   
B)   
C)   
D)   Encompassing models cannot be used to compare these specifications A

Question 2

Consider the following regression estimated using 84 observations: yt = $\beta$1 + $\beta$2X2t + $\beta$3X3t + $\beta$4X4t + ut
Suppose that a researcher wishes to test the null hypothesis: $\beta$2 = 1 and $\beta$3 + $\beta$4 = 1. The TABULATED value of the F-distribution that we would compare the result of testing this hypothesis with at the 10% level would be approximately

Accepted Answer

A)   19.48
B)   2.76
C)   2.37
D)   3.11  C

Question 3

If our regression equation is y = X$\beta$+ u, where we have T observations and k regressors, what will be the dimension of using the standard matrix notation

Accepted Answer

A)   T * k
B)   T * 1
C)   k *1
D)   k * k  C

Question 4

Which of these is a mathematical expression of the residual sum of squares?
(I)  (II)  (III)

Accepted Answer

A)   I only
B)   I and II only
C)   I and III only
D)   I, II and III

Question 5

Why is R2 a commonly used and perhaps better measure of how well a regression model fit the data than the residual sum of squares (RSS)?

Accepted Answer

A)   The RSS is often too large
B)   The RSS does not depend on the scale of the dependent variable whereas the R2 does
C)   The RSS depends on the scale of the dependent variable whereas the R2 does not
D)   The RSS depends on the scale of the independent variable whereas the R2 does not

Question 6

Trying many variables in a regression without basing the selection of candidate variables on a financial or economic theory is popularly referred to as

Accepted Answer

A)   Data fitting
B)   Data clipping
C)   Data mining
D)   None of the above

Question 7

Use the following to answer questions
Assuming you have two regression models and .  
-How can the two models be validly compared to determine the model that better represents the data yt?

Accepted Answer

A)   By observing their respective R2
B)   By observing their respective Adjusted R2
C)   By estimating an encompassing or hybrid model
D)   All of the above

Question 8

What would the restricted regression be if you are interested in testing the null hypothesis and against the alternative hypothesis or  for a regression ,?

Accepted Answer

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Question 9

Which of these statements is a characteristic of the stepwise regression procedure?
(I) It chooses the jointly most 'important' explanatory variable from a set of candidate variables
(II) It can start with no variables in the regression and then it selects first the variable with the lowest p-value
(III) It can start with no variables in the regression and then it selects first the variable with the highest p-value

Accepted Answer

A)   I only
B)   II only
C)   III only
D)   Both I and II

Question 10

Assuming that the restricted sum of squares of the restricted regression in question 3 is 436.1 and the unrestricted sum of squares is 397.2, what would the conclusion of the hypothesis test be? (The significance level is 5%)

Accepted Answer

A)   Reject the null hypothesis
B)   Do not reject the null hypothesis
C)   Reject the alternative hypothesis
D)   Cannot say

Question 11

Question  refers to the following regression estimated on 64 observations:
YS1U1B1tS1U1B0 =$\beta$S1U1B11S1U1B0 + $\beta$S1U1B12S1U1B0XS1U1B12S1U1B0S1U1B1tS1U1B0 + $\beta$S1U1B13S1U1B0XS1U1B13S1U1B0S1U1B1tS1U1B0 + $\beta$S1U1B14S1U1B0XS1U1B14S1U1B0S1U1B1tS1U1B0 + uS1U1B1tS1U1B0
-Which of the following null hypotheses could we test using an F-test?
(I) $\beta$2 = 0
(ii) $\beta$2 = 1 and $\beta$3 + $\beta$4 = 1
(iii) $\beta$3$\beta$4 = 1
(iv) $\beta$2 -$\beta$3 -$\beta$4 = 1

Accepted Answer

A)   (i)  and (ii)  only
B)   (ii)  and (iv)  only
C)   (i) , (ii) , (iii)  and (iv) 
D)   (i) , (ii) , and (iv)  only

Question 12

Which one of the following is the most appropriate as a definition of R2 in the context that the term is usually used?

Accepted Answer

A)   It is the proportion of the total variability of y that is explained by the model
B)   It is the proportion of the total variability of y about its mean value that is explained by the model
C)   It is the correlation between the fitted values and the residuals
D)   It is the correlation between the fitted values and the mean.

Question 13

Which of the following are often considered disadvantages of the use of adjusted R2 as a variable addition / variable deletion rule?
(I) Adjusted R2 always rises as more variables are added
(ii) Adjusted R2 often leads to large models with many marginally significant or marginally insignificant variables
(iii) Adjusted R2 cannot be compared for models with different explanatory variables
(iv) Adjusted R2 cannot be compared for models with different explained variables.

Accepted Answer

A)   (ii)  and (iv)  only
B)   (i)  and (iii)  only
C)   (i) , (ii) , and (iii)  only
D)   (i) , (ii) , (iii) , and (iv) .

Question 14

For question , you are given the following data 
The regression equation is
YS1U1B1tS1U1B0 = $\beta$S1U1B11S1U1B0 + $\beta$S1U1B12S1U1B0XS1U1B12S1U1B0S1U1B1tS1U1B0 + $\beta$S1U1B13S1U1B0XS1U1B13S1U1B0S1U1B1tS1U1B0 + uS1U1B1tS1U1B0
-Which of the following is the correct value for ?

Accepted Answer

A)   2.89
B)   1.30
C)   0.84
D)   We cannot determine the value of from the information given in the question t =  \beta 1 +  \beta 2X2t +  \beta 3X3t + ut -Which of the following is the correct value for ?   
A)   2.89 
B)   1.30 
C)   0.84 
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Question 15

Which one of the following statements must hold for EVERY CASE concerning the residual sums of squares for the restricted and unrestricted regressions?

Accepted Answer

A)   URSS > RRSS
B)   URSS  ≥\ge≥   RRSS
C)   RRSS > URSS
D)   RRSS  ≥\ge≥   URSS

Question 16

Consider the following two regressions   Which of the following statements are true?
(I) The RSS will be the same for the two models
(ii) The R2 will be the same for the two models
(iii) The adjusted R2 will be different for the two models
(iv) The regression F-test will be the same for the two models

Accepted Answer

A)   (ii)  and (iv)  only
B)   (i)  and (iii)  only
C)   (i) , (ii) , and (iii)  only
D)   (i) , (ii) , (iii) , and (iv) .

Question 17

Suppose that the value of R2 for an estimated regression model is exactly one. Which of the following are true?
(I) All of the data points must lie exactly on the line
(ii) All of the residuals must be zero
(iii) All of the variability of y about is mean have has been explained by the model
(I) The fitted line will be horizontal with respect to all of the explanatory variables

Accepted Answer

A)   (ii)  and (iv)  only
B)   (i)  and (iii)  only
C)   (i) , (ii) , and (iii)  only(I) , (ii) , (iii) , and (iv)

Question 18

If you are interested in conducting a multiple hypotheses test to determine whether and are both unity for a regression , what would the restricted regression be?

Accepted Answer

A)   
B)   
C)   
D)

Question 19

What is the relationship, if any, between t-distributed and F-distributed random variables?

Accepted Answer

A)   A t-variate with z degrees of freedom is also an F(1, z) 
B)   The square of a t-variate with z degrees of freedom is also an F(1, z) 
C)   A t-variate with z degrees of freedom is also an F(z, 1) 
D)   There is no relationship between the two distributions.

Question 20

Which of these statements is not true about quantile regressions?

Accepted Answer

A)   No distributional assumptions are required to optimally estimate the parameters
B)   It is a non-parametric technique
C)   It is a parametric technique
D)   The response variable is usually assumed to be independently distributed and homoscedastic

Exam 5: Classical Linear Regression Model Assumptions and Diagnostic Tests

Use the following to answer questions Assuming you have two regression models and . -What is the relevant encompassing model required to compare the two regression models?

Which of these is a mathematical expression of the residual sum of squares? (I) (II) (III)

Why is R² a commonly used and perhaps better measure of how well a regression model fit the data than the residual sum of squares (RSS) ?

Trying many variables in a regression without basing the selection of candidate variables on a financial or economic theory is popularly referred to as

Use the following to answer questions Assuming you have two regression models and . -How can the two models be validly compared to determine the model that better represents the data y_t?

What would the restricted regression be if you are interested in testing the null hypothesis and against the alternative hypothesis or for a regression ,?

Assuming that the restricted sum of squares of the restricted regression in question 3 is 436.1 and the unrestricted sum of squares is 397.2, what would the conclusion of the hypothesis test be? (The significance level is 5%)

Which one of the following is the most appropriate as a definition of R² in the context that the term is usually used?

Which one of the following statements must hold for EVERY CASE concerning the residual sums of squares for the restricted and unrestricted regressions?

If you are interested in conducting a multiple hypotheses test to determine whether and are both unity for a regression , what would the restricted regression be?

What is the relationship, if any, between t-distributed and F-distributed random variables?

Which of these statements is not true about quantile regressions?

Exam 5: Classical Linear Regression Model Assumptions and Diagnostic Tests

Use the following to answer questions Assuming you have two regression models and . -What is the relevant encompassing model required to compare the two regression models?

If our regression equation is y = X β\betaβ + u, where we have T observations and k regressors, what will be the dimension of using the standard matrix notation

Which of these is a mathematical expression of the residual sum of squares? (I) (II) (III)

Why is R2 a commonly used and perhaps better measure of how well a regression model fit the data than the residual sum of squares (RSS) ?

Trying many variables in a regression without basing the selection of candidate variables on a financial or economic theory is popularly referred to as

Use the following to answer questions Assuming you have two regression models and . -How can the two models be validly compared to determine the model that better represents the data yt?

What would the restricted regression be if you are interested in testing the null hypothesis and against the alternative hypothesis or for a regression ,?

Assuming that the restricted sum of squares of the restricted regression in question 3 is 436.1 and the unrestricted sum of squares is 397.2, what would the conclusion of the hypothesis test be? (The significance level is 5%)

Which one of the following is the most appropriate as a definition of R2 in the context that the term is usually used?

For question , you are given the following data The regression equation is Yt = β\betaβ 1 + β\betaβ 2X2t + β\betaβ 3X3t + ut -Which of the following is the correct value for ?

Which one of the following statements must hold for EVERY CASE concerning the residual sums of squares for the restricted and unrestricted regressions?

If you are interested in conducting a multiple hypotheses test to determine whether and are both unity for a regression , what would the restricted regression be?

What is the relationship, if any, between t-distributed and F-distributed random variables?

Which of these statements is not true about quantile regressions?

Why is R² a commonly used and perhaps better measure of how well a regression model fit the data than the residual sum of squares (RSS) ?

Use the following to answer questions Assuming you have two regression models and . -How can the two models be validly compared to determine the model that better represents the data y_t?

Which one of the following is the most appropriate as a definition of R² in the context that the term is usually used?