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

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

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

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

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

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. 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.

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 ?

A) 2.89 B) 1.30 C) 0.84 D) We cannot determine the value of from the information given in the question A) 2.89 B) 1.30 C) 0.84 D) We cannot determine the value of from the information given in the question

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

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

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?

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(Multiple Choice)

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Question 1

Correct Answer:

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Consider the following regression estimated using 84 observations: y_t = $\beta$ ₁ + $\beta$ ₂X₂_t + $\beta$ ₃X₃_t + $\beta$ ₄X₄_t + u_t 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

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(Multiple Choice)

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Question 2

Correct Answer:

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

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Question 3

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

(Multiple Choice)

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Question 4

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)?

(Multiple Choice)

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Question 5

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

(Multiple Choice)

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Question 6

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?

(Multiple Choice)

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Question 7

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

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Question 8

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

(Multiple Choice)

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Question 9

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%)

(Multiple Choice)

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Question 10

Question refers to the following regression estimated on 64 observations: Y_t = $\beta$ ₁ + $\beta$ ₂X₂_t + $\beta$ ₃X₃_t + $\beta$ ₄X₄_t + u_t -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

(Multiple Choice)

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Question 11

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

(Multiple Choice)

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Question 12

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.

(Multiple Choice)

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Question 13

For question , you are given the following data $For question , you are given the following data The regression equation is Yt = \beta 1 + \beta 2X2t + \beta 3X3t + ut -Which of the following is the correct value for ?$ The regression equation is Y_t = $\beta$ ₁ + $\beta$ ₂X₂_t + $\beta$ ₃X₃_t + u_t -Which of the following is the correct value for ? $For question , you are given the following data The regression equation is Yt = \beta 1 + \beta 2X2t + \beta 3X3t + ut -Which of the following is the correct value for ?$

(Multiple Choice)

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Question 14

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

(Multiple Choice)

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Question 15

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

(Multiple Choice)

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Question 16

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

(Multiple Choice)

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Question 17

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?

(Multiple Choice)

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Question 18

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

(Multiple Choice)

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Question 19

Which of these statements is not true about quantile regressions?

(Multiple Choice)

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Question 20

Showing 1 - 20 of 20

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?

Introduction

Mathematical and Statistical Foundations

A Brief Overview of the Classical Linear Regression Model

Further Development and Analysis of the Classical Linear Regression Model

Univariate Time Series Modelling and Forecasting

Multivariate Models

Modelling Long-Run Relationships in Finance

Modelling Volatility and Correlation

Switching Models

Panel Data and Limited Dependent Variable Models

Filters

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?

Introduction

Mathematical and Statistical Foundations

A Brief Overview of the Classical Linear Regression Model

Further Development and Analysis of the Classical Linear Regression Model

Univariate Time Series Modelling and Forecasting

Multivariate Models

Modelling Long-Run Relationships in Finance

Modelling Volatility and Correlation

Switching Models

Panel Data and Limited Dependent Variable Models

Filters

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?