Question 1

The n-R-squared statistic also refers to the:

Accepted Answer

D

Question 2

If _j,an unbiased estimator of _j,is consistent,then the:

Accepted Answer

Consistency means that as the sample size grows, the estimator converges to the true parameter value. As a result, the distribution of the estimator becomes more and more tightly distributed around the true parameter value. Therefore, the correct choice is B.

Question 3

Even if the error terms in a regression equation,u₁,u₂,….. ,u_n,are not normally distributed,the estimated coefficients can be normally distributed.

Accepted Answer

False

Question 4

If _jis an OLS estimator of a regression coefficient associated with one of the explanatory variables,such that j= 1,2,…. ,n,asymptotic standard error of _j will refer to the:

Accepted Answer

The answer of If _jis an OLS estimator of...

Question 5

In a multiple regression model,the OLS estimator is consistent if:

Accepted Answer

The OLS estimator is consistent if there is no correlation between the independent variables and the error term. The other options presented (A, B, C) are incorrect as they either do not relate to the consistency of the OLS estimator or are conditions that would violate the assumptions of the multiple regression model.

Question 6

If the error term is correlated with any of the independent variables,the OLS estimators are:

Accepted Answer

If the error term is correlated with any of the independent variables, the OLS estimators become biased and inconsistent. This is known as endogeneity or omitted variable bias. Therefore, option C is the correct answer.

Question 7

In a regression model,if variance of the dependent variable,y,conditional on an explanatory variable,x,or Var(y|x),is not constant,_____.

Accepted Answer

The answer of In a regression model,if variance of the...

Question 8

A normally distributed random variable is symmetrically distributed about its mean,it can take on any positive or negative value (but with zero probability),and more than 95% of the area under the distribution is within two standard deviations.

Accepted Answer

This statement accurately describes the properties of a normal distribution.

Question 9

The LM statistic requires estimation of the unrestricted model only.

Accepted Answer

The LM (Lagrange Multiplier) statistic is used to test for the significance of variables in a restricted model without estimating the parameters of the unrestricted model. It is based on the comparison between the restricted and unrestricted models, but the actual calculation of the LM statistic only requires the estimation of the restricted model and uses derivatives to assess the impact of adding additional variables.

Question 10

If OLS estimators satisfy asymptotic normality,it implies that:

Accepted Answer

Asymptotic normality implies that as the sample size gets larger and larger, the distribution of the OLS estimators approaches a normal distribution. This is why option A is correct. Options B, C, and D are incorrect because they do not accurately describe the implications of asymptotic normality.

Question 11

The F statistic is also referred to as the score statistic.

Accepted Answer

The F statistic is not commonly referred to as the score statistic. The score statistic is typically used in the context of logistic regression. The F statistic is commonly used in ANOVA and regression analyses.

Question 12

If variance of an independent variable in a regression model,say x₁,is greater than 0,or Var(x₁)> 0,the inconsistency in ₁(estimator associated with x₁)is negative,if x₁ and the error term are positively related.

Accepted Answer

The answer of If variance of an independent variable in...

Question 13

Which of the following statements is true under the Gauss-Markov assumptions?

Accepted Answer

Under the Gauss-Markov assumptions, OLS estimators are best linear unbiased and asymptotically efficient. This means that among all linear and unbiased estimators, OLS estimators have the smallest variance and converge in probability to the true value as the sample size increases. Therefore, option C is the correct statement. Option A is incorrect because OLS estimators are not asymptotically inefficient. Option B is incorrect because OLS estimators are unbiased under the Gauss-Markov assumptions. Option D is incorrect because the LM test is actually based on the Gauss-Markov assumptions.

Question 14

The LM statistic follows a:

Accepted Answer

The answer of The LM statistic follows a:
...

Question 15

If _j,an unbiased estimator of _j,is also a consistent estimator of _j,then when the sample size tends to infinity:

Accepted Answer

The statement implies that the unbiased estimator is asymptotically consistent for a particular parameter. Hence, as the sample size tends to infinity, the distribution of the estimator collapses to the true value of the parameter, which is 11eab0c9_9101_2e28_8f52_a582aa537f79_TB2132_11 _j. Thus, C is the correct choice.

Question 16

An auxiliary regression refers to a regression that is used:

Accepted Answer

An auxiliary regression is used to compute a test statistic, usually for a hypothesis test or to assess the overall significance of a model. However, the coefficients in an auxiliary regression are not of direct interest and may not be interpreted in the same way as the coefficients in the original model. Instead, the focus is on the magnitude and significance of the test statistic, such as an F-statistic or t-statistic.

Question 17

If δ₁ = Cov(x₁/x₂)/ Var(x₁)where x₁ and x₂ are two independent variables in a regression equation,which of the following statements is true?

Accepted Answer

The answer of If δ₁ = Cov(x₁/x₂)/ Var(x₁)where x₁ and...

Question 18

A useful rule of thumb is that standard errors are expected to shrink at a rate that is the inverse of the:

Accepted Answer

The standard error is expected to shrink at a rate that is the inverse of the square root of the sample size. This means that as the sample size increases, the standard error decreases indicating increased precision in the estimates. The number of parameters in the model does not relate to the rate at which standard errors shrink.

Question 19

Which of the following statements is true?

Accepted Answer

The F test and the LM (Lagrange Multiplier) test, along with the Wald test, are asymptotically equivalent in large samples, meaning that as the sample size grows, the outcomes of these tests converge and show fewer discrepancies. This is because, in large samples, the distributional differences among these test statistics become negligible, leading to similar conclusions regarding hypothesis testing.

Question 20

Which of the following statements is true?

Accepted Answer

The answer of Which of the following statements is true?
...

Quiz 5: Multiple Regression Analysis: Ols Asymptotics

The n-R-squared statistic also refers to the:

If _j,an unbiased estimator of _j,is consistent,then the:

Even if the error terms in a regression equation,u₁,u₂,….. ,u_n,are not normally distributed,the estimated coefficients can be normally distributed.

If _jis an OLS estimator of a regression coefficient associated with one of the explanatory variables,such that j= 1,2,…. ,n,asymptotic standard error of _j will refer to the:

In a multiple regression model,the OLS estimator is consistent if:

If the error term is correlated with any of the independent variables,the OLS estimators are:

In a regression model,if variance of the dependent variable,y,conditional on an explanatory variable,x,or Var(y|x) ,is not constant,_____.

A normally distributed random variable is symmetrically distributed about its mean,it can take on any positive or negative value (but with zero probability),and more than 95% of the area under the distribution is within two standard deviations.

The LM statistic requires estimation of the unrestricted model only.

If OLS estimators satisfy asymptotic normality,it implies that:

The F statistic is also referred to as the score statistic.

If variance of an independent variable in a regression model,say x₁,is greater than 0,or Var(x₁)> 0,the inconsistency in ₁(estimator associated with x₁)is negative,if x₁ and the error term are positively related.

Which of the following statements is true under the Gauss-Markov assumptions?

The LM statistic follows a:

If _j,an unbiased estimator of _j,is also a consistent estimator of _j,then when the sample size tends to infinity:

An auxiliary regression refers to a regression that is used:

If δ₁ = Cov(x₁/x₂) / Var(x₁) where x₁ and x₂ are two independent variables in a regression equation,which of the following statements is true?

A useful rule of thumb is that standard errors are expected to shrink at a rate that is the inverse of the:

Which of the following statements is true?

Which of the following statements is true?

Quiz 5: Multiple Regression Analysis: Ols Asymptotics

The n-R-squared statistic also refers to the:

If j,an unbiased estimator of j,is consistent,then the:

Even if the error terms in a regression equation,u1,u2,….. ,un,are not normally distributed,the estimated coefficients can be normally distributed.

If jis an OLS estimator of a regression coefficient associated with one of the explanatory variables,such that j= 1,2,…. ,n,asymptotic standard error of j will refer to the:

In a multiple regression model,the OLS estimator is consistent if:

If the error term is correlated with any of the independent variables,the OLS estimators are:

In a regression model,if variance of the dependent variable,y,conditional on an explanatory variable,x,or Var(y|x) ,is not constant,_____.

A normally distributed random variable is symmetrically distributed about its mean,it can take on any positive or negative value (but with zero probability),and more than 95% of the area under the distribution is within two standard deviations.

The LM statistic requires estimation of the unrestricted model only.

If OLS estimators satisfy asymptotic normality,it implies that:

The F statistic is also referred to as the score statistic.

If variance of an independent variable in a regression model,say x1,is greater than 0,or Var(x1)> 0,the inconsistency in 1(estimator associated with x1)is negative,if x1 and the error term are positively related.

Which of the following statements is true under the Gauss-Markov assumptions?

The LM statistic follows a:

If j,an unbiased estimator of j,is also a consistent estimator of j,then when the sample size tends to infinity:

An auxiliary regression refers to a regression that is used:

If δ1 = Cov(x1/x2) / Var(x1) where x1 and x2 are two independent variables in a regression equation,which of the following statements is true?

A useful rule of thumb is that standard errors are expected to shrink at a rate that is the inverse of the:

Which of the following statements is true?

Which of the following statements is true?

If _j,an unbiased estimator of _j,is consistent,then the:

Even if the error terms in a regression equation,u₁,u₂,….. ,u_n,are not normally distributed,the estimated coefficients can be normally distributed.

If _jis an OLS estimator of a regression coefficient associated with one of the explanatory variables,such that j= 1,2,…. ,n,asymptotic standard error of _j will refer to the:

If variance of an independent variable in a regression model,say x₁,is greater than 0,or Var(x₁)> 0,the inconsistency in ₁(estimator associated with x₁)is negative,if x₁ and the error term are positively related.

If _j,an unbiased estimator of _j,is also a consistent estimator of _j,then when the sample size tends to infinity:

If δ₁ = Cov(x₁/x₂) / Var(x₁) where x₁ and x₂ are two independent variables in a regression equation,which of the following statements is true?