Homework Answers
The correct option is d.) there is no correlation between the independent variables and the error term.
In a multiple regression model, the OLS estimator is consistent if there is no correlation between the independent variables and the error term.
The OLS estimators are inconsistent if the error is correlated with any of the independent variables.
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2. In a multiple regression model, the OLS estimator is consistent if a. there is no...
1. If OLS estimators satisfy asymptotic normality, it implies that a. they are approximately normally distributed b. th...
1. If OLS estimators satisfy asymptotic normality, it implies that a. they are approximately normally distributed b. they are approximately normally distributed in samples with less than 10 observations large enough sample sizes c. they have a constant mean equal to zero and variance equal to d. they have a constant mean equal to one and variance equal to o 2 In a multiple regression model, the OLS estimator is consistent if a. there is no correlation between the dependent...
Prove that the OLS estimator As for β in the linear regression model is consistent Let's first sh...
Taking the yellow parts below as a model to solve the
question above. Thank you!!!!!!!!
Prove that the OLS estimator As for β in the linear regression model is consistent Let's first show that the OLS estimator is consistent Recall the result for β LS-(Lil Xix;厂E-1 xīYi Using Yi = X(B* + ui By the WLLN Assuming that E(X,X is non-negative definite (so that its inverse exists) and using Slutsky's theorem It follows In words: ßOLs converges in probability to...
1. In a multiple regression model, changing the scale of one of the independent variables (a)...
1. In a multiple regression model, changing the scale of one of the independent variables (a) changes the standard error of its own OLS slope estimator (b) changes the standard error of all OLS slope estimators (c) changes the own t-statistic for testing its statistical significance (d) makes its confidence interval larger (e) All of the above
Question 1: Which of the following would generally cause the variance of the OLS estimator of...
Question 1: Which of the following would generally cause the variance of the OLS estimator of the slope in a regression model to be larger? 1) smaller variance of the error term 2) a larger sample size 3) smaller variance of the independent variable 4) larger variance of Xi ------------------------------------------------------------------------------------------------------------------------------ Question 2: Which of the following is the best description of the sampling distribution of the OLS estimator under the least squares assumptions? 1) it is a Student's t distribution...
How does a bivariate regression model differ from a multiple regression model? Multiple Choice A bivariate...
How does a bivariate regression model differ from a multiple regression model? Multiple Choice A bivariate regression has only one dependent and independent variable but a multiple regression has one dependent variable and may have many independent variables. A bivariate regression has more than one dependent variable and only one independent variable where a multiple regression has one dependent variable and may have many independent variables. A bivariate regression has only one dependent and many independent variables but a multiple...
What's the consequence of the homoskedasticity assumption? Unbiasedness It makes OLS the best estimator There is...
What's the consequence of the homoskedasticity assumption? Unbiasedness It makes OLS the best estimator There is no answer heteroskedasticity QUESTION 2 What's the meaning of heteroskedasticity? The error term of the regression model has a constant variance That it has the least variance That it has a multivariate regressors The variance of the error term is a function of one of the regressors QUESTION 3 Suppose both X1 and X2 are the relevant variables in explaining Y and both variables...
When evaluating a multiple regression model, for example when we regress dependent variable Y on two...
When evaluating a multiple regression model, for example when we regress dependent variable Y on two independent variables X1 and X2, a commonly used goodness of fit measure is: A. Correlation between Y and X1 B. Correlation between Y and X2 C. Correlation between X1 and X2 D. Adjusted-R2 E. None of the above
QUESTION 1 If a t-test is performed in the context of a multiple regression model and...
QUESTION 1 If a t-test is performed in the context of a multiple regression model and the null hypothesis cannot be rejected, this means that A. the independent variable for which the test has been performed has a significant relationship with the dependent variable. B. the independent variable for which the test has been performed has no significant relationship with the dependent variable. C. all independent variables have a significant relationship with the dependent variable. D. no independent variable has...
Q3. [10 points [Serial Correlation Consider a simple linear regression model with time series dat...
Q3. [10 points [Serial Correlation Consider a simple linear regression model with time series data: Suppose the error ut is strictly exogenous. That is Moreover, the error term follows an AR(1) serial correlation model. That where et are uncorrelated, and have a zero mean and constant variance a. 2 points Will the OLS estimator of P be unbiased? Why or why not? b. [3 points Will the conventional estimator of the variance of the OLS estimator be unbiased? Why or...
1. If OLS estimators satisfy asymptotic normality, it implies that a. they are approximately normally distributed b. they are approximately normally distributed in samples with less than 10 observations large enough sample sizes c. they have a constant mean equal to zero and variance equal to d. they have a constant mean equal to one and variance equal to o 2 In a multiple regression model, the OLS estimator is consistent if a. there is no correlation between the dependent...
Taking the yellow parts below as a model to solve the
question above. Thank you!!!!!!!!
Prove that the OLS estimator As for β in the linear regression model is consistent Let's first show that the OLS estimator is consistent Recall the result for β LS-(Lil Xix;厂E-1 xīYi Using Yi = X(B* + ui By the WLLN Assuming that E(X,X is non-negative definite (so that its inverse exists) and using Slutsky's theorem It follows In words: ßOLs converges in probability to...
1. In a multiple regression model, changing the scale of one of the independent variables (a) changes the standard error of its own OLS slope estimator (b) changes the standard error of all OLS slope estimators (c) changes the own t-statistic for testing its statistical significance (d) makes its confidence interval larger (e) All of the above
What's the consequence of the homoskedasticity assumption? Unbiasedness It makes OLS the best estimator There is no answer heteroskedasticity QUESTION 2 What's the meaning of heteroskedasticity? The error term of the regression model has a constant variance That it has the least variance That it has a multivariate regressors The variance of the error term is a function of one of the regressors QUESTION 3 Suppose both X1 and X2 are the relevant variables in explaining Y and both variables...
QUESTION 1 If a t-test is performed in the context of a multiple regression model and the null hypothesis cannot be rejected, this means that A. the independent variable for which the test has been performed has a significant relationship with the dependent variable. B. the independent variable for which the test has been performed has no significant relationship with the dependent variable. C. all independent variables have a significant relationship with the dependent variable. D. no independent variable has...
Q3. [10 points [Serial Correlation Consider a simple linear regression model with time series data: Suppose the error ut is strictly exogenous. That is Moreover, the error term follows an AR(1) serial correlation model. That where et are uncorrelated, and have a zero mean and constant variance a. 2 points Will the OLS estimator of P be unbiased? Why or why not? b. [3 points Will the conventional estimator of the variance of the OLS estimator be unbiased? Why or...
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