Hypothesis Testing in Linear Regression

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Questions and Answers

What is the primary purpose of a confidence interval in a classical linear model?

To test a hypothesis about the population parameter

To determine the significance of the model

To provide a range of likely values for the population parameter (correct)

To provide a point estimate of the population parameter

What happens to the confidence interval when the standard error of an estimate decreases?

The confidence interval becomes biased

The confidence interval widens

The confidence interval narrows down (correct)

The confidence interval remains unchanged

What is the correct formula for the upper bound of the confidence interval for a regression coefficient?

^β - [Critical value × standard error (^β)]

^β × [Critical value × standard error (^β)]

^β + [Critical value × standard error (^β)] (correct)

^β / [Critical value × standard error (^β)]

Which of the following tests is used to test multiple linear restrictions in a classical linear model?

F-test Signup and view all the answers

What is affected by the degrees of freedom of a distribution in a classical linear model?

Confidence intervals Signup and view all the answers

What is a common problem that can affect the estimation of confidence intervals in a classical linear model?

Heteroskedasticity Signup and view all the answers

What is the relationship between the standard error of an estimate and the width of the confidence interval?

As the standard error decreases, the width of the confidence interval decreases Signup and view all the answers

What is the primary purpose of a t-test in a classical linear model?

To test a hypothesis about the population mean Signup and view all the answers

What is the primary reason why some authors prefer to report standard errors over t-statistics?

Having standard errors makes it easier to compute confidence intervals Signup and view all the answers

If the calculated value of the t-statistic is less than the critical value, what happens to the null hypothesis?

It remains unchanged Signup and view all the answers

What is a characteristic of a dependent variable that is normally distributed?

It takes on a large range of continuous values Signup and view all the answers

What is the formula for calculating the F-statistic in a multiple linear regression?

F = [(R2ur – R2r)/q] / [(1-R2ur)/n – k – 1] Signup and view all the answers

What is the purpose of hypothesis testing in regression analysis?

To determine the significance of the regression coefficients Signup and view all the answers

What is the F-statistic used for in regression analysis?

To test the significance of multiple regression coefficients Signup and view all the answers

What is the result of a t-test when the calculated value is less than the critical value?

The null hypothesis is accepted Signup and view all the answers

What is the primary advantage of using the F-statistic over the t-statistic in regression analysis?

It can be used to test the significance of multiple regression coefficients Signup and view all the answers

Which of the following tests is used to test multiple linear restrictions?

F test Signup and view all the answers

What is true about a restricted model compared to its unrestricted model?

It has fewer parameters Signup and view all the answers

What is the correct formula for the F statistic?

SSR ur / (n - k - 1) / (SSR r - SSR ur) / q Signup and view all the answers

What can be said about the F statistic?

It is always nonnegative Signup and view all the answers

What happens when the calculated value of F statistic is higher than the critical value?

We reject the null hypothesis in favor of the alternative hypothesis Signup and view all the answers

What is true about the degrees of freedom of a restricted model compared to an unrestricted model?

It is always less Signup and view all the answers

Which of the following statements is true about the F statistic and the t statistic?

The t statistic is more flexible than the F statistic Signup and view all the answers

What is the purpose of the F test?

To test multiple linear restrictions Signup and view all the answers

Study Notes

difficulty: moderate

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Description

This quiz assesses your understanding of hypothesis testing, including the F-test and multiple linear restrictions in linear regression analysis.