Exam 7: Hypothesis Tests and Confidence Intervals in Multiple Regression

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The homoskedasticity only F-statistic is given by the formula The homoskedasticity only F-statistic is given by the formula   where SSR<sub>restricted</sub> is the sum of squared residuals from the restricted regression, SSR<sub>unrestricted</sub> is the sum of squared residuals from the unrestricted regression, q is the number of restrictions under the null hypothesis, and k<sub>unrestricted</sub> is the number of regressors in the unrestricted regression. Prove that this formula is the same as the following formula based on the regression R<sup>2</sup> of the restricted and unrestricted regression:  where SSRrestricted is the sum of squared residuals from the restricted regression, SSRunrestricted is the sum of squared residuals from the unrestricted regression, q is the number of restrictions under the null hypothesis, and kunrestricted is the number of regressors in the unrestricted regression. Prove that this formula is the same as the following formula based on the regression R2 of the restricted and unrestricted regression: The homoskedasticity only F-statistic is given by the formula   where SSR<sub>restricted</sub> is the sum of squared residuals from the restricted regression, SSR<sub>unrestricted</sub> is the sum of squared residuals from the unrestricted regression, q is the number of restrictions under the null hypothesis, and k<sub>unrestricted</sub> is the number of regressors in the unrestricted regression. Prove that this formula is the same as the following formula based on the regression R<sup>2</sup> of the restricted and unrestricted regression:

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All of the following are true, with the exception of one condition:

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The homoskedasticity-only F-statistic is given by the following formula

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Consider the regression output from the following unrestricted model: Unrestricted model: Dependent Variable: TESTSCR Method: Least Squares Date: 07/31/06 Time: 17:35 Sample: 1 420 Included observations: 420 Consider the regression output from the following unrestricted model: Unrestricted model: Dependent Variable: TESTSCR Method: Least Squares Date: 07/31/06 Time: 17:35 Sample: 1 420 Included observations: 420   To test for the null hypothesis that neither coefficient on the percent eligible for subsidized lunch nor the coefficient on the percent on public income assistance is statistically significant, you have your statistical package plot the confidence set. Interpret the graph below and explain what it tells you about the null hypothesis.  To test for the null hypothesis that neither coefficient on the percent eligible for subsidized lunch nor the coefficient on the percent on public income assistance is statistically significant, you have your statistical package plot the confidence set. Interpret the graph below and explain what it tells you about the null hypothesis. Consider the regression output from the following unrestricted model: Unrestricted model: Dependent Variable: TESTSCR Method: Least Squares Date: 07/31/06 Time: 17:35 Sample: 1 420 Included observations: 420   To test for the null hypothesis that neither coefficient on the percent eligible for subsidized lunch nor the coefficient on the percent on public income assistance is statistically significant, you have your statistical package plot the confidence set. Interpret the graph below and explain what it tells you about the null hypothesis.

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