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There are different ways to combine features of the Breusch-Pagan and White tests for heteroskedastic- ity. One possibility not covered in the text is to run the regression af on x1, X2, ..., xg. V7, i = 1, ... , n, where the û; are the OLS residuals and the ŷ; are the OLS fitted values. Then, we would test joint significance of x1, x2. ..., Xg and y. (Of course, we always include an intercept in this regression.) (i) What are the df associated with the proposed F test for heteroskedasticity? (ii) Explain why the R-squared from the regression above will always be at least as large as the R-squareds for the BP regression and the special case of the White test. (iii) Does part (ii) imply that the new test always delivers a smaller p-value than either the BP or special case of the White statistic? Explain. (iv) Suppose someone suggests also adding ŷ; to the newly proposed test. What do you think of this idea?

There are different ways to combine features of the Breusch-Pagan and White tests for heteroskedastic- ity. One possibility not covered in the text is to run the regression af on x1, X2, ..., xg. V7, i = 1, ... , n, where the û; are the OLS residuals and the ŷ; are the OLS fitted values. Then, we would test joint significance of x1, x2. ..., Xg and y. (Of course, we always include an intercept in this regression.) (i) What are the df associated with the proposed F test for heteroskedasticity? (ii) Explain why the R-squared from the regression above will always be at least as large as the R-squareds for the BP regression and the special case of the White test. (iii) Does part (ii) imply that the new test always delivers a smaller p-value than either the BP or special case of the White statistic? Explain. (iv) Suppose someone suggests also adding ŷ; to the newly proposed test. What do you think of this idea?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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There are different ways to combine features of the Breusch-Pagan and White tests for heteroskedastic- ity. One possibility not covered in the text is to run the regression af on x1, X2, ..., xg. V7, i = 1, ... , n, where the û; are the OLS residuals and the ŷ; are the OLS fitted values. Then, we would test joint significance of x1, x2. ..., Xg and y. (Of course, we always include an intercept in this regression.) (i) What are the df associated with the proposed F test for heteroskedasticity? (ii) Explain why the R-squared from the regression above will always be at least as large as the R-squareds for the BP regression and the special case of the White test. (iii) Does part (ii) imply that the new test always delivers a smaller p-value than either the BP or special case of the White statistic? Explain. (iv) Suppose someone suggests also adding ŷ; to the newly proposed test. What do you think of this idea?
Transcribed Image Text:There are different ways to combine features of the Breusch-Pagan and White tests for heteroskedastic- ity. One possibility not covered in the text is to run the regression af on x1, X2, ..., xg. V7, i = 1, ... , n, where the û; are the OLS residuals and the ŷ; are the OLS fitted values. Then, we would test joint significance of x1, x2. ..., Xg and y. (Of course, we always include an intercept in this regression.) (i) What are the df associated with the proposed F test for heteroskedasticity? (ii) Explain why the R-squared from the regression above will always be at least as large as the R-squareds for the BP regression and the special case of the White test. (iii) Does part (ii) imply that the new test always delivers a smaller p-value than either the BP or special case of the White statistic? Explain. (iv) Suppose someone suggests also adding ŷ; to the newly proposed test. What do you think of this idea?
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