There are different ways to combine features of the White test for heteroskedasticity. One possibility not covered in the lecture is to run the following regression û on T₁, T2, Tiks ŷ², i = ¹, ..., n where the û; are the OLS residuals and they are the OLS fitted values. Then we would test joint significance of ₁, 2,..., ik and y?. (1) (10pts) What is the degree of freedom associated with the proposed F test for heteroskedasticity? (2) (10pts) Explain why the R-squared from the regression above will always be at least as large as the R-squared for the White test by running û on ₁, ₁2,..., Tik (3) (10pts) Does part (2) imply that the new test always delivered a smaller p-value than the White statistic? Explain. (4) (10pts) Explain why we can put in the above regression. Suppose someone suggests also adding ; to the newly proposed test. What do you think of this idea?