Answer Happy

QUESTION 2 (20%): Consider a linear regression model with a dependent variable, Y, and two explanatory ariables, X₁ and X₂. Suppose that you test for the global significance of the model at a 1000% significance level by means of a sequential test: we reject the mull hypothesis of global significance when the individual significance hypothesis for some of the slopes is rejected at the 1000% significance level. Use a confidence ellipse at the 100(1-a)% and the corresponding individual confidence intervals for the two coefficients to show that, for a given significance level, the conclusion of the sequential test might be opposite to that of the test based on the F statistic. . Suppose that the conditional variance of the model errors is not constant and that we test the joint significance of the model coefficients using an F statistic that imposes the homoskedasticity assumption. What consequences would it have on the decisions resulting from this test? Suppose we want to test whether the partial/marginal effect between Y and X₁ depends on the value that the variable X₂ takes. Explain how you would perform this test at a 1000% significance level.