In the regression model Y_i = β₀ + β₁X_i+ β₂D_i + β₃(X_i × D_i)+ u_i, where X is a continuous variable and D is a binary variable, to test that the two regressions are identical, you must use the A)t-statistic separately for β₂ = 0, β₂= 0. B)F-statistic for the joint hypothesis that β₀= 0, β₁= 0. C)t-statistic separately for β₃= 0. D)F-statistic for the joint hypothesis that β₂= 0, β₃= 0.

Question

Quizplus · Accepted Answer

To test for the equality of the two regressions, we need to test the joint hypothesis that the coefficients on the interaction term and the dummy variable are both zero. This means we need to use an F-test for the joint hypothesis that β₂= 0, β₃= 0. Therefore, the correct answer is D.

In the Regression Model Yi = β0 + β1Xi

In the Regression Model Y_i = β₀ + β₁X_i