In the regression model Yi = β0 + β1Xi + β2Di + β3(Xi × Di)+ ui,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 identical regressions, we need to test the joint hypothesis that coefficients β2 and β3 are both equal to zero, since these are the coefficients associated with the interaction term (Xi * Di) that differentiates the two regressions. Therefore, we need to use the F-statistic for the joint hypothesis that β2 = 0 and β3 = 0.

In the Regression Model Yi = β0 + β1Xi