In the regression model $Y _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + \beta _ { 2 } D _ { i } + \beta _ { 3 } \left( X _ { i } \times D _ { i } \right) + u _ { i }$
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 $\beta _ { 2 } = 0 , \beta _ { 3 } = 0$
B) F -statistic for the joint hypothesis that $\beta _ { 0 } = 0 , \beta _ { 1 } = 0$
C) t -statistic separately for $\beta _ { 3 } = 0$
D) F -statistic for the joint hypothesis that $\beta _ { 2 } = 0 , \beta _ { 3 } = 0$

Question

In the regression model $Y _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + \beta _ { 2 } D _ { i } + \beta _ { 3 } \left( X _ { i } \times D _ { i } \right) + u _ { i }$
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 $\beta _ { 2 } = 0 , \beta _ { 3 } = 0$
B)  F -statistic for the joint hypothesis that $\beta _ { 0 } = 0 , \beta _ { 1 } = 0$
C)  t -statistic separately for $\beta _ { 3 } = 0$
D)  F -statistic for the joint hypothesis that $\beta _ { 2 } = 0 , \beta _ { 3 } = 0$

Quizplus · Accepted Answer

To test if the two regressions are identical, you need to test if both the intercept and slope differences are zero, which involves testing the joint hypothesis $\beta _ { 2 } = 0$ and $\beta _ { 3 } = 0$ using an F-statistic.

In the Regression Model Yi=β0+β1Xi+β2Di+β3(Xi×Di)+uiY _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + \beta _ { 2 } D _ { i } + \beta _ { 3 } \left( X _ { i } \times D _ { i } \right) + u _ { i }Yi​=β0​+β1​Xi​+β2​Di​+β3​(Xi​×Di​)+ui​

In the Regression Model $Y _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + \beta _ { 2 } D _ { i } + \beta _ { 3 } \left( X _ { i } \times D _ { i } \right) + u _ { i }$