Question

3. Consider the following regression: Y = Bo + B,D;. X: + X:B2+ B3D +€ (a) (3 points) Suppose D, changes from 0 to 1. What is the change in Y for a given value of X, and e? (b) (2 points) How does this depend on the value of X ? Suppose X is a dummy variable; what is the effect of D, for people with X = 1? 0? (e) (5 points) How can you interpret the value of Bs? B.? Total for Question 3: 10

Answer 1

a) If Di changes from 0 to 1, the mean of the Yi will change from

$\beta_{o}+X_{i}\beta_{2}$

to

$\beta_{o}+\beta_{1}X_{i}+X_{i}\beta_{2}+\beta_{3}$.

b) When Di=1 and Xi=1, the mean of Yi is

$\beta_{o}+\beta_{1}+\beta_{2}+\beta_{3}$

When Di=1 and Xi=0, the mean of Yi is

$\beta_{o}+\beta_{3}$

When Di=0 and Xi=1, the mean of Yi is

$\beta_{o}+\beta_{2}$

When Di=0 and Xi=0, the mean of Yi is

$\beta_{o}$

c) Interpretation of B1: When both the Di and Xi are equal to 1, the mean of Y has an effect by the interaction of the Di and Xi treatment.

B1: The mean of the Y increase by B3 when Di=1 compare with Di=0.