Question

In the regression model Yi = β0 + β1Xi + β2Di + β3(Xi × Di) + ui, where X is a continuous variable and D is a binary variable, β2

A. is usually positive.
B. indicates the difference in the intercept for D=1 versus D=0.
C. is the difference in means in Y between the two categories.

Answer 1

The correct statement is:

C. β2 is the difference in means in Y between the two categories.

In the given regression model, β2 represents the effect of the binary variable D on the outcome variable Y, while holding the continuous variable X constant. Since D is a binary variable, it can take on only two values (0 or 1). Therefore, β2 represents the difference in the mean of Y between the two categories represented by D=1 and D=0.

Option A is incorrect because β2 can be either positive or negative, depending on the direction and magnitude of the effect of D on Y.

Option B is incorrect because the difference in the intercept for D=1 versus D=0 is represented by β0, not β2.

Therefore, option C is the correct statement.