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.