We have encountered econometric models in which it was a good idea to include "interaction" variables amongst our independent variables.

a. Express in words what in general an interaction term in a regression is trying to accomplish.

b. Suppose you run the following regression:, where X is a continuous variable and is always positive. D is a dummy variable, and X*D is an interaction variable of X and D. Furthermore, suppose that you estimate the following signs for the coefficients:

On a single graph with the X variable on the X-axis, and Y variable on the Y-axis, make rough sketches of the regression lines for the cases D=0 and D=1 that are possible given the signs of the coefficients given above. Be sure to clearly label your axes, slopes, and intercept values. You should upload an image of this graph using the question below.