The parameters of the moderated regression model or the regression model with an interaction (product) term can be confusing. This applet depicts a moderated regression model in which the variable Z denotes one of two groups, each having its own regression line. The applet illustrates which parameters in the model do or do not depend on the zero point of the X predictor variable. Drag the vertical axis to create a new predictor variable X', which equals the original the predictor X with a constant subtracted. The zero points on the X and X' axes do not correspond. As you drag the vertical axis, observe the changes in the model coefficients.

The coefficient for the X (or X') variables (depicted in red) is invariant and represents the average of the separate slopes for the two groups. The coefficient for the Z' variable (depicted in green) represents the difference between the two regression lines at the value of X' = 0. As the definition of the zero point changes, the green coefficient necessarily changes. The intercept (depicted in blue) equals the average of the separate intercepts for the two groups. Finally, the coefficient for the product (depicted in black), representing the interaction, is invariant and represents the difference bewteen the separate slopes of the two groups.