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Suppose we are regressing Y = aX + bD + cXD. a and b are main effects of variables X and D, and c is the interaction effect. Assume both X and D are continuous variables.

How to interpret the effect of D? Clearly we have to use both main effect b and the interaction effect c, but how to do it? I understand that if D was an indicator variable (dummy), this could have been much easier.

However if D is a continuous variable, it seems more difficult as the units of b and c are different.

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The main effect of D (b) is the amount of change expected in Y for each unit change in D, controlling for X. The interaction of X and D allows this change to become larger or smaller based on the value of X.

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