In linear regression when additional terms are added to the regression model to account for the possibility that the relationship between an independent variable (predictor) and the dependent variable (outcome) depends on the value of another independent variable.
In simpler terms, they represent the idea that the effect of one variable on the outcome is not constant but varies depending on the level of another variable.
Mathematically, an interaction term in a linear regression model takes the form of a product between two or more independent variables. For example, if you have two independent variables, X1 and X2, and you suspect that the effect of X1 on the outcome (Y) depends on the value of X2, you can introduce an interaction term like this:
Y = β0 + β1 * X1 + β2 * X2 + β3 * (X1 * X2) + ε
In this equation:
Y represents the dependent variable (the one you’re trying to predict).
X1 and X2 are independent variables.
β0, β1, β2, and β3 are the regression coefficients that represent the relationship between the variables.
ε represents the error term.
The coefficient β3 measures the strength and direction of the interaction effect. If β3 is statistically significant and positive, it indicates that the effect of X1 on Y increases as X2 increases. If β3 is negative, it suggests that the effect of X1 on Y decreases as X2 increases. If β3 is not statistically significant, it implies that there is no interaction effect between X1 and X2.
Interaction terms are useful when you suspect that the relationship between variables is more complex than a simple additive relationship. They allow you to capture how the relationship between two variables changes in the presence of other variables, potentially leading to a better understanding of the underlying data and improved model accuracy. However, it’s essential to be cautious when adding interaction terms, as including too many can lead to overfitting (as the equation polynomial increases, the more overfit the model), and they should be based on theoretical or domain knowledge rather than testing multiple combinations blindly.