- An interaction term in model building refers to a statistical construct that represents the combined effect of two or more independent variables which is also known as predictors, on the dependent variable that is the outcome or response variable.
- Interaction terms are used in regression analysis and other statistical modeling techniques to account for situations where the relationship between the dependent variable and one independent variable depends on the level or values of another independent variable.
- In simpler terms, it allows us to assess whether the effect of one variable on the outcome changes based on the value of another variable.
- In a linear regression model, an interaction term is typically denoted by multiplying the two or more predictor variables involved.
- For example, if we have two predictors, X1 and X2, and suspect an interaction between them, we would include an interaction term like X1 * X2 in the regression equation.
- In polynomial regression model, we can see how the effect of one predictor variable changes as a function of another predictor variable. Mathematically, an interaction term between two predictors, X₁ and X₂, in a quadratic polynomial regression might look like this :Y = β₀ + β₁X₁ + β₂X₁² + β₃X₂ + β₄X₁X₂ + ε
- In this equation, the interaction term is represented by β₄X₁X₂. β₄ quantifies how the effect of X₁ on Y changes depending on the value of X₂.
INTERPRETATION :
For Linear equation:
- If the coefficient for the interaction term (e.g., X1 * X2) is statistically significant and positive, it suggests that the effect of X1 on the outcome is amplified when X2 increases.
- If the coefficient for the interaction term is statistically significant and negative, it suggests that the effect of X1 on the outcome is diminished when X2 increases.
For Polynomial equation :
- If β₄ is positive, it suggests that as X₁ increases, the effect of X₂ on Y becomes stronger.
- If β₄ is negative, it suggests that as X₁ increases, the effect of X₂ on Y becomes weaker.
- If β₄ is close to zero, it indicates little or no interaction between X₁ and X₂.