Interaction effect in linear regression

When we think that one independent variable can moderate the effect of the other independent variable on the dependent variable then we have to use interaction effect. In this case, we have two independent variables, plus the inter variable and one dependent variable.

We talk about interaction effect when the effect of one independent variable changes depending on the effect of another independent variable. The effect of the two independent variables together is different than would be expected from them alone. In real life, countless factors act on our behavior all the time. The interaction effect allows us to uncover the main effects plus interactions.

The interaction effect is actually more realistic than just a simple regression model with two independent variables.
One hypothesis could be: women tend to be more neurotic than men, but to analyze this we would have to conduct a simple linear regression. Ok, gender might have an effect on this, but what if living in a city decreases this effect? In this case we have to use interaction effect.

Interpretation

b0: average level of neurosis among men in villages (you have to see all the categories where the independent variables are 0: men-0, village-0).

b1: Here we see the values of this independent variable (men, women) and the 0 value of the other independent variable (0-Village). In the interpretation we move from the 0 category to the category coded 1.

b2: Here we see the values of this independent variable (0-villages, 1-cities) and the  0 category of the other independent variable (0-men).

b3 shows the magnitude of the interaction effect. So, this is the interaction effect. It shows us how much one independent variable alters the effect of the other independent variable in the model.

How do you know if your hypothesis requires an intercation effect?

This depends on the meaning of your hypothesis. If your hypothesis can be formed as the following questions then it means you have to use an interaction effect.

Does variable C moderate the relation between B and A?

Dos the strength of the B and A effect depend on C?

How does C affect the relationship between B and A?

How does C influence the B and A relationship?

How to decide which way to interpret the b3?

It is important to know that the way to choose between these two types of interpretation depends on our research question. So, depending on our research question we have to choose the way of interpreting b3. But no matter how we choose the value of the interaction effect will be the same.

Interaction Effect can be between two:

1. Categorical variables
2. Two scale (Continuous) variables
3. One categorical and one continuous variable