Interaction term usage In which case should I use an interaction term in regression analysis? What does it depend on that I should be using it?
 A: When you interpret coefficients in regression analysis, you look at the effect of one unit increase in a predictor that is associated with the coefficient on the response variable, while holding other variables constant. However, this ignores the scenario in which predictors have an effect on each other. 
For instance, in a multiple linear regression setting, we have a model:
$$\text{Pollution Level in a city} = \beta_0 + \beta_1 \text{Population} + \beta_2 \text{Number of Cars}$$
Normally, if the population increases by 1 (million or thousand), pollution level will be increased by $\beta_1$, while we hold the number of cars as a constant. However,this is inappropriate because with more people, we would expect the increasing purchase of vehicles. Therefore, if we add a interaction term, we will have: 
$$\text{Pollution Level in a city} = \beta_0 + \beta_1 \text{Population} + \beta_2\text{Number of Cars} + $$$$\beta_3 \text{Number of Cars} \times \text{Population}$$
$$=\beta_0 + \beta_1 \text{Population} + (\beta_2 + \beta_3 Population) \text{Number of Cars}$$
Thus, the increased population will also have an impact on the coefficient associated with the number of cars, which allows us to model the pollution level non-linearly. So if you see a non-linear pattern in the residual plot and you suspect that changes in one predictor would have effect on another, you probably should try to include an interaction term.
