Question

Why is the random error term included in a regression model?

Answer 1

We need the error term because our models are based on samples, not populations. Also because models are simplifications of reality and, so, aren't right.

If you have a regression model, you are trying to explain something. The error term will be whatever part you have not been able to explain. The only time there would be no error term is if the relationship is totally deterministic—i.e. you have a formula that provides a definitive and exact answer, not an estimate.

In OLS regression we assume that the errors are normally distributed with constant variance.