Anyone who has performed ordinary least squares (OLS) regression analysis knows that you need to check the residual plots to validate your model. Have you ever wondered why? There are mathematical reasons, of course, but I’m going to focus on the conceptual ones.

The bottom line is that randomness and unpredictability are crucial components of any regression model. If you don’t have those, your model is not valid. Why? To start, let’s break down and define the two basic components of a valid regression model:

Response = (Constant + Predictors) + Error

Another way we can say this is:

Response = Deterministic + Stochastic

The deterministic portion

This is the part that is explained by the predictor variables in the model. The expected value of the response is a function of a set of predictor variables. All of the explanatory or predictive information of the model should be in this portion.

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