 Note that the epsilon term is not a part of this equation, because this is the linear regression estimate. Like I said before, epsilon is independent of x, and cannot be determined by regression analysis. So, in other words, even if we were to somehow create a perfect linear regression model, it would still have some error epsilon. For this reason, it is also known as the irreducible error. In order to estimate these coefficients, we want to minimize the difference between the actual value y and the predicted value by the model y hat for every sample x. This difference is called the residual error, E. Now don't confuse this residual error E with the irreducible error epsilon. By definition, epsilon is a part of the residual error.