# Why residuals are a good estimator of random disturbance?

Let a linear OLS model: $$Y= X \beta + u$$ Where $$u$$ is a random disturbance. If we define the residual of the regression as $$e = Y - X \widehat{\beta}$$ where $$\widehat{\beta}$$ is the OLS vector of estimations of $$\beta$$, such that $$\widehat{\beta} = (X'X)^{-1} X' Y$$

Why does $$e$$ is a good estimator for $$u$$? In terms of estimator properties, such as efficiency, consistency, sufficiency, unbias, etc.