Standard error formula

$$ mathit{se^2}(hat beta_j) = frac{hat sigma^2}{mathit{RSS_j}} = = frac{hat sigma^2}{mathit{TSS_j} ast (1-mathit{R^2_j})} = = frac{1}{(1-mathit{R^2_j})} ast frac{hat sigma^2}{mathit{TSS_j}} $$

And $ sigma $ is $ sqrt{E[(X-mu)^2]} = sqrt{E[mathit{X^2}]-(E[mathit{X}])^2} $, where $ mu = E[mathit{X}] $

But what is statistical error $ varepsilon $? Here it is $ varepsilon=mathit{X_i-mu} $, where $ mu $ is a population mean. But we work with real values which are only part of population, its sample and the sample mean is $ mathit{bar{X}} $. Then error become the residual: $ mathit{r_i} = mathit{X_i}-mathit{bar{X}} $.