Editing Errors and residuals (section)

==Other uses of the word "error" in statistics==
{{see also|Bias (statistics)}}
The use of the term "error" as discussed in the sections above is in the sense of a deviation of a value from a hypothetical unobserved value. At least two other uses also occur in statistics, both referring to observable [[prediction error]]s:

The ''[[mean squared error]]'' (MSE) refers to the amount by which the values predicted by an estimator differ from the quantities being estimated (typically outside the sample from which the model was estimated).
The ''[[root mean square error]]'' (RMSE) is the square root of MSE.
The ''sum of squares of errors'' (SSE) is the MSE multiplied by the sample size.

''[[Sum of squares of residuals]]'' (SSR) is the sum of the squares of the deviations of the actual values from the predicted values, within the sample used for estimation. This is the basis for the [[least squares]] estimate, where the regression coefficients are chosen such that the SSR is minimal (i.e. its derivative is zero).

Likewise, the ''[[sum of absolute errors]]'' (SAE) is the sum of the absolute values of the residuals, which is minimized in the [[least absolute deviations]] approach to regression.

The '''mean error''' (ME) is the bias.
The ''mean residual'' (MR) is always zero for least-squares estimators.