Editing Mean squared error (section)

==Interpretation==

An MSE of zero, meaning that the estimator <math>\hat{\theta}</math> predicts observations of the parameter <math>\theta</math> with perfect accuracy, is ideal (but typically not possible).

Values of MSE may be used for comparative purposes. Two or more [[statistical model]]s may be compared using their MSEs—as a measure of how well they explain a given set of observations: An unbiased estimator (estimated from a statistical model) with the smallest variance among all unbiased estimators is the ''best unbiased estimator'' or MVUE ([[Minimum-variance unbiased estimator|Minimum-Variance Unbiased Estimator]]).

Both [[analysis of variance]] and [[linear regression]] techniques estimate the MSE as part of the analysis and use the estimated MSE to determine the [[statistical significance]] of the factors or predictors under study. The goal of [[experimental design]] is to construct experiments in such a way that when the observations are analyzed, the MSE is close to zero relative to the magnitude of at least one of the estimated treatment effects.

In [[one-way analysis of variance]], MSE can be calculated by the division of the sum of squared errors and the degree of freedom. Also, the f-value is the ratio of the mean squared treatment and the MSE.

MSE is also used in several [[stepwise regression]] techniques as part of the determination as to how many predictors from a candidate set to include in a model for a given set of observations.