Errors and residuals

<p>In <a href="/facts/Statistics/DNPsKGYU">statistics</a> and <a href="/facts/Mathematical_optimization/oRn8Iv5I">optimization</a>, errors and residuals are two closely related and easily confused measures of the <a href="/facts/Deviation_(statistics)/F7cqnhtF">deviation</a> of an <a href="/facts/Observed_value/lDklUzqX">observed value</a> of an <a href="/facts/Elementary_event/GXMxWpw5">element</a> of a <a href="/facts/Sample_(statistics)/URCwKNge">statistical sample</a> from its "<a href="/facts/True_value/fkJju25M">true value</a>" (not necessarily observable). The error of an <a href="/facts/Observation/NTodmzCo">observation</a> is the deviation of the observed value from the true value of a quantity of interest (for example, a <a href="/facts/Population_mean/swcEd4Pg">population mean</a>). The residual is the difference between the observed value and the <i><a href="/facts/Estimation/dsztTYcy">estimated</a></i> value of the quantity of interest (for example, a <a href="/facts/Sample_mean/Ah8VVVDT">sample mean</a>). The distinction is most important in <a href="/facts/Regression_analysis/n6z5Tf7K">regression analysis</a>, where the concepts are sometimes called the regression errors and regression residuals and where they lead to the concept of <a href="/facts/Studentized_residual/YRbAxT2r">studentized residuals</a>.
In <a href="/facts/Econometrics/7U52gzHt">econometrics</a>, "errors" are also called disturbances.
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Errors and residuals open-in-new

Errors and residuals