In statistics and optimization, errors and residuals are two closely related and easily confused measures of the deviation of an observed value of an element of a statistical sample from its "theoretical value". The error (or disturbance) of an observed value is the deviation of the observed value from the (unobservable) true value of a quantity of interest (for example, a population mean), and the residual of an observed value is the difference between the observed value and the estimated value of the quantity of interest (for example, a sample mean). The distinction is most important in regression analysis, where the concepts are sometimes called the regression errors and regression residuals and where they lead to the concept of studentized residuals.

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# Errors and Residuals

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## MATLAB Command: goodnessOfFit

Intermediate

Article / Blog

Application

Goodness of fit between test and reference data for analysis and validation of identified models

See More## MATLAB Command: resid

Intermediate

Article / Blog

Application

This MATLAB command is part of the system identification toolbox and provides a way to compute and test residuals.

See More## What is Residual Analysis?

Intermediate

Article / Blog

Theory

*Residuals* are differences between the one-step-predicted output from the model and the measured output from the validation data set. Thus, residuals represent the portion of the validation...