Title: mean squared error of prediction
Long Title: IUPAC Gold Book - mean squared error of prediction
DOI: 10.1351/goldbook.10099
Status: current

Definition
In multivariate calibration the average of the squared deviation of estimated values from the values of evaluation data. For \(N\) evaluation data where \(c_{i}\) is an observed value and \(\hat c_{i}\) is the predicted value. \[E_{\rm{MSEP}} = \frac{\sum\limits_{i\,=\,1}^{i\,=\,N} (\hat c_{i}\,-\, c_{i})^2}{N}\]

Note
Mean squared error of prediction is the square of root mean squared error of prediction.

Related Terms
- evaluation data: https://goldbook.iupac.org//terms/view/10050
- multivariate calibration: https://goldbook.iupac.org//terms/view/10153
- root mean squared error of prediction: https://goldbook.iupac.org//terms/view/10110

Source
- PAC, 2016, 88, 407. 'Vocabulary of concepts and terms in chemometrics (IUPAC Recommendations 2016)' on page 421 (https://doi.org/10.1515/pac-2015-0605)

Other Outputs
- html: https://goldbook.iupac.org/terms/view/10099/html
- json: https://goldbook.iupac.org/terms/view/10099/json
- xml: https://goldbook.iupac.org/terms/view/10099/xml

Citation: Citation: 'mean squared error of prediction' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. 10.1351/goldbook.10099
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Disclaimer: The International Union of Pure and Applied Chemistry (IUPAC) is continuously reviewing and, where needed, updating terms in the Compendium of Chemical Terminology (the IUPAC Gold Book). Users of these terms are encouraged to include the version of a term with its use and to check regularly for updates to term definitions that you are using.
Accessed: 2026-04-18T22:57:39+00:00