10110 IUPAC Gold Book - root mean squared error of prediction 10.1351/goldbook.10110 10110 current initialisms: RMSEP, RMSPE, SEP synonyms: root mean squared error of estimation, standard error of estimation, standard error of prediction 1 In multivariate calibration or classification for \(N\) evaluation data where \(c_{i}\) is an observed value and \(\hat c_{i}\) is the predicted value \[E_{\rm{RMSEP}} = \sqrt {\frac{\sum\limits_{i\,=\,1}^{i\,=\,N} (\hat c_{i}\,-\,c_{i})^2}{N}}\] RMSEP is related to the prediction error sum of squares (PRESS) by \(E_{\rm{RMSEP}} = \sqrt \frac{E_{\rm{PRESS}}}{N}\) . For completely independent, normally distributed evaluation data, RMSEP is a measure of the bias of the calibration. When prediction is by cross validation RMSEP may be termed root mean square error of cross validation. evaluation data https://goldbook.iupac.org//terms/view/10050 multivariate calibration https://goldbook.iupac.org//terms/view/10153 PAC, 2016, 88, 407. 'Vocabulary of concepts and terms in chemometrics (IUPAC Recommendations 2016)' on page 424 (https://doi.org/10.1515/pac-2015-0605) https://goldbook.iupac.org/terms/view/10110/html https://goldbook.iupac.org/terms/view/10110/json https://goldbook.iupac.org/terms/view/10110/plain Citation: 'root 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.10110 The IUPAC Gold Book is licensed under Creative Commons Attribution-ShareAlike CC BY-SA 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/) for individual terms. If you are interested in licensing the Gold Book for commercial use, please contact the IUPAC Executive Director at executivedirector@iupac.org . 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. 2026-04-19T00:32:01+00:00