In multivariate calibration or classification for \(N\) evaluation data where \(c_{i}\) is an observed value and \(\hat c_{i}\) is the predicted value \[E_{\rm{RMSEP}} = \sqrt {\frac{\sum\limits_{i\,=\,1}^{i\,=\,N} (\hat c_{i}\,-\,c_{i})^2}{N}}\]
Notes: - 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.
Source:
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)