{"term":{"id":"10153","title":"multivariate calibration","longtitle":"IUPAC Gold Book - multivariate calibration","doi":"10.1351\/goldbook.10153","code":"10153","status":"current","definitions":[{"id":1,"text":"Calibration in which the indications are multivariate data.","notes":{"1":"In multivariate regression and calibration the problem is usually posed as a relation between the indications \\(\\boldsymbol{X}\\) (which are multivariate) and the property to be measured \\(\\boldsymbol{y}\\). Note that this is a reversal of the traditional form, \\(x\\) (concentration)\/\\(y\\) (indication) of linear calibration. \\(\\boldsymbol{X}\\) is a vector of observations (indications), and \\(\\boldsymbol{c}\\) a vector of concentrations. In matrix form: \\(\\boldsymbol{X} \\boldsymbol{b} = \\boldsymbol{c} + \\boldsymbol{e}\\) where \\(\\boldsymbol{b}\\) are the coefficients of the model and \\(\\boldsymbol{e}\\) is a vector of errors.","2":"Regression establishes the coefficients \\(\\boldsymbol{b}\\) (\\(\\boldsymbol{X} \\boldsymbol{b} = \\boldsymbol{c} + \\boldsymbol{e}\\)) from given indications \\(\\boldsymbol{X}\\), or some factorization of \\(\\boldsymbol{X}\\), and values \\(\\boldsymbol{c}\\), or some factorization of \\(\\boldsymbol{c}\\). Given indications \\(\\boldsymbol{X}_{\\rm{u}}\\) from an unknown sample, the quantity value \\(c_{\\rm{u}}\\) can be calculated."},"links":[{"term":"multivariate data","url":"https:\/\/goldbook.iupac.org\/\/terms\/view\/10055"}],"sources":["PAC, 2016, 88, 407. 'Vocabulary of concepts and terms in chemometrics (IUPAC Recommendations 2016)' on page 434 (https:\/\/doi.org\/10.1515\/pac-2015-0605)"]}],"altoutputs":{"html":"https:\/\/goldbook.iupac.org\/terms\/view\/10153\/html","xml":"https:\/\/goldbook.iupac.org\/terms\/view\/10153\/xml","plain":"https:\/\/goldbook.iupac.org\/terms\/view\/10153\/plain"},"citation":"Citation: 'multivariate calibration' 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.10153","license":"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.","collection":"If you are interested in licensing the Gold Book for commercial use, please contact the IUPAC Executive Director at executivedirector@iupac.org .","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":"2026-05-09T11:50:43+00:00"}}