{"term":{"id":"10077","title":"model","longtitle":"IUPAC Gold Book - model","doi":"10.1351\/goldbook.10077","code":"10077","status":"current","definitions":[{"id":1,"text":"Equation describing the response as a function of values of the factors.","notes":{"1":"The model can be based on knowledge of the chemistry or physics of the system, but usually the model is empirical, being linear or quadratic with interaction terms.","2":"To obtain information about the significance of effects, data is usually mean centered and assessed against a coded experimental design."},"exams":{"1":"The yield of a synthesis is modelled in terms of the temperature \\(T\\) and concentration of a reactant \\(c\\): \\[\\hat Y = {\\hat \\beta}_{0} + {\\hat \\beta}_{1}T + {\\hat \\beta}_{2}c + {\\hat \\beta}_{11}T^{2} + {\\hat \\beta}_{22}c^{2} + {\\hat \\beta}_{12}Tc\\]"},"contexts":{"1":"The yield of a synthesis is modelled in terms of the temperature <span title=\"symbol\">\\(T\\)<\/span> and concentration of a reactant <span title=\"symbol\">\\(c\\)<\/span>: <span title=\"equation\">\\[\\hat Y = {\\hat \\beta}_{0} + {\\hat \\beta}_{1}T + {\\hat \\beta}_{2}c + {\\hat \\beta}_{11}T^{2} + {\\hat \\beta}_{22}c^{2} + {\\hat \\beta}_{12}Tc\\]<\/span>"},"links":[{"term":"coded experimental design","url":"https:\/\/goldbook.iupac.org\/\/terms\/view\/10067"},{"term":"interaction effect","url":"https:\/\/goldbook.iupac.org\/\/terms\/view\/10075"},{"term":"main effect","url":"https:\/\/goldbook.iupac.org\/\/terms\/view\/10076"},{"term":"mean centered","url":"https:\/\/goldbook.iupac.org\/\/terms\/view\/10053"},{"term":"n<sup>th<\/sup>-order effect","url":"https:\/\/goldbook.iupac.org\/\/terms\/view\/10078"},{"term":"response","url":"https:\/\/goldbook.iupac.org\/\/terms\/view\/10042"}],"sources":["PAC, 2016, 88, 407. 'Vocabulary of concepts and terms in chemometrics (IUPAC Recommendations 2016)' on page 415 (https:\/\/doi.org\/10.1515\/pac-2015-0605)"]}],"altoutputs":{"html":"https:\/\/goldbook.iupac.org\/terms\/view\/10077\/html","xml":"https:\/\/goldbook.iupac.org\/terms\/view\/10077\/xml","plain":"https:\/\/goldbook.iupac.org\/terms\/view\/10077\/plain"},"citation":"Citation: 'model' 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.10077","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":"2026-04-19T02:12:09+00:00"}}