Title: model
Long Title: IUPAC Gold Book - model
DOI: 10.1351/goldbook.10077
Status: current

Definition
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.

Example
The yield of a synthesis is modelled in terms of the temperature \(T\) and concentration of a reactant \(c\): \[\hat Y = {\hat \beta}_{0} + {\hat \beta}_{1}T + {\hat \beta}_{2}c + {\hat \beta}_{11}T^{2} + {\hat \beta}_{22}c^{2} + {\hat \beta}_{12}Tc\]

Related Terms
- coded experimental design: https://goldbook.iupac.org//terms/view/10067
- interaction effect: https://goldbook.iupac.org//terms/view/10075
- main effect: https://goldbook.iupac.org//terms/view/10076
- mean centered: https://goldbook.iupac.org//terms/view/10053
- n<sup>th</sup>-order effect: https://goldbook.iupac.org//terms/view/10078
- response: https://goldbook.iupac.org//terms/view/10042

Source
- 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)

Other Outputs
- html: https://goldbook.iupac.org/terms/view/10077/html
- json: https://goldbook.iupac.org/terms/view/10077/json
- xml: https://goldbook.iupac.org/terms/view/10077/xml

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
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Accessed: 2026-04-19T02:11:45+00:00