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Chemometrics applies statistics and mathematical modeling to chemical measurements and the design of chemical experiments. It connects recorded signals with chemical composition or other properties, while accounting for experimental variation. IUPAC's definition includes both analysis of chemical data and design of experiments and simulations.^[ref]

An original two-component example illustrates multivariate calibration. At two chosen wavelengths, suppose absorbance follows a calibrated linear modelwith fixed optical path and concentration units chosen so the displayed coefficients apply. This is the additive-response model suggested by the Beer-Lambert law, with no interactions or other absorbers. Readings $A_1=1.00$, $A_2=0.56$ giveNeither wavelength alone distinguishes both concentrations; their different response ratios make the pair informative.

If the second response row were instead twice the first, the matrix would be singular. More precise repeated readings would not restore the missing chemical selectivity. Nearly proportional response rows instead make the inverse sensitive to noise, connecting experimental wavelength selection with the condition number of the response matrix.

Principal component analysis can summarize patterns in many-channel measurements, while regression can predict an independently measured chemical quantity. These are different tasks: a direction of large signal variance need not identify a particular analyte. Cross-validation should keep correlated preparations or production batches together when the intended prediction is for new batches; splitting repeated readings of one preparation across training and validation can overstate performance.

A useful experiment measures known mixtures spanning the intended concentration range, reagent blanks and separately prepared validation samples. Inspecting calibration residuals tests departures from the model, while varying preparation conditions tests whether a fitted relation transfers. A mathematical fit gains chemical meaning from the materials, reference measurements and experimental design behind its data.

David Brynn Hibbert, also known as Brynn Hibbert, is an analytical chemistry researcher whose work combines chemometrics, electrochemical measurements and metrological traceability. His university profile records his tenure in the UNSW analytical-chemistry chair from1987 to2013 and his editorship of the IUPAC terminology compendium known as the Orange Book. The Royal Society of New South Wales explicitly verifies his full name.^[ref]

With Paul De Bièvre, René Dybkær and Aleš Fajgelj, David Brynn Hibbert coauthored the IUPAC report on the concepts and implementation of metrological traceability in chemical measurement. Its goal was a consistent account of how a result is related to a reference, including the concepts needed to communicate that relationship.^[ref]

An original illustration explains the value of a measurement model in chemometrics. Suppose two ideal sensors give $x_1=c+b$ and $x_2=c-b$, where $c$ is the target concentration and $b$ an interfering response. Their mean recovers $c$, while their difference diagnoses $2b$. If both instead respond as $c+b$, averaging cannot remove the interference. The chemical response model determines what additional measurements identify; having more numbers alone does not guarantee more independent information.

Matthias Otto is an analytical chemistry researcher identified in the full title-page byline of the 2004 IUPAC report on multispecies calibration, alongside Klaus Danzer and Lloyd A. Currie. That primary page gives his affiliation as the analytical chemistry department at TU Bergakademie Freiberg. The university's own directory independently lists Matthias Otto among the institute's former staff.^[ref][ref]

The report concerns multivariate calibration: relating several chemical species and their quantities to several measured signals, with uncertainty and model validation treated explicitly. Its sections distinguish classical multivariate calibration, inverse calibration and error diagnosis. This is a coauthored methodological contribution; the byline alone does not assign separate individual roles.^[ref]

An original two-species model illustrates the scientific problem. Let concentration values $c_1,c_2$ and two instrument signals $s_1,s_2$ be expressed in chosen calibrated units, withThe signals $(5,8)$ imply $c_2=s_2-s_1=3$ and $c_1=2s_1-s_2=2$. If the second channel were instead exactly twice the first, giving response matrix $\left(\begin{array}{cc}1& 1\\ 2& 2\end{array}\right)$, readings $(5,10)$ would determine only $c_1+c_2=5$. Merely recording two channels would not make the two species separately identifiable.

This distinction is why calibration mixtures must supply independent information about the species responses and why successful interpolation does not replace validation. Near-dependent response columns can also amplify measurement noise even when a formal inverse exists. Singular value decomposition and the actual calibration design help diagnose such limitations; a regression coefficient is not automatically an independently established chemical effect.

A measurement program can vary mixture composition, collect the same channels under controlled conditions, and test predictions on mixtures not used to fit the response. The example is an ideal calculation, not experimental data from the report. It explains why chemometrics combines chemical knowledge, experimental design and statistical assessment rather than treating a fitted number as a complete analytical result.