= Chemometrics
<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.<Chemometrics in the IUPAC Gold Book>[Entry CT06948, definition]{ref}
An original two-component example illustrates <multivariate calibration>. At two chosen <wavelengths>, suppose <absorbance> follows a calibrated linear model
$$
\begin{pmatrix}A_1\\A_2\end{pmatrix}
=\begin{pmatrix}1&0.5\\0.2&1\end{pmatrix}
\begin{pmatrix}c_1\\c_2\end{pmatrix},
$$
with 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 $A_1=1.00$, $A_2=0.56$ give
$$
c_1=\frac{1.00-0.5(0.56)}{0.9}=0.80,\qquad
c_2=\frac{0.56-0.2(1.00)}{0.9}=0.40.
$$
Neither 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.
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