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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.