The concentration of analytes in a complex mixture can be ascertained by spectroscopic measurement, even if the spectra of substances other than the analyte overlap with that of the analyte. Both independently measured concentrations of the analyte in a training set and of the analyte spectrum are used. Variances in the spectral data attributable to the analyte are isolated from spectral variances from other causes, such as compositional changes associated with different samples that are independent of the analyte. For the special case of noninvasive glucose measurements on the skin of biological organisms, the volume averaged glucose in the sample is predicted from the blood glucose. A test for over-fitting of the data is also described.