Gaining information on the secondary structure of a protein from its spectra is presented as a calibration problem. The secondary structures known from X-ray studies and the spectra of 21 proteins are represented by a linear model. Fourier transform infrared (FTIR) spectra from 1700 to (1600 \mathrm{~cm}^{-1}), circular dichroism (CD) spectra from 178 to (260 \mathrm{~nm}), and combined spectra are used; the secondary structure classes of interest are (\alpha)-helices, antiparallel (\beta)-sheets, parallel (\beta)-sheets, (\beta) turns, and "other." The calibration is solved in two steps: (i) the dependencies between the structures and the spectra of reference proteins are found using the least-squares estimator, and (ii) the secondary structure of a protein is predicted from its spectra using the information gained in the first step and principal component analysis. The problem of information content of the reference spectra is analyzed using the linearly independent pieces of information, the so-called principal components, provided by singular value decomposition. Attention is paid to a number of the principal components sufficient for the prediction, which may be less than the total number. A relative estimable parameter is used to determine unambiguously the number of the components corresponding to the minimum mean square error of the predictor. The analysis gives the solutions to this linear calibration relevant to the underlying protein problem, thus reducing subjective assessments as well as computations. โฒ94 Academic Press, Inc.