An improved regression-based qualitative analysis algorithm useful when the mixture to be analyzed contains a compound not in the library spectra, a so-called unknown. A regression of a measured spectrum is computed against the library spectra. This regression is referred to as a “master” regression. Estimated mixing coefficients for an estimated spectrum are computed from the regression. Next, a residual error is computed between the estimated spectrum and the measured spectrum. Peaks in the residual error are identified that extend in a direction opposite to that of peaks in the measured spectrum. These peaks are referred to as “negative” peaks. A regression is performed on the peaks. This is referred to as a “retro-regression” to be distinguished from the master regression performed on the measured spectrum. Using information from the retro-regression, corrected mixing coefficients are computed and the process repeats.