We call into question the techniques in the literature which employ least-squares procedures to estimate the mole fractions of species believed to be present. The most serious difficulties with least squares is the lack of statistical independence in the random errors, failure of homoscedasticity, and exact linear dependencies in the observed data which give rise to a singular covariance matrix of the error vector.We applied the Bayesian formalisim of Box and Draper (7) to estimate the mole fractions, the approaches of McLean et al. ( 12) and Box et al. (7) to eliminate the linear dependencies in the observed data, and some approximations given by Stewart and Sorensen (13,14), and we were able to use formulas given by Box and Tiao (15) for a linear, single response model, to find approximate HPD contours and confidence intervals for the mole fractions. The Bayesian confidence intervals are narrower than those obtained from the leastsquares analysis.