The importance of weighted regression analysis in the determination of Henry's law constants by static headspace gas chromatography

Henry's law constants, H. of volatile organic compounds are often determined using static headspace gas chromatography, From the methodology of this approach, the experimental data are expected to conform to a nonlinear function and can, accordingly, be analyzed by a nonlinear regression procedure, Alternatively, the data can be transformed to a linear function and subsequently analyzed by linear regression, A series of computer simulations was used to demonstrate the need to employ appropriate statistical weighting factors in carrying out regression analysis of experimental data, These simulations were based on error-dispersed, realistic data sets for a wide range of H input values, and were analyzed using unweighted and weighted, nonlinear and linear regression methods, For a given data set, nonlinear and linear regression analyses, when both unweighted, return different H values. This disparity is sharply reduced when weighted regression methods are used, The regression results for H (and standard deviations) were compared with the respective input values of H. Two models were used to generate random errors in the data: constant relative and constant absolute, These errors were used to construct the weighting factors in the regression analyses, The simulations clearly demonstrate that unweighted regressions, nonlinear as well as linear, may yield unreliable values of H. The use of weighted regression, nonlinear or linear, should be the method of choice in determining Henry's law constants.