Orthogonal Distance Regression: A Good Alternative to Least Squares for Modeling Sorption Data

The most used regression methods in sorption studies to estimate the isotherm parameters (least squares linearized, ordinary least squares, Marquardt's least squares (MLS), and hybrid least squares) and orthogonal distance regression (ODR) have been compared. Theoretical Langmuir isotherms were built from different selected values of q(max) and b, and from them simulated isotherms were generated by introducing a certain error. With the generated data the corresponding isotherm parameters were estimated by using the different regression methods and their values were compared to the ones of the theoretical isotherms. The results of this study show that ODR gives the most accurate estimates of the isotherm parameters when the theoretical data are perturbed with a fixed error. When the theoretical data are perturbed with an error proportional to concentration, ODR gives also accurate estimates, but they are similar to those obtained with the MLS method.