Statistical Analysis of Linear and Non-Linear Regression for the Estimation of Adsorption Isotherm Parameters

Abstract

A very common practice during the parameter estimation of adsorption isotherms, including the well-known Langmuir and Freundlich isotherms, consists in manipulating the isotherm equation to obtain a linear equation and estimate the model parameters using a linear least squares method. This procedure is also usually used for estimating the thermodynamic adsorption parameters, despite the fact that personal computers and software are available for prompt implementation of non-linear solutions of the original parameter-estimation problem. For this reason, the main purpose of this work is to show that the use of linear least-squares methods for estimating adsorption isotherm parameters leads to some serious drawbacks, which can be readily avoided through proper use of non-linear procedures and posterior statistical analyses of the parameter-estimation results, enhancing the quality of the obtained results.