Automation of a procedure to find the polynomial which best fits (κ, c1, c2, T) data of electrolyte solutions by non-linear regression analysis using mathematica® software

Abstract

A mathematica® package, ‘condu.m’, has been developed to find the polynomial in concentration and temperature which best fits conductimetric data of the type (κ, c, T) or (κ, c₁, c₂, T) of electrolyte solutions (κ: specific conductivity; c_i: concentration of component i; T: temperature). In addition, an interface, ‘tkondu’, has been written in the TCL/Tk language to facilitate the use of condu.m by an operator not familiarised with mathematica®. All this software is available on line (UPV/EHU, 2001). ‘condu.m’ has been programmed to: (i) select the optimum grade in c₁ and/or c₂; (ii) compare models with linear or quadratic terms in temperature; (iii) calculate the set of adjustable parameters which best fits data; (iv) simplify the model by elimination of ‘a priori’ included adjustable parameters which after the regression analysis result in low statistical significance; (v) facilitate the location of outlier data by graphical analysis of the residuals; and (vi) provide quantitative statistical information on the quality of the fit, allowing a critical comparison among different models. Due to the multiple options offered the software allows testing different conductivity models in a short time, even if a large set of conductivity data is being considered simultaneously. Then, the user can choose the best model making use of the graphical and statistical information provided in the output file. Although the program has been initially designed to treat conductimetric data, it can be also applied for processing data with similar structure, e.g. (P, c, T) or (P, c₁, c₂, T), being P any appropriate transport, physical or thermodynamic property.