Analytical and numerical computation of error propagation of model parameters

• Published in: Journal of mathematical chemistry Vol. 49; no. 7; pp. 1322 - 1329
• Main Authors: Tasi, Gyula, Barna, Dóra
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.08.2011; Springer
• Subjects: Chemistry; Chemistry and Materials Science; Exact sciences and technology; General and physical chemistry; Linear inference, regression; Math. Applications in Chemistry; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in probability and statistics; Original Paper; Physical Chemistry; Probability and statistics; Sciences and techniques of general use; Statistics; Theoretical and Computational Chemistry; Theory of reactions, general kinetics. Catalysis. Nomenclature, chemical documentation, computer chemistry; Parameter estimation; Least-squares method; Error estimation; Variance-covariance matrix; Simplex method; Propagation; Numerical method; Computing; Variance; Numerical computation; Least squares method; Numerical solution; Law of large numbers; Test method; Estimation error; Evaluation; Mathematical chemistry; Non linear regression; Enzyme; Linear regression; Nonlinear analysis; Regression analysis; Covariance matrix; Computation error; Kinetics
• ISSN: 0259-9791; 1572-8897
• DOI: 10.1007/s10910-011-9830-7

Linear and nonlinear regression analyses based on the least-squares method play a fundamental role in the evaluation of scientific data. A large number of valuable papers have dealt with various applications of the least-squares method in the chemical literature. They, however, usually contain tremendous formulas for computing the error estimates of the estimated parameters. This paper presents a simple numerical solution based on the well-known simplex method to this problem. Elaborate enzyme kinetic data published earlier have been chosen to test the simplex method extended with error estimation. The capability of the numerical method is demonstrated by the revision of the originally calculated error propagation. Our program might prove useful in handling either chemical or biological data.