Vol. 8, 2023-10 Cite as: Hernandez, H. (2023). Replacing the R² Coefficient in Model Analysis. ForsChem Research Reports, 8, 2023-10, 1 - 43. Publication Date: 18/07/2023. Replacing the R² Coefficient in Model Analysis Hugo Hernandez ForsChem Research, 050030 Medellin, Colombia hugo.hernandez@forschem.org doi: 10.13140/RG.2.2.26570.13769 Abstract The R² coefficient (a generalization of the determination coefficient defined in linear regression) has been widely used as a criterion for assessing and comparing the performance of mathematical models with respect to a given set of experimental data. Unfortunately, the R² coefficient can only be used to confidently compare linear models with different terms, fitted by ordinary least-squares (OLS) regression, satisfying all assumptions of OLS regression, and using the same experimental data set. In addition, the R² coefficient actually represents the relative performance of a model compared to the best constant model for the data. A new fitness coefficient (C F ) is proposed as an alternative to R², where the performance of the model is now relative to the corresponding measurement error in the data. A modeling selection procedure is suggested where the best model maximizes the fitness coefficient and the normality of the residuals, while minimizing the number of fitted parameters (parsimony principle). Keywords Correlation, Fitness Coefficient, Heteroscedasticity, Mathematical Modeling, Model Analysis, Ordinary Least Squares, R² Coefficient, Regression Analysis, Uncertainty 1. Introduction Mathematical models are valuable tools commonly used to describe, explain and even predict the behavior of any particular system. Anyone working with mathematical models must take into account two important principles of modeling: