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Symbolic regression is a nonlinear regression method which is commonlyperformed by an evolutionary computation method such as genetic programming.Quantification of uncertainty of regression models is important for theinterpretation of models and for decision making. The linear approximation andso-called likelihood profiles are well-known possibilities for the calculationof confidence and prediction intervals for nonlinear regression models. Thesesimple and effective techniques have been completely ignored so far in thegenetic programming literature. In this work we describe the calculation oflikelihood profiles in details and also provide some illustrative examples withmodels created with three different symbolic regression algorithms on twodifferent datasets. The examples highlight the importance of the likelihoodprofiles to understand the limitations of symbolic regression models and tohelp the user taking an informed post-prediction decision.

Prediction Intervals and Confidence Regions for Symbolic Regression Models based on Likelihood Profiles