In this work a new methodology for automatic selection of the free parameters in the Least Squares–Support Vector Machines (LS-SVM) regression oriented algorithm is proposed. We employ a multidimensional Generalized Cross-Validation analysis in the linear equation system of LS-SVM. Our approach does not require a prior knowledge about the influence of the LS-SVM free parameters in the results. The methodology is tested on two artificial and two real-world data sets. According to the results our methodology computes suitable regressions with competitive relative errors.