In this study, a novel procedure is proposed to determine the shape parameter of multiquadric (MQ) radial basis function (RBF) utilizing multivariate adaptive regression splines (Mars) in a free convection problem. Input data (truth data) of Mars is prepared by applying MQ-RBF pseudospectral (PS) method to a free convection problem in a cavity with differentially heated vertical walls. Shape parameter determination in this step is also proposed. The input data obtained by the numerical method and by the proposed way to determine shape parameter is used in the package earth of R project, and a model function is built to estimate the shape parameter. Then, instead of using the proposed search inside the numerical method, the model function determines the shape parameter at any truth data. Results are also compared with a benchmark study, and good agreement is observed in the same free convection problem. The model function built is also tested against the results of the original method.