Prognostics is an engineering discipline that predicts the future health of a system. In this research work, a data-driven approach for prognostics is proposed. Indeed, the present paper describes a data-driven hybrid model for the successful prediction of the remaining useful life of aircraft engines. The approach combines the multivariate adaptive regression splines (MARS) technique with the principal component analysis (PCA), dendrograms and classification and regression trees (CARTs). Elements extracted from sensor signals are used to train this hybrid model, representing different levels of health for aircraft engines. In this way, this hybrid algorithm is used to predict the trends of these elements. Based on this fitting, one can determine the future health state of a system and estimate its remaining useful life (RUL) with accuracy. To evaluate the proposed approach, a test was carried out using aircraft engine signals collected from physical sensors (temperature, pressure, speed, fuel flow, etc.). Simulation results show that the PCA-CART-MARS-based approach can forecast faults long before they occur and can predict the RUL. The proposed hybrid model presents as its main advantage the fact that it does not require information about the previous operation states of the input variables of the engine. The performance of this model was compared with those obtained by other benchmark models (multivariate linear regression and artificial neural networks) also applied in recent years for the modeling of remaining useful life. Therefore, the PCA-CART-MARS-based approach is very promising in the field of prognostics of the RUL for aircraft engines.