Several initiatives are developed to shift the current paradigm in Air Traffic Management from the tactical-based approach to more strategic-based coordination of flights. This transformation of the ATM system relies on the improvement of predictive models for the 4D flight trajectories. A variety of performance-based and data-driven approaches are developed for trajectory predictions. The accuracy of the predictions is often deterministic and can be highly impacted by uncertainties that occur in each flight. These uncertainties are commonly related to the lack of detailed information concerning the flight intent, or the inaccuracy of positional and weather-related data. To better understand prediction errors and uncertainties in data-driven predictions, this study proposes a novel two-stage Gaussian Process Regression (GPR) approach. By combining historical flight data and flown trajectory of a given flight, the predictive distributions from the GPR allow us to study both prediction errors and uncertainties. To evaluate the model, we applied the method for flights arriving at the Amsterdam Airport Schiphol. We also evaluate and quantify how flight-plan and meteorological information help to reduce prediction error and uncertainty.