Stochastic simulation is an indispensable tool in operations and management applications. However, simulation models are only approximations to reality, and often bear discrepancies with the generating processes of real output data. We investigate a framework to statistically learn these discrepancies under the presence of data on past implemented system configurations, which allows us to improve prediction using simulation models. We focus on the case of general continuous output data that generalizes previous work. Our approach utilizes (a combination of) regression analysis and optimization formulations constrained on suitable summary statistics. We demonstrate our approach with a numerical example.