The energy efficiency of ocean-going vessels can be increased through various operational considerations, such as improved cargo arrangements and weather routing. The first step toward the goal of maximizing the energy efficiency is to analyze how the ship's powering performance changes under different operational settings and weather conditions. However, existing analytical models and empirical methods have limitations in reliably estimating the powering performance of full-scale ships in real operating conditions. In this study, machine learning techniques are employed to estimate the powering performance of a full-scale ship by constructing regression models using the ship's operational data. In order to minimize the risk of overfitting in the regression process, domain knowledge based on physical principles is combined into the regression models. Also, the uncertainty of the estimated performance is evaluated with consideration of the environmental uncertainties. The obtained regression models can be used to predict the ship speed and engine power under different operational settings and weather conditions.