This work investigates a novel approach to forecasting higher education trends by integrating a multi-output Random Forest regression model with a weighting system that captures the influence of different university centers. In addition to forecasting key indicators, such as faculty, total student enrollment and teaching staff, the methodology creates an influence map that illustrates the relative impact of these centers on the overall educational landscape. The model uses a MultiOutputRegressor to predict multiple interrelated targets while incorporating influence weights. Performance is evaluated using metrics such as Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and the coefficient of determination ( \(\text {R}^{2}\) ). Forecasts extending 10 years into the future indicate high model accuracy, with \(\text {R}^{2}\) values near unity for all variables. The influence map created from the weighted predictions provides insights for strategic planning and resource allocation in higher education. This research contributes to the growing body of knowledge on predictive analytics in education by offering a framework that combines advanced machine learning with visualization of institutional impact.