Achieving full energy independence in residential settings remains a challenge with conventional grid-connected solar photovoltaic (PV) systems. This study presents a data-driven approach to designing a grid-independent solar PV and battery energy storage system (BESS) using machine learning techniques. Actual residential load profiles and solar generation data, combined with weather and calendar-based inputs, were analyzed using four regression models: Polynomial Regression, Support Vector Regression, Gradient Boosting, and Random Forest. These models were evaluated based on R², Mean Absolute Error (MAE), and Root Mean Square Error (RMSE) to determine the most accurate predictor. The Random Forest model delivered the highest accuracy, achieving an R² of 0.92 for generation and 0.90 for load forecasting. The optimized forecast supported the expansion of the PV system from 11 kW to 30 kW and the integration of a 120 kWh BESS, ensuring complete residential grid independence. This framework offers a reliable and adaptable methodology for intelligent energy management and autonomous PV–BESS system design.