Heating, ventilation, and air conditioning (HVAC) systems account for a substantial share of residential building energy consumption, making the identification of influential architectural design parameters essential for improving energy efficiency. This study proposes a multi-method analytical framework that combines statistical feature selection and machine learning to identify the architectural characteristics that most strongly influence heating and cooling loads in Mediterranean residential buildings. A dataset originally published by Tsanas and Xifara (2012), comprising 768 simulated building configurations representative of Athens, Greece, was analyzed using Spearman's rank correlation, principal component analysis (PCA), chi-squared tests, LASSO regularization, and three supervised machine learning models: (i) decision trees, (ii) artificial neural networks, and (iii) support vector regression. Hyperparameters were optimized through GridSearchCV with five-fold cross-validation. PCA demonstrated that volumetric characteristics, particularly building height and orientation, explained more than half of the total variance, whereas glazing-related variables contributed minimally. Chi-squared analysis confirmed orientation as the strongest categorical predictor, while glazing parameters showed no statistically significant association with thermal loads. LASSO further identified glazing distribution as dispensable without compromising predictive performance. All machine-learning models achieved excellent predictive accuracy, with R2 > 0.94 on the test set, with support vector regression producing the best generalization performance (test R2 = 0.945). The integrated framework also revealed distinct behavioral patterns among architectural variables, showing that orientation influences energy demand through discrete thresholds, whereas building height exhibits a continuous relationship with thermal loads. These findings demonstrate that climate-responsive volumetric optimization should take precedence over conventional fenestration-focused strategies for Mediterranean residential buildings. The proposed methodology provides a robust and interpretable framework to support energy-efficient building design, reduce HVAC energy demand, and contribute to lower operational carbon emissions in rapidly urbanizing regions with Mediterranean climates.