<p>The present study developed a probabilistic regression framework to predict maximum ground settlement and maximum wall deflection in deep braced excavations. A Heteroskedastic Gaussian Distribution Regression formulation was used to derive fitted predictive equations, allowing both the mean response and response variability to be modelled as functions of governing geotechnical parameters. The variance structure was explicitly linked to soil and excavation variables, thereby overcoming the deterministic nature of conventional machine learning approaches, which provided only point estimates without uncertainty representation. The framework enabled direct quantification of deformation uncertainty relevant to geotechnical risk assessment and excavation performance evaluation. Numerical analyses were conducted using advanced constitutive soil models capable of simulating elasto-plastic behaviour and time-dependent creep of soft clay deposits representative of eastern Indian conditions. A parametric investigation evaluated the effects of excavation rate and construction pause duration on settlement and wall deformation. Undrained, consolidation, and creep-induced settlements were separated through comparative numerical modelling. The predicted responses closely matched the simulated deformation trends. The regression model produced stable predictions with statistically interpretable uncertainty bounds, supporting probabilistic assessment of safety margins in braced excavation design and improving reliability in deformation-sensitive construction scenarios.</p>