The study of buoyancy effects in partitioned cavities has gained significant attention due to its relevance in numerous engineering and industrial applications, such as energy storage systems, electronic cooling devices, and thermal management solutions. Investigating the influence of key parameters such as Grashof number, Reynolds number, Hartmann number, and Prandtl number on heat transfer and fluid flow and bridging the knowledge gap by systematically examining computational results and statistical interpretations. Few works provide a detailed comparative analysis of buoyancy effects across various geometrical and physical parameters. Existing studies primarily focus on qualitative and computational results without integrating statistical methodologies to analyze trends and correlations. The governing equations are rendered dimensionless and numerically solved using the finite element method (FEM). The grid test and code validation criteria are established to ensure accurate solution convergence. The numerical results, presented visually for various dimensionless parameters, encompass heat transfer distributions, temperature, and velocity. At Re = 200, the heat transfer rate is 28.16 % greater than at Re = 50. At Ha = 50, it is 2.34 % lower than at Ha = 0. Furthermore, this study yields novel linear regression equations, ANOVA analysis, and predicted and residual values that are represented numerically and graphically. Based on R-squared values of 0.9523 for each, the heat transfer rates the Statistic linear regression algorithm achieves are extraordinarily high. This analysis is crucial for optimizing design parameters, improving energy efficiency, and enhancing thermal performance in real-world applications such as energy storage systems, electronics cooling, HVAC systems, renewable energy, and industrial processes.