<p>This research investigates a hybrid nanofluid that combines aurum and molybdenum disulfide nanoparticles in water (base fluid) over a rotating disk. The study emphasizes understanding the impact of various factors, such as thermal radiation, magnetohydrodynamic, viscous dissipation, Joule heating, Darcy-Forchheimer effects, and convective boundary conditions. To tackle this problem, we employ non-similarity transformations to create a suitable mathematical model, and these intricate equations are solved using NDSolve. Multiple quadratic regression analysis (predicted and <i>t</i>-statistic) is performed to understand the relationships of predicted and actual values of Nusselt number and skin friction. It is seen that the Hall effect boosts fluid flow and Nusselt number while decreasing skin friction and energy transport. The addition of aurum nanoparticles reduces velocities, while molybdenum disulfide enhances them. The volume fraction of nanomaterials enhances energy transport due to improved thermal conductive properties but decreases the Nusselt number. Both the Biot number and thermal radiation enrich the heat transfer rate and temperature distribution. The combined use of numerical solutions and regression analysis to optimize performance over an electrically conducting and heated rotating surface is a novel approach. These findings hold significant promise for practical applications in energy efficiency and sustainability, leading to potential environmental benefits and reduced energy costs.</p>