Entropy generation plays a crucial role in the design and optimization of thermal systems by quantifying irreversible energy losses. This study presents a comprehensive investigation of magnetohydrodynamic (MHD) second–grade fluid flow over an inclined permeable stretching sheet under the combined influences of quadratic thermal radiation, activation energy, chemical reaction, and porous media. The governing nonlinear equations are transformed into a system of ordinary differential equations and solved numerically using the Nachtsheim–Swigert shooting technique coupled with the sixth–order Runge–Kutta method. In addition, regression and sensitivity analyses are performed to validate the numerical model and quantify the influence of the governing parameters on entropy generation. The novelty of this study lies in the unified integration of entropy generation analysis, quadratic thermal radiation, activation energy, chemical reaction, MHD flow over an inclined porous stretching sheet, and data–driven regression and sensitivity analyses within a single mathematical framework. Furthermore, a systematic comparison between linear and quadratic thermal radiation is presented to reveal their distinct influences on thermal transport and entropy production. The results demonstrate that magnetic field intensity and porous resistance suppress the fluid velocity, whereas thermal radiation and activation energy enhance the thermal field while chemical reaction reduces it. Activation energy increases species concentration by 53.36% compared with its absence and decreases entropy generation by 37.82%, whereas quadratic thermal radiation provides 84.78% greater cooling effectiveness but increases entropy generation by 89.57% relative to linear radiation. Entropy generation increases with magnetic field strength, radiation parameter, chemical reaction, and Brinkman number, but decreases with activation energy and porosity. Moreover, regression analysis confirms excellent predictive accuracy (R² = 99.90%) at the 95% confidence level, while sensitivity analysis identifies the Brinkman number, radiation parameter, and chemical reaction as the most influential positive contributors to entropy generation. These findings provide new physical insights into irreversible transport mechanisms and offer valuable guidelines for the design and optimization of advanced thermal systems, including solar thermal energy conversion, surface coating technologies, environmental remediation, and microfluidic devices.