In this research the influences of quadratic Boussinesq approximation and quadratic thermal radiation on heat transfer analysis of magnetized Sisko nanofluid flow with Cattaneo-Christov (CC) heat flux through stretching surface was studied using response surface methodology (RSM). The upshots of the transformed differential equations is attained by bvp4c method. The heat transfer and skin friction calculations are done for acting parameters i.e., magnetic field, Eckert number, Forchheimer parameter, thermal relaxation parameter, radiation parameter, porosity parameter, and Biot number. For sensitivity analysis, the response surface method with FCC design is utilized. From the outcomes, it was concluded that the friction coefficient and Nusselt number have positive sensitivities for Forchheimer parameter. Moreover, heat transfer rate is declined with increase in magnetic field, Biot number and thermal relaxation parameter values for the conditions shear thickening (n<1) and shear thinning (n<1) .