Scaling relations between single β-model (left panels) and core-modeled single β-model (right panels) parameters and temperature. The HIFLUGCS clusters with temperatures greater than 3 keV (black points) are used for optimization. Red points mark HIFLUGCS objects below this temperature threshold for visualization. The orange lines and shaded regions show the best-fit relations and their uncertainties, respectively. The blue dashed lines correspond to the intrinsic log-normal scatter.