Comparison of our predicted M_BH − σ relation with data for all galaxies at z ≤ 0.1. The color code corresponds to the logarithm of the fraction of galaxies with different M_BH in a given log σ bin. Panel A: Predicted relation between the BH mass M_BH and the bulge velocity dispersion σ brightness-weighted averaged over the galaxy. The data points are from Kormendy & Ho (2013; black squares and triangles for elliptical galaxies and bulges, respectively), De Nicola et al. (2019; brown squares), Savorgnan & Graham (2016; red dots), and Ho & Kim (2014; orange filled squares). Panel B: Same as panel A, but including in the model the selection bias discussed in Sect. 3, i.e., considering only model galaxies that satisfy the condition in Eq. (12) with θ_crit = 0.1. Panel C: Same as panel A, but considering only model galaxies hosting AGN with bolometric luminosity L_AGN ≥ 10⁴⁴ erg/s. Bottom right panel: Histograms represent the rms values of the scatter for the distributions shown in the top left (brown), top right (blue), and bottom left panel (orange). The horizontal strip represents the range of values obtained from different observational works: the upper bound is the intrinsic scatter ϵ derived by De Nicola et al. (2019), and the lower bound is the value of ϵ derived by the least-square fit analysis by Kormendy & Ho (2013) using individual errors in log σ, adding individual errors in log M_BH to the intrinsic scatter in quadrature, and iterating the intrinsic scatter until the reduced χ² = 1.