Left: Same as the data points in Fig. 1, but this time the optimal three‐parameter log‐quadratic relation (eq. [7]) is shown. The absolute scatter in ﹩\mathrm{log}\,M_{\mathrm{bh}\,}﹩ is 0.31 dex. The shaded area corresponds to the ﹩\Delta \chi ^{2}=3.53﹩ (1 σ) confidence region. Middle and right: Inner, central, and outer solid contours denoting the ﹩\Delta \chi ^{2}=1.00﹩, 9.00, and 15.1 boundaries, respectively: their projections onto the vertical and horizontal axes give the 68.3% (1 σ), 99.73% (3 σ), and 99.99% confidence intervals on the individual parameters in eq. (7). The inner and outer dashed lines denote the ﹩\Delta \chi ^{2}=2.30﹩ and 11.8 boundaries, respectively, delineating the 1 and 3 σ two‐dimensional confidence regions. The dotted lines show the ﹩\Delta \chi ^{2}=3.53﹩ and 14.2 boundaries, respectively. They correspond to the 1 and 3 σ three‐dimensional confidence ellipsoids (see Press et al. 1992, their § 15.6).