Correlation between a galaxy’s supermassive black hole mass and the shape parameter (i.e., Sérsic index n) of its dynamically hot component. The Pearson linear correlation coefficient r is given, as is the Spearman rank‐order correlation coefficient ﹩r_{\mathrm{S}\,}﹩. (The uncertainties on the data points were not used when computing these correlation coefficients.) The regression line shown in the left panel was obtained using a modified version (Tremaine et al. 2002) of the routine FITEXY (Press et al. 1992, their § 15.3); see eq. (2). Consistent results were obtained using the ordinary least‐squares [﹩\mathrm{log}\,M_{\mathrm{bh}\,}\mid \mathrm{log}\,( n/ 3) ﹩] linear regression routine from Akritas & Bershady (1996); see eq. (4). The middle panel shows the ﹩\Delta \chi ^{2}=1.0﹩ and 2.3 boundaries around the optimal intercept, ﹩a=7.81﹩, and slope, ﹩b=2.69﹩. The projection of the ﹩\Delta \chi ^{2}=1.0﹩ ellipse onto the vertical and horizontal axes gives the 1 σ uncertainties ﹩\delta a﹩ and ﹩\delta b﹩, respectively. The ﹩\Delta \chi ^{2}=2.3﹩ ellipse denotes the 1 σ two‐dimensional confidence region. This has been mapped into the right panel and is traced by the two solid curves. The dashed lines in this panel are the (more commonly used) approximations obtained using ﹩a\pm \delta a﹩ and ﹩b\pm \delta b﹩. The two confidence regions agree well, although the region traced by the dashed lines is, as expected, smaller.