and PG 1704$+$608 (from Kaspi et al. 2000).

The best-fit regression line ($R_{\rm BLR} \propto L^{0.62 \pm 0.02}$), based on all objects from Table 5 of Kaspi et al. (2000) except NGC 4051, is shown as a dotted line. NGC 4051 lies approximately 2.8$\sigma$ above this regression line, although all the other narrow-line objects clearly fall in the locus defined by the AGNs with broader lines. It is difficult to argue that NGC 4051 is somehow different from the other AGNs, as there are several AGNs that have large displacements from the regression line. This is reflected in the large value of the reduced $\chi^2$ statistic, $\chi^2_{\nu} = 15.7$, for this fit.

In Fig. 7, we plot the mass–luminosity relationship for the AGNs from Kaspi et al., and we show (a) the best-fit regression line based on all objects [*except*]{} the seven narrow-line objects and (b) that based on the narrow-line objects alone. Formally, the slopes $\alpha$ (for $M \propto L^{\alpha}$) are significantly different, with $\alpha = 0.46 \pm 0.06$ for the narrow-line objects (including NGC 4051), and $\alpha = 0.27 \pm 0.03$ for the others. These two fits are separated by typically an order of magnitude in black-hole mass; 