and the combination of a large number of measurements and a poorly constrained virial product conspired to disguise real correlations.

All SDSS-RM spectra have been reduced and processed as described by [@Shen15] and [@Shen16b], including post-processing with [PrepSpec]{} (Horne, in preparation). We note that only lags ($\tau$), line dispersion in the rms spectrum (${\mbox{$\sigma_{\rm R}$}}$), and virial products (${\mbox{$\mu_{\rm RM}$}}= {\mbox{$\sigma_{\rm R}$}}^2 c \tau/G$) are taken from [@Grier17b] and [@Grier19]; all luminosities and other line-width measures are from [@Shen19] (Tables A3 and A4 are included here for the sake of clarity).

For each SDSS AGN, there are two determinations of both  and ; one is the best-fit (BF) to the mean spectrum, and the other is the mean of multiple Monte Carlo (MC) realizations. For each MC realization, $N$ independent random selections of the $N$ spectra are combined and the line width is measured for both  and . After a large number of realizations, the mean $\langle V
\rangle$ and rms $\Delta V$, for $V = {\mbox{${\rm FWHM}_{\rm M}$}}$ and $V = {\mbox{$\sigma_{\rm M}$}}$ are computed, and the rms values are adopted as the uncertainties in each line-width measure.

For the purpose of mass estimation, we need to establish relationships 