& 0.121 \[table:LW\]

We also show in the right panel of Figure \[Figure:windowhbwidths\] the relationship between () and the FWHM of  in the mean spectrum, (). The fit coefficients are given in the second row of Table 3. The relationship is far from linear (slope $= 0.535 \pm 0.042$), and the scatter $\varepsilon_y$ is larger than it is for the ()–() relationship, even after removal of the notable outliers. While it is clear that () is an excellent proxy for (), the value of () is less clear. Nevertheless we will fit both versions in order to understand the relative merits of each.

Single-Epoch Predictors of the Virial Product {#section:hbpredictor}
---------------------------------------------

In the previous subsections, we have re-established the correlations between $\tau({\mbox{\rm H$\beta$}})$ and $L({\mbox{\rm H$\beta$}}_{\rm broad})$ and between () and both () and (). As a first approximation for a formula to estimate single-epoch masses, we fit the following equations: $$\log {\mbox{$\mu_{\rm RM}$}}({\mbox{\rm H$\beta$}}) = a + b\left[\log L({\mbox{\rm H$\beta$}}_{\rm broad}) - x_0\right]
+c\left[\log{\mbox{$\sigma_{\rm M}$}}({\mbox{\rm H$\beta$}}) - y_0\right],
\label{eq:Fit_139}$$ and $$\log {\mbox{$\mu_{\rm RM}$}}({\mbox{\rm H$\beta$}}) = a + b\left[ \log L({\mbox{\rm H$\beta$}}_{\rm broad}) - x_0\right]
+c\left[ \log {\mbox{${\rm FWHM}_{\rm M}$}}({\mbox{\rm H$\beta$}}) - y_0\right].
\label{eq:Fit_141}$$

The results of these fits based 