1 \sigma$ and $\pm 2.6 \sigma$ envelopes, respectively, and the red dotted lines indicate where the two line-width measures are equal. Crosses are points that were rejected at the 2.6$\sigma$ (99%) level and are colored-coded like the circles. The relationship on the left is nearly linear (slope $= 1.085 \pm 0.045$) and the scatter $\varepsilon_y$ is low (0.079dex). It is clear in the right panel that () and () are well-correlated, but the relationship is significantly non-linear (slope $= 0.535 \pm 0.042$), the scatter $\varepsilon_y$ is slightly larger (0.106dex), and there are several significant outliers.[]{data-label="Figure:windowhbwidths"}](Figure3.eps)

[llccccc]{} $\log {\mbox{$\sigma_{\rm M}$}}({\mbox{\rm H$\beta$}})$ & $\log {\mbox{$\sigma_{\rm R}$}}({\mbox{\rm H$\beta$}})$ & $3.260 \pm 0.008$ & $1.085 \pm 0.045$ & 3.297 & $0.079 \pm 0.006$ & 0.087\
$\log {\mbox{${\rm FWHM}_{\rm M}$}}({\mbox{\rm H$\beta$}})$ & $\log {\mbox{$\sigma_{\rm R}$}}({\mbox{\rm H$\beta$}}) $ & $3.205 \pm 0.011$ & $0.535 \pm 0.042$ & 3.559 & $0.106 \pm 0.001$ & 0.114\
$\log {\mbox{$\sigma_{\rm M}$}}({\mbox{\rm C\,{\sc iv}}})$ & $\log {\mbox{$\sigma_{\rm R}$}}({\mbox{\rm C\,{\sc iv}}})$ & $3.436 \pm 0.009$ &$0.822 \pm 0.059$ & 3.394 & $0.064 \pm 0.008$ & 0.067\
$\log {\mbox{${\rm FWHM}_{\rm M}$}}({\mbox{\rm C\,{\sc iv}}})$ & $\log {\mbox{$\sigma_{\rm R}$}}({\mbox{\rm C\,{\sc iv}}})$ & $3.447 \pm 0.016$ & $0.445 \pm 0.101$ & 3.580 & $0.121 \pm 0.014$ 