the reverberation-mapped sample from Kaspi [et al.]{} (2000). Treating [$L_{5100}$]{} as the independent variable (under the assumption that [$L_{5100}$]{}traces the continuum that powers the line emission) and accounting for errors in both variables (Press [et al.]{} 1992), an ordinary least-squares fit yields

$${\ensuremath{L_{\mathrm{H{\alpha}}}}}= (5.25 \pm 0.02) \times 10^{42} 
\left( \frac{{\ensuremath{L_{5100}}}}{10^{44}~{\rm erg~s^{-1}}}\right)^{(1.157 \pm
                          0.005)}~{\rm erg~s^{-1}}$$

and

$${\ensuremath{L_{\mathrm{H{\beta}}}}}= (1.425 \pm 0.007) \times 10^{42} 
\left(\frac{{\ensuremath{L_{5100}}}}{10^{44}~{\rm erg~
s^{-1}}} \right)^{(1.133 \pm 0.005)}~{\rm erg~s^{-1}}.$$

+0.35cm

The rms scatter in the above luminosity-luminosity relations is quite small, being only $\sim 0.2$ dex in each case. The correlation strengths are correspondingly strong, with Kendall’s $\tau = 0.8$, and do not improve when FWHM is included as a third parameter using the partial correlation test of Akritas & Siebert (1996). These relations are fit for the combined broad and narrow components. However, the best-fit parameters are virtually unchanged when only the broad component is considered, since the narrow component accounts for only $\sim 7 \%$ and $\sim 10 \%$ of the total [H$\alpha$]{} and [H$\beta$]{}flux, respectively. Note that the slopes of both correlations are formally larger than unity, which can be excluded at a confidence level of $>99$% based on bootstrap simulations.

-1mm +5mm We also find a well-defined 