(a) + (b) + (c) & 96 & 299\
All + BAL removal & 96 & 248 \[table:qcuts\]

Fitting Procedure
-----------------

Throughout this work, we use the fitting algorithm described by [@Cappellari13] that combines the Least Trimmed Squares technique of [@Rousseeuw06] and a least-squares fitting algorithm which allows errors in all variables and includes intrinsic scatter, as implemented by [@DallaBonta18]. Briefly, the fits we perform here are of the general form $$\label{eq:powerlaw}
y = a + b\left(x - x_0 \right),$$ where $x_0$ is the median value of the observed parameter $x$. The fit is done iteratively with $5 \sigma$ rejection (unless stated otherwise) and the best fit minimizes the quantity $$\label{eq:chi2line}
    \chi^2=\sum_{i=1}^N \frac{[a+b (x_i-x_0) - y_i]^2}
    {(b \Delta x_i)^2 + (\Delta y_i)^2 + \varepsilon_y^2},$$ where $\Delta x_i$ and $\Delta y_i$ are the errors on the variables $x_i$ and $y_i$, and $\varepsilon_y$ is the sigma of the Gaussian describing the distribution of intrinsic scatter in the $y$ coordinate; $\varepsilon_y$ is iteratively adjusted so that the $\chi^2$ per degree of freedom $\nu=N-2$ has the value of unity expected for a good fit. The observed scatter is $$\label{eq:Deltadef}
\Delta = \left\{ \frac{1}{N-2} \sum_{i=1}^N
\left[y_i - a - b\left(x_i - x_0\right) \right]^2 \right\}^{1/2}.$$ The 