﹩\mathrm{log}{L}_{2500\,\mathring{\rm A} }﹩ vs. redshift for each of the X-ray subsamples included in our analysis. Our 25 Chandra/HST targets are shown as green triangles, the Timlin et al. (2020a) subset is shown with blue circles, the SDSS-RM objects are represented by orange stars, the Lusso et al. (2020) objects are represented by purple squares, and the Nardini et al. (2019) objects are represented by black squares. The bulk of the sample is contained within 1.5 < z < 3.5 because of the need to include enough of the C IV absorption trough in the SDSS spectra to identify BAL quasars (lower limit) and to have high enough S/N spectra to perform an ICA reconstruction (upper limit).