Plot of the relations which do not involve X-ray data extending the data sample. Left panel: v_C․IV vs. log(M_s, Edd) linear relation; Right panel: v_C․IV vs. z linear relation. The orange circles and the yellow squares represent the HYPERION and non-HYPERION QSOs in our sample, respectively. The green triangles and the purple diamonds represent the QSOs from Farina et al. 2022 and Mazzucchelli et al. 2023, respectively. the red circles with errorbars correspond to the median value for each bin. The dashed black lines are the linear regressions while the shaded regions represent the combined 1σ error on the slope and normalization (see Table 6).