Equivalent width of the Mg ii line versus a) bolometric luminosity; b) black hole mass; c) Eddington ratio; and d) accretion rate for the rWLQ sample. Filled red squares: FIRST detected WLQs, open red squares: FIRST undetected, magenta frames: rWLQ-EWS subsample. Straight lines: linear regression curves for the rWLQ sample. The distributions for the comparison sample are indicated by equally spaced logarithmic local point density contours estimated with a grid size of Δx,Δy = 0.1,0.05 dex.