Upper left panel: mock sample of 100,000 quasars assuming a L_X − L_UV relation with zero intrinsic dispersion, a contribution from variability to the observed dispersion of 0.08 dex, and an inclination angle between 0 and π/2. For each object, a redshift is assigned using the redshift distribution of the L20 sample. To derive the luminosity, we correct the L20 luminosity distribution for the inclination effect. The red solid line represents the starting sample, with a slope γ = 0.6 and a zero dispersion. The blue points show the sample after the dispersion due to variability is added and the objects are assigned a random inclination. The total dispersion of the sample is δ_tot = 0.21 dex, and the inclination effect accounts for δ_inc = 0.19 dex. Upper right panel: histogram of the fit residuals, in filled green. This distribution has a skewness parameter of s = 1.74, and the peak is shifted from zero, at −0.16. In dot-dashed orange, the histogram of the residuals for the L20 sample is shown. We see that the L20 distribution, which is the observed one, is instead much more symmetric, with a skewness parameter of s_L20 = 0.20. The histograms of the residuals for the silver sample and the golden sample of Sacchi et al. (2022) (details in Section 6) are also shown. The red solid vertical line corresponds to zero, while the dashed black vertical line corresponds to the peak of the mock sample distribution, equal to −0.16. Lower left panel: same as the upper Left panel, but assuming the presence of an obscurer with an angular width of ψ_torus = 25°, which means that the inclination angle for the objects in the mock sample can go from 0 to 65°. The total dispersion is reduced to δ_tot = 0.10 dex, and the inclination effect accounts for δ_inc = 0.06 dex. Lower right panel: same as the upper right panel, but assuming the presence of an obscurer with an angular width of ψ_torus = 25°. Here we see that the residuals distribution is symmetric, with a skewness parameter of s = 0.20, which perfectly matches the L20 value of s_L20 = 0.20. We also note that the residuals distribution is now slightly wider than the one for the Sacchi et al. (2022) sample.