Distribution of the observed values for the ESZ sample with best-fit results from a linear fit in the logarithmic space (using LIRA; Sereno 2016). Predictions from the semi-analytic model (best-fit values in Table 3) are overplotted with dashed lines in magenta (for the D14 c − M − z relation) and blue (B13). Bottom panels: dashed lines indicate the ratios of the model (M) to the observed (O) best-fit relations.