Relations of the CF with redshift. The top panel shows the relation between log CF and log M_BH for quasars with the Spitzer M24 and VAC data. The red line represents the cut on log M_BH/M_⊙ = 8.5. The bottom panel shows the relation between log CF and redshift for quasars with log M_BH/M_⊙ > 8.5. The orange and red points in both panels represent the low-z and high-z quasars, respectively. The large symbols with MAD error bars stand for the medians calculated for each data sample: low-z with no cut in M_BH (red triangle), high-z (orange triangle), low-z with the cut in log M_BH/M_⊙ > 8.2 (pink triangle), low-zSpitzer with no cut in M_BH (black square), high-zSpitzer (green square), low-zSpitzer with the cut in log M_BH/M_⊙ > 8.5 (blue square). For the luminosity and Eddington ratio selection, see Appendix E.