by a zero-centred and normally distributed random noise with flux density uncertainty as the standard deviation. For non-detections, the observed flux density is assumed to be zero. As the data fitting is done in log-log space, all simulated flux densities with negative value are sign-flipped (it does not change the flux density probability distribution for non-detections and only has negligible impact on detected objects as the detection threshold is 3-$\sigma$). We find the index of best-fit power law model for the full sample including all upper limits (magenta line) is consistent with unity. The scatter of detected objects around the best-fit model is about 0.34 dex (y axis direction), confirming a good correlation over four orders of magnitude. We note that we get similar result by using the Schmitt’s binning method [@1985ApJ...293..178S].

We find no significant difference between massive and dwarf galaxies (red and blue lines in Figure \[fig:frc\]). They are both consistent with the full sample relation. Yet the result may be slightly different if the upper limits are excluded from analysis. We notice that the index of best-fit power law model for detection-only (cyan line in Figure \[fig:frc\]) is slightly larger than one with $\sim2$-$\sigma$ significance. We compare 