Monte Carlo analysis of the noise effects on the β(T_c) relation. The black dots correspond to a synthetic sample, where the source flux densities have been scaled to be consistent with a constant value of β. The green points show the T_c and β values extracted from data, where we have added to these flux densities the estimated observational noise. The red line is the fit to these points. The observed relation obtained using C3PO sources (blue line, cf. Fig. 14) is significantly steeper.