Comparison of the contributions from the observational noise and from the intrinsic scatter to the different elements of the covariance matrix as a function of the amplitude of the stochastic component and for different configurations of B_reg. We show the total elements of the covariance matrix (solid lines) along with the contribution from the noise (dashed lines) and from the intrinsic scatter (dotted lines). Blue, green and orange correspond to C_int,qq, C_int,uu and C_int,qu respectively. The lines and shaded areas show the median and 16 and 84 percentile of the values obtained while repeating the analysis for 10,000 simulations in which both the noise and the intrinsic scatter vary. In this simulation we have set p_reg = 0.6% and σ_p = σ_q = σ_u = 0.2% corresponding roughly to a S/N of 3 for the individual star polarization measurement.