Projected posterior distribution and density plots of the free parameter (slope α, intercept , and fractional intrinsic scatter f_ΔR) of the power law fitted to the sample data points. The plot additionally shows the 50 %, 16 %, and 84 % quartiles (vertical dashed lines), representing the distribution median and the 1 σ uncertainties (lower and upper bound), respectively. The 1D histograms represent the probability distributions of each parameter marginalized over the other two. The contour maps represent the central 68.3%, 95.5%, and 99.73% of the 2D probability distributions of different pairs of parameters, marginalized over the third.