Distributions of the fitted parameters obtained from 1000 simulated datasets (see Appendix D). From top to bottom : intercept, slope, and intrinsic scatter. The blue histograms show the results from our likelihood-based fitting method, with the solid and dotted blue lines indicating the mean and the ±1σ intervals. The true input value used to generate the simulations is shown as a dashed green line. Each panel is annotated with the mean and standard deviation of the fitted parameter and the true input value in the top left corner.