Empirical distance-scaling relationship using data from Gagné et al. (2018b) and Cantat-Gaudin & Anders (2020). The x-axis represents the distance to stellar clusters; the y-axis shows the dispersion ratio of positional over kinematic subspaces. This dispersion directly corresponds to the velocity scaling factor, c_v, as discussed in Sect. 3.3.3. The gray line represents the best fit linear regression line, while the gray band indicates the 1σ highest density interval obtained from sampling the posterior predictive distribution.