Visualisation of the parameter importance for responses EW_Lyα (top panels), f_esc^Lyα (middle panels), and L_Lyα (bottom panels) from a conditional perspective using step-wise regression in a multivariate linear regression framework (see Sect. 4.1.2 for details). The panels on the left- and right-hand sides visualise the distribution of rankings p(r(x_i)) for the parameters x_i from the observational and physical parameter sets, respectively, where each set includes the kinematical parameters that have been derived in this work. Low values of r(x_i) indicate a high importance of x_i, whereas high values indicate a low importance. All but two of the curves were obtained using a kernel-density estimator (Gaussian kernel, width = 0.5) on the ranks from N_MC = 10³ Monte Carlo realisations. The exceptions are the ${\sigma }_0^{\text{obs}}$ curves for the response EW_Lyα (see footnote 7). The four most important parameters according to Eq. (5) are shown with bold lines, whereas the remaining ranks are shown with thin lines and in subdued colours. The legend at the top of each panel is sorted according to the ranks from Eq. (5), which are also listed in Table 2.