Pearson coefficients for the (partial) correlations of δ_L with halo properties, z_f (left panel), v_max/v₂₀₀ (middle panel), and λ (right panel), as a function of halo mass. As indicated in each panel, the red lines show the results of the correlations between δ_L and halo properties, the blue and green lines show the results with another property controlled, and the black lines show the results with δ_e controlled. The error bar shows the standard deviation calculated from 200 bootstrap samples.