Random Forest classification analysis to predict the quenching of central galaxies in the SDSS. Left panel: random Forest analysis for the bulge-disk parameters (i.e. M_B, M_D, M_* and B/T). The y-axis indicates the relative importance of each parameter for predicting whether central galaxies are star forming or quenched, and the x-axis indicates each parameter used to train the Random Forest in turn (ordered from most to least predictive of quenching). The Random Forest classification analysis is repeated for four different samples: (i) raw data (as in Mendel et al. 2014; ii) raw data with a pure Sérsic cut (defined and motivated in Sect. 2); (iii) 1/V_max volume weighted sample; (iv) volume weighted sample with pure Sérsic cut. The error on each relative importance for each sample is taken as the dispersion across ten independent training and testing runs. It is clear, and highly significant, that bulge mass is the most predictive parameter governing quenching in all sample variants. Right panel: random Forest analysis for a broader set of parameters, shown for comparison. Here stellar velocity dispersion (σ_⋆), dark matter halo mass (M_H), and local galaxy over-density (δ₅) are added to the bulge–disk parameters. This analysis is performed with the raw (unweighted) sample with Sérsic cuts (shown in blue), and with a sample with an additional cut in axial ratio (shown in magenta). It is clear that σ_⋆ is overwhelmingly the most predictive parameter of central galaxy quenching in the expanded data set.