BFJR in galaxy groups, elliptical galaxies, and dwarf galaxies. Left: Total baryonic mass (M_bar) versus velocity dispersion within the effective radius (σ_e) for the full sample. The data points are color-coded by the internal median baryonic acceleration, ⟨g_bar⟩. Middle: BFJR for the low-acceleration subsample only (⟨g_bar⟩ < 0.6a₀). In both panels, the dashed green line shows the MOND prediction in the low-acceleration regime, the solid black line is the best fit from the orthogonal MCMC, and the orange region is its 1σ credible interval. Right: Variation in the fitted parameters with the acceleration cutoff value, ⟨g_bar⟩/a₀: slope (m; top) and intercept (b; bottom). Orange diamonds are the result from orthogonal MCMC fitting, blue circles from vertical MCMC fitting. The number of objects at each cutoff is listed in the upper-right panel. The horizontal dashed lines mark the theoretical expectations from MOND modified gravity theories (m = 4, b = 3.1).