Percentage change of the β parameter. The black histogram shows the results of our Montecarlo simulations of the errors affecting the observational parameters (M_s,  L,  R_e,  σ,  Ie and their effects on log $L_0^{\prime }$ and β). The blue histogram shows the variations with the analytical method and Gaussian random distribution of the uncertainties affecting the characterizing parameters of each galaxy that is described in Appendix B obtained from the calculus of the derivatives. The green histogram shows the results obtained using the analytical method with the flat random distribution of uncertainties (see also Appendix B).