Probability density function p(L_R | M_⋆,  z) of a SFG with a given stellar mass M_⋆ hosting a radio-excess AGN as a function of 1.4 GHz luminosity L_R (left column) and the corresponding best-fit parameters (right column). Left column: At each redshift bin (from top to bottom) the different colors represent different M_⋆ bins. Each dashed line represents the best-fit power-law relation for p(L_R | M_⋆,  z) as a function of L_R in each M_⋆ bin (defined by Equation 23). Right column: Best-fit slope d (upper panel at each redshift bin) and intercept c (bottom panel at each redshift bin) of the above power-law relation. The different colors represent different M_⋆ bins (same as the left column). In the upper right panel of each redshift bin, the gray dashed line shows the mean of slopes over all the M_⋆ bins ($\overline{d}$), while the gray region represents $\overline{d}\pm 0.1$. In the bottom right panel of each redshift bin, the pink dashed line shows the mean of intercepts over all the M_⋆ bins ($\overline{c}$), while the pink region represents $\overline{c}\pm 0.1$. The region scale (±0.1) is just a reference value to show the difference between each data point with the mean value.