Probability density function p(L_R | M_⋆,  z) of a SFG hosting a radio-excess AGN with a given 1.4 GHz luminosity L_R as a function of stellar mass M_⋆ (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 L_R bins. Each dashed line represents the best-fit power-law relation for p(L_R | M_⋆,  z) as a function of M_⋆ in each L_R bin (defined by Equation 22). Right column: Best-fit slope b (upper panel at each redshift bin) and intercept a (bottom panel at each redshift bin) of the above power-law relation. The different colors represent different L_R bins (same as those in the left column). In the upper right panel of each redshift bin, the gray dashed line shows the mean of slopes over all the L_R bins ($\overline{b}$), while the gray region represents $\overline{b}\pm 0.1$. In the bottom right panel of each redshift bin, the pink dashed line shows the mean of intercepts over all the L_R bins ($\overline{a}$), while the pink region represents $\overline{a}\pm 0.1$. The region scale (±0.1) is just a reference value to show the difference between each data point with the mean value.