Occurrence rate, F, the fraction of stars hosting planetary system, η_system, and the average multiplicity, k, as a function of stellar metallicity [Fe/H] for Kepler-like planets (R_p: 1–4R_⊕, P < 400 d, left panels), planets with radii between 2–4 R_⊕ (middle panels), and planets with radii between 1–2 R_⊕ (right panels) from the synthetic population by Bern planet formation and evolution model at 5 Gyr. In the left panels, we also plot the observational results derived from Kepler data (Zhu 2019) as grey points and error bars. As mentioned before, we were more concerned with trends and thus we renormalized the amplitude of observed occurrence rate tracer of Kepler systems with planets into the average synthetic η_system.