In low mass galaxies, gas outflows driven by stellar feedback can generate fluctuations in gravitational potential and lower the central density of dark matter halos, which can solve the cusp-core problem. We compare observational signals of feedback driven outflows in simulated low redshift galaxies from the Feedback in Realistic Environments (FIRE) project, as well as new baryonic zooms of galaxies from the Romulus25 run. The FIRE simulations predict a correlation between sSFR and gas velocity dispersion at low redshift, however the Romulus simulations do not. We analyze dwarf galaxies observed with Keck DEIMOS for correlations between specific star formation rates (sSFR) and H-alpha velocity dispersion at redshift below 0.35, and compare to simulation predictions. We find no correlation between sSFR and H-alpha velocity dispersion in our observed data. Our results support the scenario that if dwarf galaxies are cored by stellar feedback, the coring process is completed at intermediate redshifts.