  Renormalization Group correction to General Relativity (RGGR) proposes a
logarithmic running of the gravitational coupling $\left(G\right)$, resulting
in a modified description of gravity. This has the potential to explain the
observed kinematics of the galaxies, including the missing-mass problem. We,
for the first time, based on the galaxy morphological types, investigate the
dynamics of a diverse collection of galaxies present in the Spitzer Photometry
for Accurate Rotation Curve (SPARC) catalog. We phenomenologically constrain
the RGGR model parameter $\left(\bar\nu\right)$ along with the mass-to-light
ratio for a sample of 100 SPARC galaxies, selected from four different
morphological types, viz. early, spiral, late, and starburst. Our statistical
analysis finds RGGR to fit the observed galaxy kinematics consistently. The
constrained RGGR model parameter also supports the claim that it has a
near-linear dependence on the galactic baryonic mass. From our morphology
study, we find that the parameter $\bar\nu$ decreases from the early-type to
the starburst galaxies. Finally, the renormalization group improved gravity is
tested against the two established empirical relations for the SPARC catalog,
viz., the Radial Acceleration Relation (RAR) and the Baryonic Tully Fisher
relation (BTFR), both are found to be satisfied consistently.
