  A Bayesian method is used in this extensive work to generate a large set of
minimally constrained equations of state (EOSs) for matters in neutron stars
(NS). These EOSs are analyzed for their correlations with key NS properties,
such as the tidal deformability, radius, and maximum mass, within the mass
range of $1.2-2M_\odot$. The observed connections between the pressure of
$\beta$-equilibrated matter and the properties of neutron stars at different
densities offer significant insights into the behavior of NS matter in a nearly
model-independent manner. The study also examines the influence of various
factors on the correlation of symmetry energy parameters, such as slope and
curvature parameters at saturation density ($\rho_0=0.16 ~\text{fm}^{-3}$) with
the tidal deformability and radius of neutron stars. This study investigates
the robustness of the observed correlations by considering the distributions
and interdependence of symmetry energy parameters. Furthermore, the utilization
of Principal Component Analysis (PCA) is employed to unveil the complicated
relationship between various nuclear matter parameters and properties of
neutron stars. This analysis highlights the importance of employing
multivariate analysis techniques in order to comprehend the variety in tidal
deformability and radius observed across distinct masses of NS. This
comprehensive study aims to establish a connection between the parameters of
nuclear matter and the properties of neutron stars, providing significant
insights into the behavior of NS matter across different circumstances.
