Abstract: Neutron star matter is mainly composed of asymmetric dense nuclear matter. At present, there is still great uncertainty in the understanding of the high-density asymmetric nuclear matter through the terrestrial experiments, such as the heavy ion collisions. With the improvement of astronomical observation accuracy and the increase of observable measurements of neutron stars, it is possible to reverse constraint the state of high-density nuclear matter based on astronomical observation of neutron stars. Theoretically investigating the correlation between the observable measurements of neutron stars and the equation of states (EOSs) at different density sections will be helpful to the research of the reverse constraints. In this work, by employing the piecewise polytrope EOSs, the observable measurements of the radius(R), tidal deformability(\varLambda), moment of inertia(I) of the neutron star etc. are calculated and analyzed, and the correlations between these observations and each density segment of the EOSs are given. The results show that tidal deformability (\varLambda) and f-mode frequency (\nu) of a canonical neutron star (M \!=\! 1.4\, M_\odot) are mainly correlated with 0.5\rho_\rmsat \!\sim\! 1.5\rho_ sat, 2.5\rho_\rmsat \!\sim\! 3.5\rho_\rmsat and 3.5\rho_\rmsat \!\sim\! 4.5\rho_\rmsat segments of EOSs; the neutron star radius (R) are mainly correlated with 1.5\rho_\rmsat \!\sim\! 3.5\rho_\rmsat and the crust segments of EOSs; the moment of inertia (I) are mainly correlated with the density below 4.5\rho_\rmsat segments of EOSs.