  The recently observed an intimate link between the nature of the strange
metallic normal-state and superconductivity in the overdoped electron-doped
cuprate superconductors is calling for an explanation. Here the intrinsic
correlation between the strength of the low-temperature linear-in-temperature
normal-state resistivity and superconducting transition temperature $T_{\rm c}$
in the overdoped electron-doped cuprate superconductors is studied within the
framework of the kinetic-energy-driven superconductivity. On the one hand, the
main ingredient is identified into a electron pairing mechanism involving {\it
the spin excitation}, and then $T_{\rm c}$ has a dome-like shape doping
dependence with the maximal $T_{\rm c}$ that occurs at around the optimal
electron doping. On the other hand, in the normal-state above $T_{\rm c}$, the
low-temperature linear-in-temperature normal-state resistivity in the overdoped
regime arises from the momentum relaxation due to the electron umklapp
scattering mediated by {\it the same spin excitation}. This {\it same spin
excitation} that governs both the electron umklapp scattering responsible for
the low-temperature linear-in-temperature normal-state resistivity and electron
pairing responsible for superconductivity naturally generates a correlation
between the strength of the low-temperature linear-in-temperature normal-state
resistivity and $T_{\rm c}$ in the overdoped regime.
