  From analysis of the in-plane resistivity $\rho_{ab}(T)$ of
La$_{2-x}$Sr$_x$CuO$_4$, we show that normal state transport in overdoped
cuprates can be delineated into two regimes in which the electrical resistivity
varies approximately linearly with temperature. In the low temperature limit,
the $T$-linear resistivity extends over a very wide doping range, in marked
contrast to expectations from conventional quantum critical scenarios. The
coefficient of this $T$-linear resistivity scales with the superconducting
transition temperature $T_c$, implying that the interaction causing this
anomalous scattering is also associated with the superconducting pairing
mechanism. At high temperatures, the coefficient of the $T$-linear resistivity
is essentially doping independent beyond a critical doping $p_{\rm crit}$ =
0.19 at which the ratio of the two coefficients is maximal. Taking our cue from
earlier thermodynamic and photoemission measurements, we conclude that the
opening of the normal state pseudogap at $p_{\rm crit}$ is driven by the loss
of coherence of anti-nodal quasiparticles at low temperatures.
