Recent progress in extremely correlated Fermi liquid theory (ECFL) and dynamical mean field theory (DMFT) enables us to compute in the $d to infty$ limit the resistivity of the $t-J$ model after setting $Jto0$. This is also the $U=infty$ Hubbard model. We study three densities $n=.75,.8,.85$ that correspond to a range between the overdoped and optimally doped Mott insulating state. We delineate four distinct regimes characterized by different behaviors of the resistivity $rho$. We find at the lowest $T$ a Gutzwiller Correlated Fermi Liquid regime with $rho propto T^2$ extending up to an effective Fermi temperature that is dramatically suppressed from the non-interacting value. This is followed by a Gutzwiller Correlated Strange Metal regime with $rho propto (T-T_0)$, i.e. a linear resistivity extrapolating back to $rho=0$ at a positive $T_0$. At a higher $T$ scale, this crosses over into the Bad Metal regime with $rho propto (T+T_1)$ extrapolating back to a finite resistivity at $T=0$, and passing through the Ioffe-Regel-Mott value where the mean free path is a few lattice constants. This regime finally gives way to the High $T$ Metal regime, where we find $rho propto T$. The present work emphasizes the first two, where the availability of an analytical ECFL theory is of help in identifying the changes in related variables entering the resistivity formula that accompany the onset of linear resistivity, and the numerically exact DMFT helps to validate the results. We also examine thermodynamic variables such as the magnetic susceptibility, compressibility, heat capacity and entropy, and correlate changes in these with the change in resistivity. This exercise casts valuable light on the nature of charge and spin correlations in the strange metal regime, which has features in common with the physically relevant strange metal phase seen in strongly correlated matters.
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