  The in-plane resistivity and Hall coefficient have been measured for the
single-layer compound Bi$_2$Sr$_2$CuO$_{6+\delta}$ for the whole range of
doping states. The deviation of the Hall coefficient, $R_H$, from a
high-temperature linear behavior and the temperature dependence of the Hall
angle are both only weakly dependent upon doping, contrasting with
Bi$_2$Sr$_{2-x}$La$_x$CuO$_{6+\delta}$ and Bi$_2$Sr$_2$CaCuO$_{8+\delta}$. This
is in contradiction with former proposals that the transverse transport detects
the formation of incoherent Cooper pairs in the pseudogap state. Conversely,
the analysis of the data using a phenomenological angular dependent scattering
rate clearly allows to distinguish between underdoped and overdoped states, and
we propose that the maximum in $R_H(T)$ simply arises due to the combination of
a large isotropic scattering rate and an anisotropic temperature dependent one.
