  The Hall coefficient is measured in YBa$_2$Cu$_3$O$_y$ untwinned single
crystals for a wide range of doping. We show that the Hall conductivity and the
Hall angle of the {\it CuO$_2$ planes} in YBa$_2$Cu$_3$O$_y$ can be extracted
from measurable transport properties regardless of the conduction of the Cu-O
chains nor the in-plane anisotropy of the CuO$_2$ planes. The present analysis
allows us to discuss the genuine Hall effect in the CuO$_2$ planes alone in
YBa$_2$Cu$_3$O$_y$ without any complications due to the Cu-O chains.
