EPR spectra of the high $T_c$ superconductor $YBa_2Cu_3O_{7-y}$ (YBCO) doped with $Pd^{2+} or Zn^{2+}$ have been measured at several temperatures and dopant concentrations. The spectral intensity of $YBa_2({Cu_{1-x}}{Pd_x})_3O_{7-y}$ is proportional to the dopant concentration. The behavior of $YBa_2(Cu_{1-x}Zn_x)_3O_{7-y}$ is quite different: the spectral intensity remains almost constant up to x=0.10 and then increases rapidly above x=0.10. The results are interpreted in terms of localized and antiferromagnetically spin-paired d holes in both CuO chain and planes. The $Pd_{2+}$ ion substitutes on the CuO chain consisting of "CuOCu dimers", and a $Cu_{2+}$ ion with an unpaired spin is gene rated for each $Pd_{2+}$ ion substituted. On the other hand, $Zn_{2+}$ substitutes on the CuO planes, and all or most of the spins in the two-dimensional plane manage to pair up in the region of low dopant concentration. When the dopant concentration exceeds a certain limit, it becomes more difficult for the spins to find partners, and the number of unpaired spins increases rapidly with increasing dopant concentration. The $Zn_{2+}$ ion is more effective than the $Pd_{2+}$ ion in suppressing the superconductivity of YBCO. This is attributed to the fact that $Zn_{2+}$ substitutes on the CuO planes which are mainly responsible for the superconductivity, while $Pd_{2+}$ substitutes on the CuO chain which is of secondary importance in the superconductivity.