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Figure 11. the observed fractions of optically-selected quasar pairs that have radio counterparts are almost equal amongst our bins. there does not seem to be any significant trend from bin to bin as the bin error bars largely overlap. The the x and y uncertainties were calculated as described in the statistical analysis section. The error seems to decrease with an increase in projected separation. separation because the number of points increases. The straight line at 0.10 shows that the typical fraction of radio detection is $\approx 10\%$ of SDSS-selected quasars. \cite{Jiang_2007}