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\subsection{Sample Selection}  We draw our obseravational data from Data Release 7 (DR7) of the Sloan Digital Sky Survay (SDSS), making use of derived data products from the NYU Value-Added Galactic Catalog (VAGC). The magnitudes from the NYU VAGC that we use have been k-corrected to z = 0.1 using the code Kcorrect. Additionally, we restrict ourselves to regions of SDSS where the spectroscopic completeness parameter FGOTMAIN exceeds 0.7. In selecting our sample, we initially adhere closely to the procudure of I14. We select a sample of hosts in the magnitude range $-23 \lt r \lt -20$ and within a redshift range of $0.002 \lt z \lt 0.05$. A host considered isolated if there are no brighter objects within 500 kpc on the sky in projection and within 1500 km/s in velocity space. Only isolated hosts are retained. There were 22780 isolated hosts in the sample. From there we identified satellites around each host, identifying a galaxy as a satellite if it is brighter than r = -16 but fainter than one magnitude fainter than its host