We use the Sloan Digital Sky Survey (SDSS) BOSS galaxies and their overlap with approximately 416 sq. degree of deep $grizy$-band imaging from the Subaru Hyper Suprime-Cam Survey (HSC). We measure three two-point correlations that form the basis of the cosmological inference presented in our companion papers, Miyatake et al. and Sugiyama et al. We use three approximately volume limited subsamples of spectroscopic galaxies by their $i$-band magnitude from the SDSS-BOSS: LOWZ (0.1Comment: 31 pages, 24 figures, version accepted for publication in PRD together with other HSC Y3 weak lensing cosmology papers - see https://hsc-release.mtk.nao.ac.jp/doc/index.php/wly3/