  The connection between the escape fraction of ionizing radiation ($f_{esc}$)
and the properties of galaxies, such as stellar mass (M*), age, star-formation
rate (SFR), and dust content, are key inputs for reionization models, but many
of these relationships remain untested at high redshift. We present an analysis
of a sample of 96 z~3 galaxies from the Keck Lyman Continuum Spectroscopic
Survey (KLCS). These galaxies have both sensitive Keck/LRIS spectroscopic
measurements of the Lyman continuum (LyC) region, and multi-band photometry
that places constraints on stellar population parameters. We construct
composite spectra from subsamples binned as a function of galaxy property and
quantify the ionizing-photon escape for each composite. We find a significant
anti-correlation between $f_{esc}$ and M*, consistent with predictions from
cosmological zoom-in simulations. We also find significant anti-correlation
between $f_{esc}$ and E(B-V), encoding the underlying physics of LyC escape in
our sample. We also find no significant correlation between $f_{esc}$ and
either stellar age or specific SFR (=SFR/M*), challenging interpretations that
synchronize recent star formation and favorable conditions for ionizing escape.
The galaxy properties now shown to correlate with $f_{esc}$ in the KLCS are
Ly$\alpha$ equivalent width, UV Luminosity, M*, SFR, and E(B-V), but not age or
sSFR. To date, this is the most comprehensive analysis of galaxy properties and
LyC escape at high redshift, and will be used to guide future models and
observations of the reionization epoch.
