  We consider nonlinear biasing models of galaxies with particular attention to
a correlation between linear and quadratic biasing coefficients, b_1 and b_2.
We first derive perturbative expressions for b_1 and b_2 in halo and peak
biasing models. Then we compute power spectra and bispectra of dark matter
particles and halos using N-body simulation data and of volume-limited
subsamples of Sloan Digital Sky Survey (SDSS) galaxies, and determine their b_1
and b_2. We find that the values of those coefficients at linear regimes
(k<0.2h/Mpc) are fairly insensitive to the redshift-space distortion and the
survey volume shape. The resulting normalized amplitudes of bispectra, Q, for
equilateral triangles, are insensitive to the values of b_1 implying that b_2
indeed correlates with b_1. The present results explain the previous finding of
Kayo et al. (2004) for the hierarchical relation of three-point correlation
functions of SDSS galaxies. While the relations between b_1 and b_2 are
quantitatively different for specific biasing models, their approximately
similar correlations indicate a fairly generic outcome of the biasing due to
the gravity in primordial Gaussian density fields.
