  We assess evolution in the black hole mass - stellar velocity dispersion
relationship (M-sigma relationship) for quasars in the Sloan Digital Sky Survey
Data Release 7 for the redshift range 0.1 < z < 1.2. We estimate the black hole
mass using the "photoionization method," with the broad Hbeta or Mg II emission
line and the quasar continuum luminosity. For the stellar velocity dispersion,
we use the narrow [O III] or [O II] emission line as a surrogate. This study is
a follow-up to an earlier study in which we investigated evolution in the
M-sigma relationship in quasars from Data Release 3. The greatly increased
number of quasars in our new sample has allowed us to break our lower-redshift
subsample into black hole mass bins and probe the M-sigma relationship for
constant black hole mass. The M-sigma relationship for the highest-mass (log M
> 9 solar masses) and lowest-mass (log M < 7.5 solar masses) black holes
appears to evolve significantly, however most or all of this apparent evolution
can be accounted for by various observational biases due to intrinsic scatter
in the relationship and to uncertainties in observed quantities. The M-sigma
relationship for black holes in the middle mass range (7.5 < log M < 9 solar
masses) shows minimal change with redshift. The overall results suggest a limit
of +/- 0.2 dex on any evolution in the M-sigma relationship for quasars out to
z ~ 1 compared with the relationship observed in the local universe. Intrinsic
scatter may also provide a plausible way to reconcile the wide range of results
of several different studies of the black hole - galaxy relationships.
