  Several Type Ia supernova analyses make use of non-simultaneous regressions
between observed supernova and host galaxy properties and supernova luminosity:
first the supernova magnitudes are corrected for their light curve shape and
color, and then they are separately corrected for their host galaxy masses.
This two-step regression methodology does not introduce any biases when there
are no correlations between the variables regressed in each correction step.
However, correlations between these covariates will bias estimates of the size
of the corrections, as well as estimates of the variance of the final
residuals. In this work, we analyze the general case of non-simultaneous
regression with correlated covariates to derive the functional forms of these
biases. We also simulate this effect on data from the literature to provide
corrections to remove these biases from the data sets studied. The biases
examined here can be entirely avoided by using simultaneous regression
techniques.
