Abnormal returns (market model prediction errors) are the subject of many event studies in accounting and finance literature. Conditional on the event of interest, researchers have recently used cross-sectional regressions to examine relations between abnormal returns and firm specific variables. This paper demostrates that non-constant variences and covariances in market model residuals across firms introduced bias in the estimated slope coefficients of the independent variables, i.e., the expected signs of the estimated slope coefficients can be predicted a priori. A method is develope to removed the bias in the estimated slope coefficiets and is found to be effective. This method explicitly takes the dependence among abnormal returns across firms into account. Methods that assume abnormal returns across firms to be independent do not control for such bias.