FAMA, FISHER, JENSEN AND ROLL the first order auto-correlation coefficient of the estimated residuals from(1) has been computed for every twentieth split in the sample (ordered al phabetically by security ). The mean (and median) value of the forty-seven coefficients is-0. 10, which suggests that serial dependence in the residuals is not a serious problem. For these same forty-seven splits scatter diagrams of (a) monthly security return versus market return, and(b)estimated re- sidual return in month t+1 versus estimated residual return in month t have been prepared, along with(c) normal probability graphs of estimated residual returns. The scatter diagrams for the individual securities support very well the regression assumptions of linearity, homoscedasticity, and serial independence It is important to note however, that the data do not conform well to the normal, or Gaussian linear regression model. In particular, the distributions of the estimated residuals have much longer tails than the Gaussian. The typical normal probability graph of residuals looks much like the one shown for Timken Detroit Axle in Figure 1. The departures from normality in the distributions of regression residuals are of the same sort as those noted by Fama [3] for the distributions of returns themselves. Fama(following Timken Detroit Axle 0 0.03-0.02-0.0100.01002003004 Regression residuals-Uit FiGure 1 NORMAL PROBABILITY PLOT OF RESIDUALS* left and upper right corners of the graph represent the most extreme sample For clarity, only every tenth point is plotted in the central portion of the