A note on the correlation betweenS 2 and the least squares estimator in the linear regression model

In the following we consider the correlation betweenS ² and the least squares estimator in the linear regression model. We are interested in situations where these two statistics are uncorrelated though the errors are correlated. Conditions are developed without normality assumption, only assuming finite fourth moments of the error distributions. Support by Deutsche Forschungsgemeinschaft Grant No. Tr 253/1-2 is gratefully acknowledged.