The OLS estimator is a weighted average of the slopes delineated by adjacent observations. These weights depend only on the independent variable. Equal weights are obtained if and only if the independent variable is normally distributed. This feature is used to develop a new test for normality...

Yitzhaki (1996) showed that the OLS estimator of the slope coefficient in a simple regression is a weighted average of the slopes delineated by adjacent observations. The weights depend only on the distribution of the independent variable. In this paper I demonstrate that equal weights can only...