Abstract
A distribution-free estimator of the slope of a regression line is introduced. This estimator is designated Sm and is given by the median of the set of n(n − 1)/2 slope estimators, which may be calculated by inserting pairs of points (Xi, Yi)and (Xj, Yj)into the slope formula Si = (Yi − Yj)/(Xi − Xj),1 ≤ i k (median {|Ri − Rm|}). If no outliers are found, the Y-intercept is given by Rm. Confidence limits on Rm and Sm can be found from the sets of Ri and Si, respectively. The distribution-free estimators are compared with the least-squares estimators now in use by utilizing published data. Differences between the least-squares and distribution-free estimates are discussed, as are the drawbacks of the distribution-free techniques.
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