Least-squares linear regression is the best of statistics and it is the worst of statistics. The reasons for this paradoxical claim, arising from possible inapplicability of the method and the excessive influence of "outliers", are discussed and substitute regression methods based on median selection, which is both robust and resistant, are introduced. A simple Excel macro to perform median-based linear regression, as suggested by Theil and by Siegel, is described and made available.
Supplement
An Excel workbook and visualization are available.
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