Pyrrho's lemma

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In statistics, Pyrrho's lemma is the result that if one adds just one extra variable as a regressor from a suitable set to a linear regression model, one can get any desired outcome in terms of the coefficients (signs and sizes), as well as predictions, the R-squared, the t-statistics, prediction- and confidence-intervals. The argument for the coefficients was advanced by Herman Wold and Lars Juréen[1] but named, extended to include the other statistics and explained more fully by Theo Dijkstra.[2] Dijkstra named it after the sceptic philosopher Pyrrho and concludes his article by noting that this lemma provides "some ground for a wide-spread scepticism concerning products of extensive datamining". One can only prove that a model 'works' by testing it on data different from the data that gave it birth. [3]

The result has been discussed in the context of econometrics.[4]


  1. ^ Wold, Herman and L. Juréen (1953) Demand Analysis: A Study in Econometrics, John Wiley & Sons (2nd Ed)
  2. ^ Dijkstra, Theo K (1995). "Pyrrho's lemma, or have it your way". Metrika. 42 (1): 119–125. doi:10.1007/BF01894292. 
  3. ^ (Dijkstra, p. 122)
  4. ^ Hendry, David F. (1995) Dynamic Econometrics, Oxford University Press