A note on the use of residuals for detecting an outlier in linear regression

Ajit C. Tamhane*

*Corresponding author for this work

Research output: Contribution to journalComment/debatepeer-review

21 Scopus citations


SUMMARY: Consider the usual linear regression model y = Xß +ε, where the vector ε has E(ε) = 0, cov (ε) = σ2 V, where V is known. Let e = y-ŷ be the least squares residual vector. It is shown that a test based on the transformed residual vector d* = V-1 e has, in the class of linear transformations of e, certain optimal power properties for detecting the presence of a single outlier when the label of the outlier observation is unknown. The outlier model considered here is that of shift in location.

Original languageEnglish (US)
Pages (from-to)488-489
Number of pages2
Issue number2
StatePublished - Aug 1982


  • Linear regression
  • Outlier
  • Power
  • Residual

ASJC Scopus subject areas

  • Statistics and Probability
  • General Mathematics
  • Agricultural and Biological Sciences (miscellaneous)
  • General Agricultural and Biological Sciences
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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