Statistical Science

Influential Observations, High Leverage Points, and Outliers in Linear Regression

Samprit Chatterjee and Ali S. Hadi

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Abstract

A bewilderingly large number of statistical quantities have been proposed to study outliers and influence of individual observations in regression analysis. In this article we describe the inter-relationships which exist among the proposed measures. An examination of these relationships leads us to conclude that only three of these measures along with some graphical displays can provide an analyst a complete picture of outliers (major discrepant points) and points which excessively influence the fitted regression equation. Illustrative examples based on real data are presented.

Article information

Source
Statist. Sci., Volume 1, Number 3 (1986), 379-393.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.ss/1177013622

Digital Object Identifier
doi:10.1214/ss/1177013622

Mathematical Reviews number (MathSciNet)
MR858516

Zentralblatt MATH identifier
0633.62059

JSTOR
links.jstor.org

Keywords
Influence leverage outliers regression diagnostics residuals

Citation

Chatterjee, Samprit; Hadi, Ali S. Influential Observations, High Leverage Points, and Outliers in Linear Regression. Statist. Sci. 1 (1986), no. 3, 379--393. doi:10.1214/ss/1177013622. https://projecteuclid.org/euclid.ss/1177013622


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See also

  • See Comment: R. Dennis Cook. [Influential Observations, High Leverage Points, and Outliers in Linear Regression]: Comment. Statist. Sci., Volume 1, Number 3 (1986), 393--397.
  • See Comment: A. C. Atkinson. [Influential Observations, High Leverage Points, and Outliers in Linear Regression]: Comment: Aspects of Diagnostic Regression Analysis. Statist. Sci., Volume 1, Number 3 (1986), 397--402.
  • See Comment: Roy E. Welsch. [Influential Observations, High Leverage Points, and Outliers in Linear Regression]: Comment. Statist. Sci., Volume 1, Number 3 (1986), 403--405.
  • See Comment: Rollin Brant. [Influential Observations, High Leverage Points, and Outliers in Linear Regression]: Comment. Statist. Sci., Volume 1, Number 3 (1986), 405--407.
  • See Comment: David C. Hoaglin, Peter J. Kempthorne. [Influential Observations, High Leverage Points, and Outliers in Linear Regression]: Comment. Statist. Sci., Volume 1, Number 3 (1986), 408--412.
  • See Comment: Paul F. Velleman. [Influential Observations, High Leverage Points, and Outliers in Linear Regression]: Comment. Statist. Sci., Volume 1, Number 3 (1986), 412--413.
  • See Comment: Sanford Weisberg. [Influential Observations, High Leverage Points, and Outliers in Linear Regression]: Comment. Statist. Sci., Volume 1, Number 3 (1986), 414--415.
  • See Comment: Samprit Chatterjee, Ali S. Hadi. [Influential Observations, High Leverage Points, and Outliers in Linear Regression]: Rejoinder. Statist. Sci., Volume 1, Number 3 (1986), 415--416.