Skip to main content
SpringerLink
Log in
Book cover

The Concise Encyclopedia of Statistics pp 5–9Cite as

Analysis of Residuals

  • Reference work entry

  • 633 Accesses

An analysis of residuals is used to test the validity of the statistical model and to control the assumptions made on the error term. It may be used also for outlier detection.

HISTORY

The analysis of residuals dates back to Euler (1749) and Mayer (1750) in the middle of the eighteenth century, who were confronted with the problem of the estimation of parameters from observations in the field of astronomy. Most of the methods used to analyze residuals are based on the works of Anscombe (1961) and Anscombe and Tukey (1963). In 1973, Anscombe also presented an interesting discussion on the reasons for using graphical methods of analysis. Cook and Weisberg (1982) dedicated a complete book to the analysis of residuals. Draper and Smith (1981) also addressed this problem in a chapter of their work Applied Regression Analysis.

MATHEMATICAL ASPECTS

Consider a general model of multiple linear regression:

$$ Y_i = \beta_0 + \sum_{j=1}^{p-1} \beta_j X_{ij} + \varepsilon_i\:,\quad i =...

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   299.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

REFERENCES

  1. Anscombe, F.J.: Examination of residuals. Proc. 4th Berkeley Symp. Math. Statist. Prob. 1, 1–36 (1961)

    MathSciNet  Google Scholar 

  2. Anscombe, F.J.: Graphs in statistical analysis. Am. Stat. 27, 17–21 (1973)

    Article  Google Scholar 

  3. Anscombe, F.J., Tukey, J.W.: Analysis of residuals. Technometrics 5, 141–160 (1963)

    Article  MATH  MathSciNet  Google Scholar 

  4. Cook, R.D., Weisberg, S.: Residuals and Influence in Regression. Chapman & Hall, London (1982)

    MATH  Google Scholar 

  5. Cook, R.D., Weisberg, S.: An Introduction to Regression Graphics. Wiley, New York (1994)

    MATH  Google Scholar 

  6. Cook, R.D., Weisberg, S.: Applied Regression Including Computing and Graphics. Wiley, New York (1999)

    MATH  Google Scholar 

  7. Draper, N.R., Smith, H.: Applied Regression Analysis, 3rd edn. Wiley, New York (1998)

    MATH  Google Scholar 

  8. Euler, L.: Recherches sur la question des inégalités du mouvement de Saturne et de Jupiter, pièce ayant remporté le prix de l'année 1748, par l'Académie royale des sciences de Paris. Republié en 1960, dans Leonhardi Euleri, Opera Omnia, 2ème série. Turici, Bâle, 25, pp. 47–157 (1749)

    Google Scholar 

  9. Mayer, T.: Abhandlung über die Umwälzung des Monds um seine Achse und die scheinbare Bewegung der Mondflecken. Kosmographische Nachrichten und Sammlungen auf das Jahr 1748 1, 52–183 (1750)

    Google Scholar 

Download references

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag

About this entry

Cite this entry

(2008). Analysis of Residuals. In: The Concise Encyclopedia of Statistics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-32833-1_7

Download citation

Publish with us

Policies and ethics

Search

Navigation