2008 Edition

# Analysis of Residuals

Reference work entry
DOI: https://doi.org/10.1007/978-0-387-32833-1_7

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 =...
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## REFERENCES

1. 1.
Anscombe, F.J.: Examination of residuals. Proc. 4th Berkeley Symp. Math. Statist. Prob. 1, 1–36 (1961)
2. 2.
Anscombe, F.J.: Graphs in statistical analysis. Am. Stat. 27, 17–21 (1973)
3. 3.
Anscombe, F.J., Tukey, J.W.: Analysis of residuals. Technometrics 5, 141–160 (1963)
4. 4.
Cook, R.D., Weisberg, S.: Residuals and Influence in Regression. Chapman & Hall, London (1982)
5. 5.
Cook, R.D., Weisberg, S.: An Introduction to Regression Graphics. Wiley, New York (1994)
6. 6.
Cook, R.D., Weisberg, S.: Applied Regression Including Computing and Graphics. Wiley, New York (1999)
7. 7.
Draper, N.R., Smith, H.: Applied Regression Analysis, 3rd edn. Wiley, New York (1998)
8. 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
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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