Analysis of Residuals

Reference work entry

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.


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.


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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    Anscombe, F.J.: Examination of residuals. Proc. 4th Berkeley Symp. Math. Statist. Prob. 1, 1–36 (1961)MathSciNetGoogle Scholar
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    Anscombe, F.J.: Graphs in statistical analysis. Am. Stat. 27, 17–21 (1973)CrossRefGoogle Scholar
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    Anscombe, F.J., Tukey, J.W.: Analysis of residuals. Technometrics 5, 141–160 (1963)zbMATHCrossRefMathSciNetGoogle Scholar
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    Cook, R.D., Weisberg, S.: Residuals and Influence in Regression. Chapman & Hall, London (1982)zbMATHGoogle Scholar
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