Regression diagnostic

For a broader coverage related to this topic, see Regression validation.

In statistics, a regression diagnostic is one of a set of procedures available for regression analysis that seek to assess the validity of a model in any of a number of different ways.[1] This assessment may be an exploration of the model's underlying statistical assumptions, an examination of the structure of the model by considering formulations that have fewer, more or different explanatory variables, or a study of subgroups of observations, looking for those that are either poorly represented by the model (outliers) or that have a relatively large effect on the regression model's predictions.

A regression diagnostic may take the form of a graphical result, informal quantitative results or a formal statistical hypothesis test,[2] each of which provides guidance for further stages of a regression analysis.


Regression diagnostics have often been developed or were initially proposed in the context of linear regression or, more particularly, ordinary least squares. This means that many formally defined diagnostics are only available for these contexts.

Assessing assumptions

Distribution of model errors
Correlation of model errors

Assessing model structure

Adequacy of existing explanatory variables
Adding or dropping explanatory variables
Change of model structure between groups of observations
Comparing model structures

Important groups of observations

Influential observations


  1. Everitt, B.S. (2002) The Cambridge Dictionary of Statistics, CUP. ISBN 0-521-81099-X (entry for Regression diagnostics)
  2. Dodge, Y. (2003) The Oxford Dictionary of Statistical Terms, OUP. ISBN 0-19-920613-9
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