Multicollinearity
In statistics, multicollinearity or collinearity is a situation where the predictors in a regression model are linearly dependent.
Perfect multicollinearity refers to a situation where the predictive variables have an exact linear relationship. When there is perfect collinearity, the design matrix has less than full rank, and therefore the moment matrix cannot be inverted. In this situation, the parameter estimates of the regression are not well-defined, as the system of equations has infinitely many solutions.
Imperfect multicollinearity refers to a situation where the predictive variables have a nearly exact linear relationship.
The Gauss–Markov theorem assumes absence of perfect multicollinearity.
The adverse effect of highly correlated variables is widely known and proven many times.12
To address the high collinearity of a dataset, variance inflation factor can be used to identify the collinearity of the predictor variables.
Printed 2026-07-15.
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Footnotes
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Kim, Jong Hae (December 2019). “Multicollinearity and misleading statistical results”. Korean Journal of Anesthesiology. 72 (6): 558–569. doi:10.4097/kja.19087. ISSN 2005-7563. PMC 6900425. PMID 31304696. ↩
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Ellsworth, Susannah G.; van Rossum, Peter S. N.; Mohan, Radhe; Lin, Steven H.; Grassberger, Clemens; Hobbs, Brian (1 December 2023). “Declarations of Independence: How Embedded Multicollinearity Errors Affect Dosimetric and Other Complex Analyses in Radiation Oncology”. International Journal of Radiation Oncology, Biology, Physics. 117 (5): 1054–1062. doi:10.1016/j.ijrobp.2023.06.015. ISSN 1879-355X. PMC 12458133. PMID 37406827. ↩