Multicollinearity

(noun)

a phenomenon in which two or more predictor variables in a multiple regression model are highly correlated, so that the coefficient estimates may change erratically in response to small changes in the model or data

Related Terms

(noun)

Statistical phenomenon in which two or more predictor variables in a multiple regression model are highly correlated, meaning that one can be linearly predicted from the others with a non-trivial degree of accuracy.

Related Terms

Examples of Multicollinearity in the following topics:

  • Some Pitfalls: Estimability, Multicollinearity, and Extrapolation

    • Some problems with multiple regression include multicollinearity, variable selection, and improper extrapolation assumptions.
    • In addition, multicollinearity between explanatory variables should always be checked using variance inflation factors and/or matrix correlation plots .
    • Examine how the improper choice of explanatory variables, the presence of multicollinearity between variables, and extrapolation of poor quality can negatively effect the results of a multiple linear regression.

  • Checking the Model and Assumptions

    • Multicollinearity.
    • Paraphrase the assumptions made by multiple regression models of linearity, homoscedasticity, normality, multicollinearity and sample size.

  • Model Assumptions

    • Lack of multicollinearity in the predictors.
    • For standard least squares estimation methods, the design matrix $X$ must have full column rank $p$; otherwise, we have a condition known as multicollinearity in the predictor variables.

  • Least-Squares Regression

    • The OLS estimator is consistent when the regressors are exogenous and there is no perfect multicollinearity.

  • Models with Both Quantitative and Qualitative Variables

    • Test Multicollinearity.