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

  • collinearity
  • spurious variable
  • homoscedasticity

(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

  • collinearity
  • spurious variable
  • homoscedasticity

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.
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