Multicollinearity (in Regression Analysis)

In a regression analysis, multicollinearity occurs when two or more predictor variables (independent variables) show a high correlation. This leads to the fact that the regression coefficients are unstable and can no longer be interpreted.

To avoid multicollinearity, there must be no linear dependence between the predictors; this is the case, for example, when one variable is the multiple of another variable. In this case, since the variables are perfectly correlated, one variable explains 100% of the other variable and there is no added value in taking both variables in a regression model. If there is no correlation between the independent variables, then there is no multicollinearity.

In reality, a perfect linear correlation hardly ever occurs, which is why we speak of multicollinearity when individual variables are highly correlated with each other, in which case the effect of individual variables cannot be clearly separated from each other.

It should be noted that the regression coefficients can no longer be interpreted in a meaningful way, but the prediction with the regression model is possible.

Multicollinearity test
To find out whether multicollinearity is present, the tolerance of the individual predictors is considered. Another measure of multicollinearity is the VIF (Variance Inflation Factor).

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Regression Analysis: An introduction to Linear and Logistic Regression
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Simple and Multiple Linear Regression
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Assumptions of Linear Regression
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Logistic Regression: An Introduction
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Dummy Variables in Multiple Regression
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Regression with categorical independent variables
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Multicollinearity
   • Multicollinearity (in Regression Analysis)  
Causality, Correlation and Regression
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