As the value increases, the severity of multicollinearity grows; a common threshold of 5 or 10 signals that the coefficient estimates are too sensitive to minor changes in the model or the data, making them statistically unreliable. Tolerance is the reciprocal of the VIF, calculated as 1 minus the R-squared from the auxiliary regression.
Simplified Variance Inflation Factor Definition Explained
Foundational Mechanics of the Variance Inflation Factor At its core, the variance inflation factor definition is rooted in an auxiliary regression for each predictor in the model. Mathematical Formula and Theoretical Rationale The formal variance inflation factor definition is expressed as 1 / (1 - R²), where R² represents the quality of the collinear relationship.
A VIF of 1 indicates that there is no correlation between the predictor and other variables, meaning the variance is not inflated at all. Practical Implications for Model Building Applying the variance inflation factor definition requires a balance between theoretical purity and empirical necessity.
Variance Inflation Factor Definition Simplified
For a given independent variable, you treat it as the dependent variable and regress it against all other independent variables in the equation. The variance inflation factor definition provides the precise mathematical framework for diagnosing this issue, quantifying how much the variance of an estimated regression coefficient increases due to linear dependencies among predictors.
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