Variation Inflation Factor (VIF) is the ratio of variance of the model to variance of the model with only one independent variable. VIF gives the estimate of volume of multicollinearity in a set of many regression variables.

VIF = Variance of model Variance of model with one independent variable.

The Variance Inflation Factor (VIF) is a measure used in regression analysis to quantify the severity of multicollinearity in a set of predictor variables. Multicollinearity occurs when two or more independent variables in a regression model are highly correlated, which can cause issues with the interpretation of the model coefficients and increase the variance of the coefficient estimates.

The VIF assesses how much the variance of an estimated regression coefficient is inflated due to multicollinearity. Specifically, the VIF for a particular predictor variable is calculated as the ratio of the variance of the coefficient estimate when that variable is included in a regression model to the variance of the coefficient estimate when that variable is excluded from the model.

A high VIF (typically greater than 10) indicates that the variance of the coefficient estimate for that variable is inflated due to multicollinearity, suggesting that the variable may be redundant in the model or that multicollinearity is severe enough to impact the reliability of the coefficient estimates.

In summary, the Variance Inflation Factor is a measure used to detect and quantify multicollinearity in regression analysis, helping analysts and researchers identify potential issues with the regression model.