Statistics Dictionary

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Variance Inflation Factor

The variance inflation factor (VIF) is a way to measure the amount of multicollinearity in a set of independent variables. A variance inflation factor is computed for each independent variable, using the following formula:

VIFk = 1 / ( 1 - R2k )

where VIFk is the variance inflation factor for variable k, and R2k is the coefficient of multiple determination for variable k. R2k measures the proportion of variance in variable k that can be accounted for by all of the other independent variables.

In many statistical packages (e.g., SAS, SPSS, Minitab), the variance inflation factor is available as an optional regression output. In MiniTab, for example, the variance inflation factor can be displayed as part of the regression coefficient table.

If VIFk = 1, variable k is not correlated with any other independent variable. As a rule of thumb, multicollinearity is a potential problem for the analysis of regression coefficients when VIFk is greater than 4; and, a serious problem when it is greater than 10. The output above shows a VIF of 2.466, which indicates some multicollinearity but not enough to worry about.

See also:  Multicollinearity and Regression Analysis