what is a variance inflation factor vif 
a variance inflation factor vif is a measure of the amount of multicollinearity in regression analysis multicollinearity exists when there is a correlation between multiple independent variables in a multiple regression model this can adversely affect the regression results thus the variance inflation factor can estimate how much the variance of a regression coefficient is inflated due to multicollinearity understanding a variance inflation factor vif a variance inflation factor is a tool to help identify the degree of multicollinearity multiple regression is used when a person wants to test the effect of multiple variables on a particular outcome the dependent variable is the outcome that is being acted upon by the independent variables the inputs into the model multicollinearity exists when there is a linear relationship or correlation between one or more of the independent variables or inputs multicollinearity creates a problem in the multiple regression model because the inputs are all influencing each other therefore they are not actually independent and it is difficult to test how much the combination of the independent variables affects the dependent variable or outcome within the regression model while multicollinearity does not reduce a model s overall predictive power it can produce estimates of the regression coefficients that are not statistically significant in a sense it can be thought of as a kind of double counting in the model in statistical terms a multiple regression model where there is high multicollinearity will make it more difficult to estimate the relationship between each of the independent variables and the dependent variable in other words when two or more independent variables are closely related or measure almost the same thing then the underlying effect that they measure is being accounted for twice or more across the variables when the independent variables are closely related it becomes difficult to say which variable is influencing the dependent variables small changes in the data used or in the structure of the model equation can produce large and erratic changes in the estimated coefficients on the independent variables this is a problem because the goal of many econometric models is to test exactly this sort of statistical relationship between the independent variables and the dependent variable to ensure the model is properly specified and functioning correctly there are tests that can be run for multicollinearity the variance inflation factor is one such measuring tool using variance inflation factors helps to identify the severity of any multicollinearity issues so that the model can be adjusted variance inflation factor measures how much the behavior variance of an independent variable is influenced or inflated by its interaction correlation with the other independent variables variance inflation factors allow a quick measure of how much a variable is contributing to the standard error in the regression when significant multicollinearity issues exist the variance inflation factor will be very large for the variables involved after these variables are identified several approaches can be used to eliminate or combine collinear variables resolving the multicollinearity issue formula and calculation of vifthe formula for vif is vif i 1 1 r i 2 where r i 2 unadjusted coefficient of determination for regressing the ith independent variable on the remaining ones begin aligned text vif i frac 1 1 r i 2 textbf where r i 2 text unadjusted coefficient of determination for text regressing the ith independent variable on the text remaining ones end aligned vifi 1 ri2 1 where ri2 unadjusted coefficient of determination forregressing the ith independent variable on theremaining ones 