The variance inflation factor for the 
th explanatory variable in a multiple regression is
 |
where 
is the coefficient of determination
obtained by regressing that variable on all the other
explanatory variables. It is the factor by which the
variance of the estimated 
th regression coefficient
exceeds the value it would have if that variable were
uncorrelated with the other explanatory variables, with
the remaining scale quantities held fixed. Large values therefore diagnose multicollinearity
involving that variable.
