VIF shows how the variance of an estimator is inflated by the presence of multicollinearity. As r|3 approaches 1, the VIF approaches infinity. That is, as the extent of collinearity increases, the variance of an estimator increases, and in the limit it can become infinite. As can be readily seen, if there is no collinearity between X2 and X3, VIF will be 1.
Using this definition, we can express (7.4.12) and (7.4.15) as var(02) =
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