ما معنى Multicollinearity, variance inflation factor؟

Multicollinearity is near-linear dependence among the columns of the design. The variance inflation factor of regressor $j$ is $\mathrm{VIF}_j = 1/(1 - R_j^2)$, with $R_j^2$ the $R^2$ of regressing $x_j$ on the other regressors.