VIF

[stineb]

I don't understand the VIF. @pepaaran , you write: where $R^2_i$ is the coefficient of determination for regressing the i$^{th}$ predictor on the remaining ones. How is R^2 (a scalar) between one and multiple other variables to be understood and calculated?

[pepaaran]

That $R^2$ is defined the usual way. Instead of having the regression $Y ~ X_1 + ... X_n$ , you are using the regression $X_i ~ X1 + ... X{i-1} + X_{i+1} + ... + X_n$. And the coefficient of determination is always computed on the observed vs fitted target. So instead of $Y$ and $\hat{Y}$, it's computed on $X_i$ and $\hat{X_i}$. Does that make sense? Should I add this?