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I encountered a lot of references that talk about R squared but I can't understand what the difference is between the R squared in regression of the response on the predictors and the R squared that is mentioned in the image.

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Use all the other variables besides $X_j$ to predict $X_j$, and then we can get an $R^2$ value.

For examples, if your variables are $X_1, X_2, X_3$, we could use $X_2$ and $X_3$ to predict $X_1$ and obtain an $R^2$ value.

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