What is the distinction between

  • $R^2_{pop}$ – the population R-squared
  • $R^2_{out}$ – the out-of-sample R-squared
  • $R^2_{c.v.}$ – the squared population cross-validity coefficient ?

These objects have been mentioned in earlier posts here, here and here.

I would appreciate an intuitive explanation. Ideally, some counter-examples would illustrate when the differences between these objects matter, and what goes wrong if one is used in place of another.


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