Nice paradoxical example here by Andrew Gelman of R^2 = 0.01 for a strong linear predictor.

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is there a ref (book or paper) for using the ratio of R2’s or it’s just common sense? It’s intuitive but i might be required to provide a reference and i don’t see it in RMS eg section 4.7.1 on ‘redundancy analysis’, or in the tutorial on ‘multivariable prognostic models’ in stats in medicine 1996. thanks

I’m sure ratios of R^2 or the equivalent regression sum of squares has been written up; I just don’t know where. It’s so easy to define—fraction of explainable variation in Y that was explained by a subset of the predictors.

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