How to summarize R-squared of several regressions, one per subject I will explain my question, I have made a study and I have 10 regression (one for each subject). I have a significance for each regression, but in some subjects the value of R-squared is 0.5 and in others really high i.e. >= 0.8. 
I cannot put all the data together and have one regression because the absolute values are different for each subject, therefore, which one is the best way to summarize all the R-squared values? I was thinking to take the mean of all of the r-squared values and report that. But is there a better approach? 
 A: This problem is related to Doddington's Zoo (cf. Introduction to Biometrics by Jain, Ross, Nandakumar), which basically states that no (biometric) method will work equally well for all individuals in a population, but you will always have individuals for which it works better or worse.
Consequently, it would be a good idea to report statistics over the individual results for the subjects that the approach has been tried with in the evaluation. Such could be mean, standard deviation, quantiles, etc. Those reflect the performance variation over individuals, hence give an idea of how likely it might be that the approach just does not work for certain individuals (e.g. if applied in an application scenario), and what good or bad results for such individuals might look like. This is also why such evaluation frequently use leave-subject-out-cross-validation (each partition is composed solely from one individual, hence cross validation is always done on data from an unseen individual) - therefore gives an idea of how the model would perform on data of unseen individuals.
PS: this too is similar to what is frequently done with model selection, where statistics over results for different model types and model parametrizations over partitions are used to decide upon using a particular model type and parametrization. Usually, those too consider more than the average performance (like the performance spread).
A: R-squared values are often over-emphasized relative to what information they actually convey (they are good for choosing among models but otherwise aren't all that informative). If your values fit awkwardly in a table in your results section you could easily include a similar table in an appendix instead. You could also include a range of R-squared values across subjects, though I'm not sure that combining the measure from several independent regressions is appropriate unless you are assessing the model itself (as opposed to using the model to demonstrate something).
Is there a particular reason you want to report the R-squared values, or are you intending to include them only for completeness? If it's the former then how they are presented will depend a lot on what you want to express or explain with the R-squared statistic.
