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I was wondering if it's possible to calculate one (global) coefficient of determination for multiple regression models.

Context: I've set up a batch regression process which generates sales predictions for a sample of SKUs. Each SKU forecast is produced using it's own dataset. The dependent variable is the same for all models, while independent variables may vary since I incorporate a stepwise process to find the final model for each SKU. I can report on each model's individual r^2 easily, I was wondering if it's possible to calculate one global metric instead.

Disclaimer: I'm not an expert here, so feel free to let me know if this is not possible. If more details are required, just comment and I'll modify the post.

kjetil b halvorsen
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macsmith
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    What is this "global metric" intended to represent?? – whuber Feb 25 '20 at 15:42
  • @whuber A global r^2 for all the models, so I could communicate to stakeholders that the system produced an r^2 in training of x%. – macsmith Feb 25 '20 at 16:08
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    Are you saying you are viewing the collection of models as if it were a *single* model? There are ways to do that, but to give you a sense of how problematic $R^2$ might be for your purpose, please see my example at https://stats.stackexchange.com/a/13317/919, which shows how the $R^2$ of the union of datasets can be totally different than the $R^2$ of any of the individual datasets. – whuber Feb 25 '20 at 16:13
  • @whuber The collection of models are derived from subsets of a larger dataset. I see your point about the difference in r^2 between totals and subsets of data. – macsmith Feb 25 '20 at 16:30

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