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I'm a bit confused about when to use RMSE, R2 or Pearsons Correlation Coefficient (Rp). I've read some papers that reported RMSE and Rp and didn't even mention R2, but I also found papers reporting only R2. My doubt is in which kind of problems should I use each of these metrics. By reading these papers I noticed the authors were more concerned about the magnitude of errors and used RMSE and Rp to evaluate the performance.

On the other hand, the papers reporting R2 were more interested in comparing different models to solve a specific problem, for example Xu et al compared the performance of single- and multi-task neural network to predict the binding affinity of molecules on different protein targets using R2 values (https://www.ncbi.nlm.nih.gov/pubmed/28872869).

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  • $\begingroup$ This will depend on your modeling goal. RMSE is similar to "average magnitude of error". R-squared tells you what fraction of the dependent data variance is explained by the model. I have also used "peak magnitude of error" in industrial work to report expected worst-case error. For some industrial work we were interested in the percent errors. $\endgroup$ – James Phillips Jun 17 '19 at 15:55
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A very broad distinction can be made in the following manner:

  1. If one wants to develop models/theories to explain the variation in Y (for example if Y is stock return, and, we want to explain why returns vary across stocks), we often use $R^2$ as a metric for the model performance.
  2. If we are trying to predict Y, we often use $RMSE$ (or $MAPE$) as a metric for model performance.
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