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I have a regression problem and I am in doubt about how I can calculate RMSE in my life-cycle.

I deal with time-series and for every prediction, I want to look N points in the future. It is apparent how to calculate RMSE for a single iteration. My question is how to calculate RMSE for N predictions of N points to get a meaningful prediction performance metric.

I guess, I can average RMSE of all iterations though as I said I am not sure at all if this would reflect actual performance.

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The natural choice would be the total squared error across the N predicted values, averaged across all examples. This is the simple extension of mean squared error from the univariate case. If you're using multivariate linear regression, this is in fact what you want to optimize in order to get the maximum likelihood estimate of the parameters as well.

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  • $\begingroup$ Ok. How can we prove it? What if we average every corresponding point from all examples? i.e average all first predicted points together, so forth, then average of all N points. $\endgroup$ – Anonymous programmer Aug 15 '16 at 4:31
  • $\begingroup$ Prove what, that minimizing squared error leads to the MLE? I think most texts or online resources can explain that best; it's not something to show in a comment. What would averaging do that you're not already doing by computing root-mean-squared-error? or, what are you objecting to there? $\endgroup$ – Sean Owen Aug 15 '16 at 9:20

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