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If a model predicting 'days to payment etc.' has an RMSE of 25 days and MAE of 20 days. How to explain RMSE of 25 days easily to them, just like the MAE of 20 days (which is average prediction error)

I have looked at various posts, but with no luck. Is there a simple explanation o rmse like the mae to explain to business folks (not an elaborate one). MAE is the average difference in the prediction from the true value.

can we explain RMSE as the 'spread of predictions', or is it 'spread in the errors of the predictions'? By spread I mean standard deviations.

can someone please clarify, spent hours at this already.

Conceptual understanding of root mean squared error and mean bias deviation

Explain Root Mean Square Error to non-technical audience

How to interpret root mean squared error (RMSE) vs standard deviation?

tjt
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    Well, it's the square root of the mean squared error. I'm afraid there is really little more to it. Your second link is a very good answer. Can you indicate what about it is not helpful to you? I don't think you will get much more. – Stephan Kolassa Oct 05 '20 at 04:54
  • I am looking for a simple explanation for rmse as the MAE one. can we say rmse represent the spread in predictions or the spread in prediction errors? – tjt Oct 05 '20 at 05:25
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    Honestly, there is not much to be said about it, than in the links you provided. It is a square root of average squared differences between predictions and the predicted values. It is not spread of the predictions, you could calculate it directly. "Spread" in statistics is ambiguous, but you could say that it is a kind of spread of prediction errors, though this definition would apply to many other error metrics as well. – Tim Oct 05 '20 at 07:06
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    Extremely briefly: MSE is based on squared discrepancies, which may be a better approach in some situations than looking at absolute discrepancies. (Also, MSE = Var + Bias$^2$.) However, MSE has squared units, so looking at RMSE returns to the original units. – BruceET Oct 05 '20 at 08:15
  • @Tim, thanks, by spread I mean standard deviation. So, I guess I can explain it as spread of prediction errors. – tjt Oct 05 '20 at 19:07
  • This question is tagged as duplicate tagging it with a duplicate question I already mentioned in this question. I am looking for a simple and easy way to explain it to business folks not for an elaborate explanation as it was in the another question tagged as duplicate. – tjt Oct 05 '20 at 19:08
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    I am sympathetic, because I like to answer questions like this, but given that the very first answer to the duplicate, "RMSE is a measure of error," is exceptionally simple, you should consider being much more specific about what kind of answer you seek, commenting on the duplicate to encourage more elaborate answers, or offering a bounty on the duplicate (or any combination of these measures). – whuber Oct 05 '20 at 21:49

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