How do you interpret the value of RMSE/MSE in English to stakeholders?

Question

For example, if you have a R^2 of 0.95, you can explain this number to stakeholders in a presentation as:

Our model explains 95% of the total variance within the data.

However, if we have a RMSE of 11, how do you interpret this?

I'm imagining something like "On average, our model's prediction will be incorrect by +/-11 units." Yes I know that lower error = better but that isn't the full explanation of what the number actually means.

And an equivalent interpretation for MSE would be incredibly helpful as well.

Note how easy it is to break the “proportion of variance explained” interpretation of $R^2$ (1) (2). — Dave, Mar 15 '23 at 11:57

score 1 · Accepted Answer · answered Feb 03 '23 at 18:33

I think people have decided to take the root of MSE to make it more interpretable by rescaling it to that of data. And I don't see any problem with your interpretation of on average being wrong by about 11 units. This becomes more sensible when you take into account the range of your data. For example, an RMSE of 11 for predicting people's height in 'mm' could be very good but not satisfactory in 'cm'. Hence, interpreting RMSE and judging how good it is depends on the context of the problem you are trying to solve.

RMSE is not quite a measure of the average absolute deviation, though RMSE does put an upper bound on that value. — Dave, Nov 22 '23 at 20:25

How do you interpret the value of RMSE/MSE in English to stakeholders?

1 Answers1