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I was calculating the root mean squared error for a regressive model, and while calculating, its mean squared error (MSE) came out to be less than 1 (>0), and its root (the root mean squared error, RMSE) as obvious came out to be greater than it. What does that mean?
like MSE = 0.0929285270191
and hence, RMSE = 0.894951677992

How do I see it?
Was there any problem in calculation or training of the model?
Is it that MSE is coming out very less that is not likely possible?

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  • $\begingroup$ Martin Kramer in the answers is right. But what is your question, really? I cannot understand it. $\endgroup$ Jan 25, 2017 at 17:56

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Your calculation must be wrong somewhere.

As the name says the RMSE is the square root of the MSE, so for MSE = 0.09 the RMSE would be 0.3. Yours is approximately off by a factor of 3.

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It means that the $MSE$ is less than $1$, which might be spectacular performance, dreadful performance, or somewhere in between, depending on your problem. Performance out of context is fairly meaningless.

That's just how the square root works: $ x\in(0, 1)\implies x < \sqrt{x} $.

Note that the example values you gave are not possible, as the $RMSE$ corresponding to your $MSE = 0.0929285270191$ would be $RMSE=\sqrt{0.0929285270191}\approx 0.305$, though I think you just picked two numbers arbitrarily that satisfy $MSE < RMSE$.

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