HELP - RMSE equivalent to sqrt[(1-R^2)] * SD(y)?

Hi everyone

Can someone mathematically tell me why RMSE is equivalent to this formular (Or have i misunderstood something?):


R^2 is the coefficient of determination and SD(y) is the standart deviation of y.

As stated in this article:

The shortcut rmse formula only applies to linear regression rmse.

I tried to wright detailed answer but the formulas didn’t show as it suppose to.
as R^2 is calculated as in this article:
so if you multiply inside the square root in rmse’s formula by sum(y_i - mean(y))^2 / sum(y_i - mean(y))^2
you should be able to see how they are equal.

Hi Abdelrahman

Thanks I think I figured it out. I also replaced sdev(y) with the formular for standard deviation.
I was able to use calculus to get the formula for RMSE.



Ok thanks

Weird it doesn’t say in the article. The pictures show it though.


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