What is the difference between RMSE and standard deviation?

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RMSE (Root Mean Square Error) and standard deviation serve different purposes in statistical analysis. Standard deviation measures the variability of a dataset, representing a population parameter, while RMSE assesses the accuracy of a model's predictions, derived from the model's residuals. RMSE can be seen as an estimator of standard deviation when applied to model results. The distinction lies in RMSE being model-specific, whereas standard deviation applies to the entire population. Understanding these differences is crucial for accurate data interpretation in multivariate analysis.
evidenso
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hello
can anyone explain what the difference is between RMSE and standard deviation. I am using RMSE in multivariate analysis but is it just the standard dev. why another name?
 
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It may be a quibble, but sometimes standard deviation means the theoretical value, while RMSE might be used for the value derived from the data. (I could be wrong).
 
evidenso said:
hello
can anyone explain what the difference is between RMSE and standard deviation. I am using RMSE in multivariate analysis but is it just the standard dev. why another name?

If I recall correctly, the standard deviation is an actual population parameter whereas the RMSE is based on a model (e.g. regression analysis). In other words, the RMSE is an estimator of the standard deviation based on your model results. If it is an unbiased estimator, then it will be equal to the standard error.

CS
 
I was reading a Bachelor thesis on Peano Arithmetic (PA). PA has the following axioms (not including the induction schema): $$\begin{align} & (A1) ~~~~ \forall x \neg (x + 1 = 0) \nonumber \\ & (A2) ~~~~ \forall xy (x + 1 =y + 1 \to x = y) \nonumber \\ & (A3) ~~~~ \forall x (x + 0 = x) \nonumber \\ & (A4) ~~~~ \forall xy (x + (y +1) = (x + y ) + 1) \nonumber \\ & (A5) ~~~~ \forall x (x \cdot 0 = 0) \nonumber \\ & (A6) ~~~~ \forall xy (x \cdot (y + 1) = (x \cdot y) + x) \nonumber...
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