Synonym: Root Mean Square Deviation (RMSD) = Root Mean Square Error (RMSE)
A number characterizing the model prediction quality ( goodness of fit ) between the datasets of a given variable x and its estimator \hat x :
| (1) | RMSD(x, \hat x) = \sqrt{MSE(x, \hat x)} = \sqrt{ \frac{1}{n} \sum_{i=1}^n (x_i - \hat x_i)^2 } |
where
x | a variable represented by data set |
|---|---|
\hat x | estimator of variable x |
\{ x_1, \, x_2, \, x_3 , ... x_N \} | discrete set of numerical samples of variable x |
\{ \hat x_1, \, \hat x_2, \, \hat x_3 , ... \hat x_N \} | discrete set of predictors for the corresponding samples of variable x |
MSE(x, \hat x) | Mean Square Error (MSE) |
The RMSD is a square root of Mean Square Error (MSE) between the datasets of a given variable x and its estimator \hat x.
The key benefit of using RMSD instead of MSE is that it is expressed in the same units as the base property ( x) while MSE is expressed in square units of the base property.
The terms RMSE and RMSD are used in mathematics and engineering interchangeably.
See also
Formal science / Mathematics / Statistics / Mean Square Error (MSE)