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Synonym: Root Mean Square Deviation (RMSD) = Root Mean Square Error (RMSE)
A number characterising Statistical metric characterizing the model prediction quality ( goodness of fit ) between the datasets of a given variable 𝑥variable
and its estimator 𝑥̂ LaTeX Math Inline body x
:LaTeX Math Inline body \hat x
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RMSD(x, \hat x) = \sqrt{MSEMSD(x, \hat x)} = \sqrt{ \frac{1}{n} \sum_{i=1}^n (x_i - \hat x_i)^2 } |
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| a variable represented by data set | ||||||||
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| estimator of variable | ||||||||
| discrete set of numerical samples of variable | ||||||||
| discrete set of predictors for the corresponding samples of variable | ||||||||
| Mean Square Error Deviation (MSEMSD) |
The RMSD is a square root of Mean Square Error Deviation (MSEMSD) between the datasets of a given variable
and its estimator LaTeX Math Inline body x
:.LaTeX Math Inline body \hat x
The key benefit of using RMSD instead of MSE is MSD is that it is expressed in the same units as the base property (
) while MSE is MSD is expressed in square units of the base property.LaTeX Math Inline body x
The terms RMSD and RMSE and RMSD are used in mathematics and engineering interchangeably.
See also
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Human / Science / Formal Science / System / Model / Model Validation / Goodness of fit
[ Mathematics / Statistics / Mean Square Error (MSE) Statistical Metric ]
[ Natural Science ]