@wikipedia
Synonym: Root Mean Square Error Deviation (RMSERMSD) = Root Mean Square Deviation Error (RMSDRMSE)
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 :
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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 } |
where
| a variable represented by data set |
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| body | \{ x_1, \, x_2, \, x_3 , ... x_N \} |
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| discrete set of numerical samples of variable |
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| body | \{ \hat x_1, \, \hat x_2, \, \hat x_3 , ... \hat x_N \} |
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| discrete set of predictors for the corresponding samples of variable |
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MSE Error MSE
The RMSD is a square root of Mean Square Error Deviation (MSEMSD) between the datasets of a given variable and its estimator :.
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.
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 ]
