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Synonym: Root Mean Square Error (RMSE) = Root Mean Square Deviation (RMSD)
A square root of Mean Square Error (MSE) between number characterising the model prediction quality ( goodness of fit ) between the datasets of a given variable 𝑥 and its estimator 𝑥̂ :
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RMSD(x, \hat x) = \sqrt{MSE(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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| Mean Square Error (MSE) |
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The RMSD is a square root of Mean Square Error (MSE) between the datasets of a given variable and its estimator :
The key benefit of using RMSD instead of MSE is that it is expressed in the same units as the base property () 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
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