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R^2 = 1 - \frac{MSD(x, \hat x)}{MSD(x, \bar x)} = 1 - \frac{\sum_i (x_i -\hat x_i)^2}{\sum_i (x_i -\bar x)^2} |
where
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| body | x = \{ x_1, \, x_2, \, x_3 , ... x_N \} |
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| observed variable represented by a discrete datasetof numerical samples |
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| body | \hat x = \{ \hat x_1, \, \hat x_2, \, \hat x_3 , ... \hat x_N \} |
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| predictor of variable , represented by another discrete dataset of numerical samples, with the same number of samples predicted at the same conditions as the original samples | LaTeX Math Inline |
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| body | \{ x_1, \, x_2, \, x_3 , ... x_N \} |
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| body | --uriencoded--\bar x = \frac%7B1%7D%7BN%7D \sum_i x_i |
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| mean value of the variable , which can be considered as some sort of extreme predictor with zero variability |
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| mean square deviation between a variable and its predictor |
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The
values falling outside the above range indicate a substantial mismatch between variable
and model prediction
and have a meaning that gap between predicted and actual values is higher than the variance of the actual data.
See also
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Formal science / Mathematics / Statistics / Statistical Metric
