@wikipedia
A real number characterising the real-value model prediction quality ( goodness of fit ):
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R^2 = 1 - \frac{MSEMSD(x, \hat x)}{MSEMSD(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 data set of 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 data setdiscrete 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 error between deviation between a variable and its predictor |
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| mean square errordeviation between a variable and its mean value |
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It is similar to to Mean Square Error Deviation (MSEMSD) but quantifies the model prediction efficiency in normalized way which sometimes is normally more suitable for computationsassessment goodness of fit.
The coefficient of determination
normally ranges between :
...
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
Statistics
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Formal science / Mathematics / Statistics / Statistical Metric