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R^2 = 1 - \frac{MSE(x, \hat x)}{MSE(x, \bar x)}, \quad 0 \leq R^2 \leq 1 |
where
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| body | x = \{ x_1, \, x_2, \, x_3 , ... x_N \} |
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| a observed variable represented by a discrete data set of 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 set 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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| 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 a variable and its predictor |
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| mean square error between a variable and its mean value |
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The coefficient of determination
normally ranges between :
- 0, indicating a course fit, trending to the mean average that prediction error is within the variance of the observed variable around its mean value
and
- 1, indicating a fine fit, fairly reproducing the variability of the
The Negative
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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Statistics
[ Mean Square Error (MSE) ]
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