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A number characterising the prediction quality ( goodness of fit ):
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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 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 poor fit and 1, indicating a good fit.
See also
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Mean Square Error (MSE)Thje