@wikipedia
A real number characterising the real-value model prediction quality (goodness of fit):
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MSER^2 = 1 - \frac{MSD(x, \hat x)}{MSD(x, \bar x)} = 1 - \frac{1}{n} \sum_{i=1}^n (x_i -\hat \hat x_i)^2}{\sum_i (x_i -\bar x)^2} |
where
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| body | x = \{ x_1, \, x_2, \, x |
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a variable represented by data set | 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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, represented by another discrete dataset of numerical samples, with the same number of samples predicted at the same conditions as the original samples |
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| body | \{ x_1, \, x_2, \, x_3 , ... x_N \} |
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discrete set of numerical samples of | LaTeX Math Inline |
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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 |
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, which can be considered as some sort of extreme predictor with zero variability |
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\{ \hat x_1, \ x_2, \, \hat x_3 , ... \hat x_N \}discrete set of predictors for the corresponding samples of variable
It is similar to Mean Square Deviation (MSD) but quantifies the model prediction efficiency in normalized way which is normally more suitable for assessment goodness of fit.
The coefficient of determination
normally ranges between :- 0, indicating 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
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
...
Formal science / Mathematics / Statistics / Statistical Metric
