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{{Unreferenced|date=February 2007}}
In [[statistics]], the '''fraction of variance unexplained''' (or '''FVU''') in the context of a [[Regression analysis|regression task]] is the amount of variance of the [[
For a more general definition of explained/unexplained variation/randomness/variance, see the article [[explained variation]].
==Formal definition==
Given a regression function ''f''(·) yielding for each ''y<sub>i</sub>'', <math>1\leq i\leq N</math>, an estimate <math>\widehat{y}_i = f(x_i)</math>, we have:
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==Explanation==
It is useful to consider the second definition to get the idea behind FVU. When trying to predict ''Y'', the most naïve regression function that we can think of is the constant function predicting the mean of ''Y'', i.e., <math>f(x_i)=\bar{y}</math>. It follows that the MSE of this function equals the variance of ''Y''; that is, ''SS<sub>E</sub>'' = ''SS<sub>T</sub>'', and ''SS<sub>R</sub>'' = 0. In this case, the variations in ''Y'' cannot be accounted for, and the FVU then has its maximum value of 1.
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==See also==
* [[Coefficient of determination]]
* [[Correlation]]
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* [[Linear regression]]
{{DEFAULTSORT:Fraction Of Variance Unexplained}}
[[Category:Estimation theory]]
[[Category:Parametric statistics]]
[[Category:Regression analysis]]
[[Category:Statistical ratios]]
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