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Table 2 Statistical criteria for model selection applied to biomass estimation of different woody species indigenous of the Tropical Atlantic Rain Forest, Brazil

From: Selection criteria for linear regression models to estimate individual tree biomasses in the Atlantic Rain Forest, Brazil

  Criterion Formula
1 Sum of squares of the residuals \( SSR = \sum\limits_{i - 1}^{n} {e_{i}^{2} } = \sum\limits_{i - 1}^{n} {(w_{i} - \hat{w}_{i} )^{2} } \) (7)
2 Adjusted coefficient of determination \( R^{2}_{adj.} = 1 - \frac{(n - 1)}{(n - p)}(1 - R^{2} ) \)
where \( R^{2} = 1 - \frac{{\sum\nolimits_{i - 1}^{n} {e_{i}^{2} } }}{{\sum\nolimits_{i - 1}^{n} {(w_{i} - \bar{w})^{2} } }} \)
(8)
3 Relative standard error of the estimate \( Syx\% = \frac{syx}{{\bar{y}}}100 \)
where \( Syx = \sqrt {\frac{{\sum\nolimits_{i - 1}^{n} {e_{i}^{2} } }}{n - p}} \)
(10)
4 Akaike information criterion [20] \( AIC = - 2n\left( {\frac{ - n}{2}\ln \left( {\frac{1}{n}\sum\limits_{i - 1}^{n} {e_{i}^{2} } } \right)} \right) + 2p \) (11)
5 Akaike information criterion not biased for small samplesa, when (n/p) < 40 \( AIC_{c} = - 2n\left( {\frac{ - n}{2}\ln \left( {\frac{1}{n}\sum\limits_{i - 1}^{n} {e_{i}^{2} } } \right)} \right) + 2p\frac{n}{(n - p - 1)} \) (12)
6 Schwartz’s information criterion [21] \( BIC = - 2n\left( {\frac{ - n}{2}\ln \left( {\frac{1}{n}\sum\limits_{i - 1}^{n} {e_{i}^{2} } } \right)} \right) + \ln (n)p \) (13)
7 Residuals (in %) \( r_{i} = \frac{{(w_{i} - \hat{w}_{i} )}}{{w_{i} }}100 \) (14)
  1. \( \hat{w}_{i} \) = estimated biomass. wi = actual biomass. In AIC, AICc and BICp must be increased by 1, which refers to one degree of freedom for variance
  2. aAccording to [11]. Where n = number of data; p = number of parameters of the model (number of coefficients including the intercept + 1)
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