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) |