Table 2 Model parameters, formula, threshold values, and models scores

\(R^{2}\)

\(\frac{{\left[ {\sum \left\{ {\left( {Y_{{{\text{obs}}}} - \overline{Y}_{{{\text{obs}}}} } \right) \times \left( {Y_{{{\text{pred}}}} - \overline{Y}_{{{\text{pred}}}} } \right)} \right\}} \right]^{2} }}{{\sum \left( {Y_{{{\text{obs}}}} - \overline{Y}_{{{\text{obs}}}} } \right)^{2} \times \sum \left( {Y_{{{\text{pred}}}} - \overline{Y}_{{{\text{pred}}}} } \right)^{2} }}\)

\(R^{2} >\) 0.6

\(R_{{{\text{adj}}}}^{2}\)

\(\frac{{\left( {N - 1} \right) \times R^{2} - P}}{N - 1 - P}\)

\(R_{{{\text{adj}}}}^{2} >\) 0.6

\(R_{{{\text{pr}}}}^{2}\)

\(1 - \frac{{\sum \left( {y_{{{\text{exp}}\left( {{\text{Test}}} \right)}} - y_{{{\text{est}}\left( {{\text{Test}}} \right)}} } \right)^{2} }}{{\sum \left( {y_{{{\text{exp}}\left( {{\text{Test}}} \right)}} - \overline{y}_{{{\text{Training}}}} } \right)^{2} }}\)

\(R_{{{\text{pr}}}}^{2} > 0.6\)

\(Q^{2}\)

\(1 - \frac{{\mathop \sum \nolimits_{i = 1}^{n} \left( {Y_{{{\text{exp}}}} - Y_{{{\text{pred}}}} } \right)^{2} }}{{\mathop \sum \nolimits_{i = 1}^{n} \left( {Y_{{{\text{exp}}}} - Y} \right)^{2} }}\)

\(Q^{2} > 0.6\)

F

\(\frac{{\sum \left( {Y_{{{\text{pred}}}} - \overline{Y}_{{{\text{obs}}}} } \right)^{2} }}{{\sum \left( {Y_{{{\text{obs}}}} - Y_{{{\text{pred}}}} } \right)^{2} }} \times \frac{N - P - 1}{P}\)

F > 0.33

SEE

Standard Error of Estimate

Smaller the better

MAE

Mean Average Error

Smaller the better

\(R_{{\text{r}}}\)

An average of the correlation coefficient for randomized data

\(R_{{\text{r}}} < 0.5\)

\(R_{{\text{r}}}^{2}\)

An average of determination coefficient for randomized data

\(R_{{\text{r}}}^{2} < 0.5\)

\(^{{\text{c}}} R_{{\text{r}}}^{2}\)

\(R \times \sqrt {R^{2} - R_{{\text{r}}}^{2} }\)

\(^{{\text{c}}} R_{{\text{r}}}^{2} > 0.5\)