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# Table 2 Some equations and parameters used for the model validation

Parameter | Equation | Eq | Significance | Threshold value |
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Friedman Lack-Of-Fit (LOF) | \({\text{LOF}} = \frac{{{\text{SEE}}}}{{\left( {1 - \frac{c + d \times p}{M}} \right)^{2} }}\) \({\text{SEE}} = \sqrt {\frac{{\left( {Y_{\exp } - Y_{{{\text{pred}}}} } \right)^{2} }}{N - P - 1}}\) | 4 | Allows for the best fitness score to be obtained | – |

Correlation coefficient ( | \(R^{2} = 1 - \left[ {\frac{{\sum \left( {Y_{\exp } - Y_{{{\text{pred}}}} } \right)^{2} }}{{\sum \left( {Y_{\exp } - \overline{Y}_{{{\text{training}}}} } \right)^{2} }}} \right]\) | 5 | Measures the degree of fitness of the regression equation | ≥ 0.6 |

Adjusted | \(R_{{{\text{adj}}}}^{2} = \frac{{R^{2} - p\left( {n - 1} \right)}}{n - p + 1}\) | 6 | Ensures model’s stability and reliability | ≥ 0.5 |

Cross-validation regression coefficient ( | \(Q_{{{\text{cv}}}}^{2} = 1 - \left[ {\frac{{\sum \left( {Y_{{{\text{pred}}}} - Y_{\exp } } \right)^{2} }}{{\sum (Y_{\exp } - \overline{Y}_{{{\text{training}}}} )^{2} }}} \right]\) | 7 | Indicates a high internal predictive power | ≥ 0.5 |

The coefficient of determination (\(cR_{{\text{p}}}^{2}\)) of Y-Randomization | \(cR_{{\text{p}}}^{2} = R X [R^{2} - \left( {R_{r} } \right)^{2} ]^{2}\) | 8 | This is for a confirmation that the QSAR model built is strong and not created by chance | \(cR_{{\text{p}}}^{2}\) > 0.50 |

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Predicted | \(R_{{{\text{test}}}}^{2} = 1 - \frac{{\sum \left( {Y{\text{pred}}_{{{\text{test}}}} - Y\exp_{{{\text{test}}}} } \right)^{2} }}{{\sum \left( {Y{\text{pred}}_{{{\text{test}}}} - \overline{Y}_{{{\text{training}}}} } \right)^{2} }}\) | 9 | Measures the ability of the model to predict activity values of external set of compounds | ≥ 0.6 |

Golbraikh and Tropsha acceptable model criteria | \(\left| {r_{o}^{2} - r_{o}^{^{\prime}2} } \right|\) \(\left| {r^{2} - \frac{{r_{o}^{{{^{\prime}}2}} }}{{r^{2} }}} \right|\)
| – | Assess the robustness and stability of the model | < 0.3 < 0.1 0.85 ≤ k′ ≤ 1.15 |