Table 7 Mathematical expressions given by EPR.

From: Enhancement of groundwater resources quality prediction by machine learning models on the basis of an improved DRASTIC method

Model. no

Formulations

MSE

Model#1

\(\begin{aligned} NVI = & \left( {4.2744{ } \times {ln}\left( {LU^{{0.5}} } \right)} \right) + \left( {7.5974{ }C_{r}^{{0.5}} { }LU^{{1.5}} } \right) \\ & \quad + \left( {0.58939{ }C_{r} \times \ln \left( {C_{r}^{{0.5}} } \right)} \right) + \left( {3.4229{ }S_{r}^{{0.5}} LU \times \ln \left( {R_{r}^{2} } \right)} \right) \\ & \quad + \left( {20.0097{ }A_{r}^{{0.5}} LU \times \ln \left( {I_{r}^{{0.5}} } \right)} \right) + \left( {4.6166{ }D_{r}^{{0.5}} T_{r}^{{0.5}} LU} \right) + 5.166 \\ \end{aligned}\)

0.123

Model#2

\(\begin{aligned} NVI = & \left( {0.51714{ } \times {ln}\left( {C_{r} } \right)} \right) + \left( {3.0519{ }C_{r}^{{0.5}} { }LU^{{1.5}} \times \ln \left( {C_{r} } \right)} \right) \\ & \quad + \left( {6.491{ }T_{r} ^{{0.5}} LU} \right) + \left( {3.4285{ }S_{r}^{{0.5}} LU \times \ln \left( {R_{r}^{2} } \right)} \right) \\ & \quad + \left( {22.1852{ }A_{r}^{{0.5}} LU \times \ln \left( {I_{r}^{{0.5}} } \right)} \right) + \left( {26.2349\frac{{D_{r} \times LU}}{{I_{r}^{{1.5}} }}} \right) + 0 \\ \end{aligned}\)

0.089

Model#3

\(\begin{aligned} NVI = & \left( {0.5473 \times ln\left( {C_{r} } \right)} \right) + \left( {2.411C_{r}^{{0.5}} LU^{{1.5}} \times \ln \left( {I_{r}^{{0.5}} \times C_{r} } \right)} \right) \\ & \quad + \left( {6.2099T_{r}^{{0.5}} LU} \right) + \left( {3.4313S_{r}^{{0.5}} LU \times \ln \left( {R_{r}^{2} } \right)} \right) \\ & \quad + \left( {21.5222A_{r}^{{0.5}} LU \times \ln \left( {I_{r}^{{0.5}} } \right)} \right) + \left( {26.9076\frac{{D_{r} \times LU}}{{I_{r}^{{1.5}} }}} \right) + 0.19457 \\ \end{aligned}\)

0.080

Model#4

\(\begin{aligned} NVI = & \left( {{2}{.4808 }C_{r}^{{0.5}} LU^{{1.5}} \times \ln \left( {I_{r}^{{0.5}} \times C_{r} } \right)} \right) + \left( {6.1836T_{r} ^{{0.5}} LU} \right) \\ & \quad + \left( {3.3946{ }S_{r}^{{0.5}} LU \times \ln \left( {R_{r}^{2} } \right)} \right) + \left( {10.7933{ }A_{r}^{{0.5}} LU \times \ln \left( {I_{r} } \right)} \right) \\ & \quad + \left( {0.13577{ }R_{r} \times \ln \left( {C_{r} } \right)} \right) + \left( {27.139\frac{{D_{r} \times LU}}{{I_{r}^{{1.5}} }}} \right) + 0.21202 \\ \end{aligned}\)

0.071

Model#5

\(\begin{aligned} NVI = & \left( {{2}{.3201 }C_{r}^{{0.5}} LU^{{1.5}} \times \ln \left( {I_{r}^{{0.5}} \times C_{r} } \right)} \right) + \left( {6.0645{ }T_{r} ^{{0.5}} LU} \right) \\ & \quad + \left( {3.3586{ }S_{r}^{{0.5}} LU \times \ln \left( {R_{r}^{2} } \right)} \right) + \left( {10.9199{ }A_{r}^{{0.5}} LU \times \ln \left( {I_{r} } \right)} \right) \\ & \quad + \left( {0.29264R_{r} LU^{{0.5}} \times \ln \left( {C_{r} } \right)} \right) + \left( {27.4567\frac{{D_{r} \times LU}}{{I_{r}^{{1.5}} }}} \right) + 0.24993 \\ \end{aligned}\)

0.069

Model#6

\(\ \begin{aligned} NVI = & \left( {{2}{.3307 }C_{r}^{{0.5}} LU^{{1.5}} \times \ln \left( {I_{r}^{{0.5}} \times C_{r} } \right)} \right) + \left( {6.2175{ }T_{r} ^{{0.5}} LU} \right) \\ & \quad + \left( {3.3575{ }S_{r}^{{0.5}} LU \times \ln \left( {R_{r}^{2} } \right)} \right) + \left( {10.8407{ }A_{r}^{{0.5}} LU \times \ln \left( {I_{r} } \right)} \right) \\ & \quad + \left( {0.2844{ }R_{r} LU^{{0.5}} \times \ln \left( {D_{r}^{{0.5}} \times C_{r} } \right)} \right) + \left( {25.9049\frac{{D_{r} \times LU}}{{I_{r}^{{1.5}} }}} \right) + 0.24597 \\ \end{aligned}\)

0.066

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