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The maximum R² (regression coefficient which is the square of correlation coefficient) equal to 0.37 was obtained for total alkalinity with all the parameters as independent variables. Then, nonlinear regressions are performed for all the models shown in Table 1 for all the WQPs. For most nonlinear regression models, a good convergence could not be obtained or estimated in the optimization process. The regression coefficients could be estimated for only the nonlinear model numbers 1 (Asymptotic Regression), 18 (Weibull), 11 (Morgan-Mercer-Florin), and 10 (Michaelis Menten). These are mostly lower than linear regression coefficients and are shown in Tables 4–6.

Table 4

The nonlinear regression results with climate parameters

Parameter	P, T_max, T_min
	R² (of nonlinear model number)
	1	11	18	10
DO (mg/L)	0.00	0.00	0.06	0.08
pH	0.01	0.01	na	0.05
Electrical conductivity (mS/cm)	0.01	0.01	0.05	0.05
BOD (mg/L)	0.01	0.01	na	0.04
COD (mg/L)	0.04	0.03	na	0.12
Nitrate	0.09	0.10	0.04	0.02
Total Coliform (MPN/100 ml)	0.05	0.06	0.02	0.05
Turbidity (NTU)	0.02	0.02	0.00	0.02
Total Alk. (mg/L)	0.00	0.02	0.02	0.04
Chloride (mg/L)	0.00	0.00	0.04	0.05
Hardness (mg/L)	0.00	0.04	0.04	0.04
Calcium (mg/L)	0.04	0.04	na	0.04
Magnesium (mg/L)	na	0.01	0.04	0.05
Sulphate (mg/L)	0.05	0.04	0.03	0.03
Sodium % (mg/L)	0.03	0.12	0.13	0.11
TDS (mg/L)	0.00	0.02	0.05	0.05
TSS (mg/L)	0.00	0.01	0.01	0.02
Total Phosphate (mg/L)	0.00	0.00	0.06	0.06
Potassium (mg/L)	0.01	0.02	0.03	0.03
Fluoride (mg/L)	0.05	0.08	0.02	0.03
Sodium	0.03	0.02	na	0.04
SAR	0.03	0.02	0.03	0.04

Parameter	P, T_max, T_min
	R² (of nonlinear model number)
	1	11	18	10
DO (mg/L)	0.00	0.00	0.06	0.08
pH	0.01	0.01	na	0.05
Electrical conductivity (mS/cm)	0.01	0.01	0.05	0.05
BOD (mg/L)	0.01	0.01	na	0.04
COD (mg/L)	0.04	0.03	na	0.12
Nitrate	0.09	0.10	0.04	0.02
Total Coliform (MPN/100 ml)	0.05	0.06	0.02	0.05
Turbidity (NTU)	0.02	0.02	0.00	0.02
Total Alk. (mg/L)	0.00	0.02	0.02	0.04
Chloride (mg/L)	0.00	0.00	0.04	0.05
Hardness (mg/L)	0.00	0.04	0.04	0.04
Calcium (mg/L)	0.04	0.04	na	0.04
Magnesium (mg/L)	na	0.01	0.04	0.05
Sulphate (mg/L)	0.05	0.04	0.03	0.03
Sodium % (mg/L)	0.03	0.12	0.13	0.11
TDS (mg/L)	0.00	0.02	0.05	0.05
TSS (mg/L)	0.00	0.01	0.01	0.02
Total Phosphate (mg/L)	0.00	0.00	0.06	0.06
Potassium (mg/L)	0.01	0.02	0.03	0.03
Fluoride (mg/L)	0.05	0.08	0.02	0.03
Sodium	0.03	0.02	na	0.04
SAR	0.03	0.02	0.03	0.04

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Table 5

The nonlinear regression results with land use parameters

Parameter	AL, FL, GL, SL, UL
	R² (of nonlinear model number)
	1	11	18	10
DO (mg/L)	0.07	0.14	0.02	0.17
pH	0.00	0.06	0.06	0.41
Electrical conductivity (mS/cm)	0.06	0.06	na	0.41
BOD (mg/L)	0.04	0.11	na	0.05
COD (mg/L)	0.07	0.16	0.00	0.12
Nitrate	0.04	0.05	na	0.16
Total Coliform (MPN/100 ml)	0.01	0.00	0.00	0.13
Turbidity (NTU)	0.01	0.08	0.02	0.06
Total Alk. (mg/L)	0.07	0.02	0.17	0.35
Chloride (mg/L)	0.06	0.02	0.11	0.12
Hardness (mg/L)	0.19	0.01	0.09	0.35
Calcium (mg/L)	0.17	0.00	0.10	0.34
Magnesium (mg/L)	0.07	0.02	0.09	0.25
Sulphate (mg/L)	0.08	0.02	na	0.21
Sodium % (mg/L)	0.01	0.01	0.04	0.22
TDS (mg/L)	0.09	0.02	0.16	0.24
TSS (mg/L)	0.01	0.02	0.01	0.27
Total Phosphate (mg/L)	0.04	0.05	0.08	0.12
Potassium (mg/L)	0.04	0.07	0.07	0.08
Fluoride (mg/L)	0.00	0.01	na	0.17
Sodium	0.05	0.01	0.10	0.12
SAR	0.04	0.01	0.02	0.16

Parameter	AL, FL, GL, SL, UL
	R² (of nonlinear model number)
	1	11	18	10
DO (mg/L)	0.07	0.14	0.02	0.17
pH	0.00	0.06	0.06	0.41
Electrical conductivity (mS/cm)	0.06	0.06	na	0.41
BOD (mg/L)	0.04	0.11	na	0.05
COD (mg/L)	0.07	0.16	0.00	0.12
Nitrate	0.04	0.05	na	0.16
Total Coliform (MPN/100 ml)	0.01	0.00	0.00	0.13
Turbidity (NTU)	0.01	0.08	0.02	0.06
Total Alk. (mg/L)	0.07	0.02	0.17	0.35
Chloride (mg/L)	0.06	0.02	0.11	0.12
Hardness (mg/L)	0.19	0.01	0.09	0.35
Calcium (mg/L)	0.17	0.00	0.10	0.34
Magnesium (mg/L)	0.07	0.02	0.09	0.25
Sulphate (mg/L)	0.08	0.02	na	0.21
Sodium % (mg/L)	0.01	0.01	0.04	0.22
TDS (mg/L)	0.09	0.02	0.16	0.24
TSS (mg/L)	0.01	0.02	0.01	0.27
Total Phosphate (mg/L)	0.04	0.05	0.08	0.12
Potassium (mg/L)	0.04	0.07	0.07	0.08
Fluoride (mg/L)	0.00	0.01	na	0.17
Sodium	0.05	0.01	0.10	0.12
SAR	0.04	0.01	0.02	0.16

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Table 6

The nonlinear regression results with all the parameters

Parameter	P, T_max, T_min, AL, FL, GL, SL, UL
	R² (of nonlinear model number)
	1	11	18	10
DO (mg/L)	0.05	0.04	0.06	0.24
pH	0.01	0.06	0.07	0.45
Electrical conductivity (mS/cm)	0.06	0.01	0.06	0.45
BOD (mg/L)	0.04	0.08	na	0.09
COD (mg/L)	0.09	0.11	0.12	0.22
Nitrate	0.08	0.12	0.11	0.17
Total Coliform (MPN/100 ml)	0.02	0.06	0.07	0.18
Turbidity (NTU)	0.00	0.01	0.01	0.06
Total Alk. (mg/L)	0.16	0.10	0.04	0.38
Chloride (mg/L)	0.01	0.02	0.05	0.16
Hardness (mg/L)	0.17	0.12	0.12	0.37
Calcium (mg/L)	0.07	0.14	0.08	0.37
Magnesium (mg/L)	0.14	0.00	0.04	0.29
Sulphate (mg/L)	0.21	0.11	na	0.23
Sodium % (mg/L)	0.08	0.16	0.16	0.24
TDS (mg/L)	0.17	0.02	0.06	0.28
TSS (mg/L)	0.02	0.00	0.27	0.27
Total Phosphate (mg/L)	0.03	0.02	0.13	0.17
Potassium (mg/L)	0.01	0.01	0.04	0.10
Fluoride (mg/L)	0.01	0.04	0.07	0.19
Sodium	0.11	0.05	0.08	0.15
SAR	0.12	0.06	0.09	0.19

Parameter	P, T_max, T_min, AL, FL, GL, SL, UL
	R² (of nonlinear model number)
	1	11	18	10
DO (mg/L)	0.05	0.04	0.06	0.24
pH	0.01	0.06	0.07	0.45
Electrical conductivity (mS/cm)	0.06	0.01	0.06	0.45
BOD (mg/L)	0.04	0.08	na	0.09
COD (mg/L)	0.09	0.11	0.12	0.22
Nitrate	0.08	0.12	0.11	0.17
Total Coliform (MPN/100 ml)	0.02	0.06	0.07	0.18
Turbidity (NTU)	0.00	0.01	0.01	0.06
Total Alk. (mg/L)	0.16	0.10	0.04	0.38
Chloride (mg/L)	0.01	0.02	0.05	0.16
Hardness (mg/L)	0.17	0.12	0.12	0.37
Calcium (mg/L)	0.07	0.14	0.08	0.37
Magnesium (mg/L)	0.14	0.00	0.04	0.29
Sulphate (mg/L)	0.21	0.11	na	0.23
Sodium % (mg/L)	0.08	0.16	0.16	0.24
TDS (mg/L)	0.17	0.02	0.06	0.28
TSS (mg/L)	0.02	0.00	0.27	0.27
Total Phosphate (mg/L)	0.03	0.02	0.13	0.17
Potassium (mg/L)	0.01	0.01	0.04	0.10
Fluoride (mg/L)	0.01	0.04	0.07	0.19
Sodium	0.11	0.05	0.08	0.15
SAR	0.12	0.06	0.09	0.19

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