A single linear variable and multivariate regression models are developed first for each of the WQPs by treating the mean daily precipitation, maximum and minimum temperatures, urban, forest, agricultural, grass land and shrub land use factors as independent variables. Then nonlinear regression models are developed for each WQP using the model expressions of SPSS given in Table 1. The A1, A2, etc., are the model constants or undetermined coefficients specific to those model expressions. The nonlinear regression models are developed separately for all the climate parameters, land use parameters, and combined climate and land use parameters.

Table 1

The nonlinear regression models using SPSS

Nonlinear model numberNonlinear model nameNonlinear model expression
Asymptotic Regression A1 + A2·exp(A3·x)
Asymptotic Regression A1 − (A2·(A3^x))
Density (A1 + A2·x)^(−1/A3)
Gauss A1·(1 − A3·exp(−A2·x^2))
Gompertz A1·exp(−A2·exp(−A3·x))
Johnson-Schumacher A1·exp(−A2/(x + A3))
Log-Modified (A1 + A3·x)^A2
Log-Logistic A1 − ln(1 + A2·exp(−A3·x))
Metcherlich Law of Diminishing Returns A1 + A2·exp(−A3·x)
10 Michaelis Menten A1·x/(x + A2)
11 Morgan-Mercer-Florin (A1·A2 + A3·x^A4)/(A2 + x^A4)
12 Peal-Reed A1/(1 + A2·exp(−(A3·x + A4·x^2 + A5·x^3)))
13 Ratio of Cubics (A1 + A2·x + A3·x^2 + A4·x^3)/(A5·x^3)
14 Ratio of Quadratics (A1 + A2·x + A3·x^2)/(A4·x^2)
15 Richards A1/((1 + A3·exp(−A2·x))^(1/A4))
16 Verhulst A1/(1 + A3·exp(−A2·x))
17 Von Bertalanffy (A1^(1 − A4) − A2·exp(−A3·x))^(1/(1 − A4))
18 Weibull A1 − A2·exp(−A3·x^A4)
19 Yield Density (A1 + A2·x + A3·x^2)^(−1)
Nonlinear model numberNonlinear model nameNonlinear model expression
Asymptotic Regression A1 + A2·exp(A3·x)
Asymptotic Regression A1 − (A2·(A3^x))
Density (A1 + A2·x)^(−1/A3)
Gauss A1·(1 − A3·exp(−A2·x^2))
Gompertz A1·exp(−A2·exp(−A3·x))
Johnson-Schumacher A1·exp(−A2/(x + A3))
Log-Modified (A1 + A3·x)^A2
Log-Logistic A1 − ln(1 + A2·exp(−A3·x))
Metcherlich Law of Diminishing Returns A1 + A2·exp(−A3·x)
10 Michaelis Menten A1·x/(x + A2)
11 Morgan-Mercer-Florin (A1·A2 + A3·x^A4)/(A2 + x^A4)
12 Peal-Reed A1/(1 + A2·exp(−(A3·x + A4·x^2 + A5·x^3)))
13 Ratio of Cubics (A1 + A2·x + A3·x^2 + A4·x^3)/(A5·x^3)
14 Ratio of Quadratics (A1 + A2·x + A3·x^2)/(A4·x^2)
15 Richards A1/((1 + A3·exp(−A2·x))^(1/A4))
16 Verhulst A1/(1 + A3·exp(−A2·x))
17 Von Bertalanffy (A1^(1 − A4) − A2·exp(−A3·x))^(1/(1 − A4))
18 Weibull A1 − A2·exp(−A3·x^A4)
19 Yield Density (A1 + A2·x + A3·x^2)^(−1)

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