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.
The nonlinear regression models using SPSS
| Nonlinear model number . | Nonlinear model name . | Nonlinear model expression . |
|---|---|---|
| 1 | Asymptotic Regression | A1 + A2·exp(A3·x) |
| 2 | Asymptotic Regression | A1 − (A2·(A3^x)) |
| 3 | Density | (A1 + A2·x)^(−1/A3) |
| 4 | Gauss | A1·(1 − A3·exp(−A2·x^2)) |
| 5 | Gompertz | A1·exp(−A2·exp(−A3·x)) |
| 6 | Johnson-Schumacher | A1·exp(−A2/(x + A3)) |
| 7 | Log-Modified | (A1 + A3·x)^A2 |
| 8 | Log-Logistic | A1 − ln(1 + A2·exp(−A3·x)) |
| 9 | 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 number . | Nonlinear model name . | Nonlinear model expression . |
|---|---|---|
| 1 | Asymptotic Regression | A1 + A2·exp(A3·x) |
| 2 | Asymptotic Regression | A1 − (A2·(A3^x)) |
| 3 | Density | (A1 + A2·x)^(−1/A3) |
| 4 | Gauss | A1·(1 − A3·exp(−A2·x^2)) |
| 5 | Gompertz | A1·exp(−A2·exp(−A3·x)) |
| 6 | Johnson-Schumacher | A1·exp(−A2/(x + A3)) |
| 7 | Log-Modified | (A1 + A3·x)^A2 |
| 8 | Log-Logistic | A1 − ln(1 + A2·exp(−A3·x)) |
| 9 | 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) |