加载数据完成4 Hill 模型拟合
4.1 加载数据
4.2 模型定义
Hill 吸附等温线模型：
\[Q_e = \frac{a \cdot C_e^b}{c^b + C_e^b}\]
其中： - \(Q_e\)：平衡吸附量 (mg/g) - \(C_e\)：平衡浓度 (mg/L) - \(a\)：最大吸附量 (Qmax) - \(b\)：Hill 系数（协同性指标） - \(c\)：半饱和浓度
4.3 批量拟合
成功拟合的 Hill 模型数量： 12 4.4 提取参数
| term | estimate | std.error | statistic | p.value | model | AIC |
|---|---|---|---|---|---|---|
| a | 8.0038762 | 0.7200401 | 11.115875 | 0.0000000 | MSP550.Cd | 76.52788 |
| b | 1.4287481 | 0.3642669 | 3.922256 | 0.0007823 | MSP550.Cd | 76.52788 |
| c | 2.5665532 | 0.5982800 | 4.289886 | 0.0003249 | MSP550.Cd | 76.52788 |
| a | 19.2470357 | 1.3350737 | 14.416460 | 0.0000000 | OSR550.Cd | 119.09724 |
| b | 3.0353059 | 0.8659666 | 3.505108 | 0.0021068 | OSR550.Cd | 119.09724 |
| c | 0.7139736 | 0.0616499 | 11.581092 | 0.0000000 | OSR550.Cd | 119.09724 |
| a | 20.5042393 | 0.5390578 | 38.037184 | 0.0000000 | OSR700.Cd | 79.58973 |
| b | 6.4295712 | 0.6163833 | 10.431125 | 0.0000000 | OSR700.Cd | 79.58973 |
| c | 0.3350948 | 0.0056165 | 59.662223 | 0.0000000 | OSR700.Cd | 79.58973 |
| a | 18.3108051 | 1.1382199 | 16.087230 | 0.0000000 | WSP550.Cd | 111.44485 |
| b | 6.2979755 | 1.8118992 | 3.475897 | 0.0022570 | WSP550.Cd | 111.44485 |
| c | 1.5353873 | 0.0593481 | 25.870893 | 0.0000000 | WSP550.Cd | 111.44485 |
| a | 41.1812272 | 8.0386367 | 5.122912 | 0.0000449 | MSP550.Pb | 157.14994 |
| b | 0.6617788 | 0.2010828 | 3.291075 | 0.0034816 | MSP550.Pb | 157.14994 |
| c | 1.3904100 | 1.2357966 | 1.125112 | 0.2732370 | MSP550.Pb | 157.14994 |
| a | 46.3375991 | 4.0909387 | 11.326887 | 0.0000000 | OSR550.Pb | 167.40250 |
| b | 2.7074090 | 0.6668066 | 4.060261 | 0.0005626 | OSR550.Pb | 167.40250 |
| c | 0.2195488 | 0.0286679 | 7.658353 | 0.0000002 | OSR550.Pb | 167.40250 |
| a | 55.5964829 | 1.4609837 | 38.054144 | 0.0000000 | OSR700.Pb | 150.23208 |
| b | 3.1925942 | 0.3172106 | 10.064589 | 0.0000000 | OSR700.Pb | 150.23208 |
| c | 0.1371422 | 0.0053845 | 25.469577 | 0.0000000 | OSR700.Pb | 150.23208 |
| a | 42.4195992 | 2.7891334 | 15.208882 | 0.0000000 | WSP550.Pb | 174.70681 |
| b | 2.0984723 | 0.5419719 | 3.871921 | 0.0007278 | WSP550.Pb | 174.70681 |
| c | 0.1882348 | 0.0283675 | 6.635580 | 0.0000007 | WSP550.Pb | 174.70681 |
| a | 3.2975458 | 0.3072202 | 10.733492 | 0.0000000 | MSP550.Zn | 56.46378 |
| b | 0.9247301 | 0.4849506 | 1.906854 | 0.0703138 | MSP550.Zn | 56.46378 |
| c | 0.1077068 | 0.0604857 | 1.780700 | 0.0894344 | MSP550.Zn | 56.46378 |
| a | 8.5814960 | 0.2958041 | 29.010738 | 0.0000000 | OSR550.Zn | 58.29593 |
| b | 1.6328404 | 0.2274833 | 7.177846 | 0.0000004 | OSR550.Zn | 58.29593 |
| c | 0.0684596 | 0.0088296 | 7.753425 | 0.0000001 | OSR550.Zn | 58.29593 |
| a | 10.7458416 | 0.4229413 | 25.407408 | 0.0000000 | OSR700.Zn | 74.83078 |
| b | 4.0051805 | 0.5739579 | 6.978179 | 0.0000007 | OSR700.Zn | 74.83078 |
| c | 0.0454366 | 0.0024306 | 18.693380 | 0.0000000 | OSR700.Zn | 74.83078 |
| a | 6.1890590 | 0.6251819 | 9.899612 | 0.0000000 | WSP550.Zn | 94.71990 |
| b | 3.7048709 | 1.2920266 | 2.867488 | 0.0092181 | WSP550.Zn | 94.71990 |
| c | 0.0344481 | 0.0044329 | 7.771001 | 0.0000001 | WSP550.Zn | 94.71990 |
4.5 模型比较（AIC）
| Biochar.Metal | AIC_Langmuir | AIC_Hill | Delta_AIC | Better | |
|---|---|---|---|---|---|
| MSP550.Cd | MSP550.Cd | 76.99019 | 76.52788 | -0.4623153 | Hill |
| OSR550.Cd | OSR550.Cd | 131.95024 | 119.09724 | -12.8530029 | Hill |
| OSR700.Cd | OSR700.Cd | 145.80662 | 79.58973 | -66.2168895 | Hill |
| WSP550.Cd | WSP550.Cd | 125.14517 | 111.44485 | -13.7003226 | Hill |
| MSP550.Pb | MSP550.Pb | 157.76040 | 157.14994 | -0.6104548 | Hill |
| OSR550.Pb | OSR550.Pb | 175.85644 | 167.40250 | -8.4539465 | Hill |
| OSR700.Pb | OSR700.Pb | 195.78422 | 150.23208 | -45.5521407 | Hill |
| WSP550.Pb | WSP550.Pb | 183.26278 | 174.70681 | -8.5559694 | Hill |
| MSP550.Zn | MSP550.Zn | 54.48690 | 56.46378 | 1.9768824 | Langmuir |
| OSR550.Zn | OSR550.Zn | 67.43911 | 58.29593 | -9.1431740 | Hill |
| OSR700.Zn | OSR700.Zn | 100.98682 | 74.83078 | -26.1560454 | Hill |
| WSP550.Zn | WSP550.Zn | 101.68844 | 94.71990 | -6.9685356 | Hill |
4.6 拟合曲线
4.7 残差诊断
4.8 保存结果
Hill 模型结果已保存