指数回归
对输入的分布表进行e指数回归分析并绘制图表。
指数回归:y=AeBx
相关系数r的解读
0.7<|r|≦1 相关性强
0.4<|r|<0.7 相关性中等
0.2<|r|<0.4 相关性弱
0≦|r|<0.2 无相关性0-1:\normalsize\ e{\tiny -}Exponential\ regression\\
(1)\ mean:\ \bar{x}={\large \frac{{\small \sum}{x_i}}{n}},\hspace{10px}\overline{\ln y}={\large \frac{{\small \sum}{\ln y_i}}{n}}\\
(2)\ trend\ line:\ y=Ae^{Bx},\hspace{10px} B={\large\frac{Sxy}{Sxx}},\hspace{10px} A=\exp({\overline{\ln y}-B\bar{x}})\\
\\
(3)\ correlation\ coefficient:\ r=\frac{\normalsize S_{xy}}{\normalsize \sqrt{S_{xx}}\sqrt{S_{yy}}}\\
\hspace{20px}S_{xx}={{\small \sum}(x_i-\bar{x})^2}={{\small \sum} x_i^2}- n \cdot \bar{x}^2\\
\hspace{20px}S_{yy}={{\small \sum}(\ln y_i-\overline{\ln y})^2}={{\small \sum} \ln y_i^2}- n \cdot \overline{\ln
y}^2\\
\hspace{20px}S_{xy}={{\small \sum}(x_i-\bar{x})(\ln y_i-\overline{\ln y})}={{\small \sum} x_i \ln y_i}- n \cdo
0.7<|r|≦1 相关性强
0.4<|r|<0.7 相关性中等
0.2<|r|<0.4 相关性弱
0≦|r|<0.2 无相关性0-1:\normalsize\ e{\tiny -}Exponential\ regression\\
(1)\ mean:\ \bar{x}={\large \frac{{\small \sum}{x_i}}{n}},\hspace{10px}\overline{\ln y}={\large \frac{{\small \sum}{\ln y_i}}{n}}\\
(2)\ trend\ line:\ y=Ae^{Bx},\hspace{10px} B={\large\frac{Sxy}{Sxx}},\hspace{10px} A=\exp({\overline{\ln y}-B\bar{x}})\\
\\
(3)\ correlation\ coefficient:\ r=\frac{\normalsize S_{xy}}{\normalsize \sqrt{S_{xx}}\sqrt{S_{yy}}}\\
\hspace{20px}S_{xx}={{\small \sum}(x_i-\bar{x})^2}={{\small \sum} x_i^2}- n \cdot \bar{x}^2\\
\hspace{20px}S_{yy}={{\small \sum}(\ln y_i-\overline{\ln y})^2}={{\small \sum} \ln y_i^2}- n \cdot \overline{\ln
y}^2\\
\hspace{20px}S_{xy}={{\small \sum}(x_i-\bar{x})(\ln y_i-\overline{\ln y})}={{\small \sum} x_i \ln y_i}- n \cdo
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