Exponential Regression (y = ABˣ)

Interpreting the Correlation Coefficient r
0.7＜|r|≦1 Strong correlation
0.4＜|r|＜0.7 Moderate correlation
　　0.2 < |r| < 0.4 Weak correlation
0 ≤ |r| < 0.2 No correlation

\(\normalsize\ ab{\tiny -}Exponential\ regression\\ (1)\ mean:\ \bar{x}={\large \frac{{\small \sum}{x_i}}{n}},\hspace{10px}\overline{\ln y}={\large \frac{{\small \sum}{\ln y_i}}{n}}\\ (2)\ trend\ line:\ y=AB^x,\hspace{10px} B=\exp({\normalsize \frac{Sxy}{Sxx}}),\hspace{10px} A=\exp ({\overline{\ln y}-\bar{x}\ln B})\\ \\ (3)\ correlation\ coefficient:\ r=\frac{\normalsize S_{xy}}{\normalsize \sqrt{S_{xx}}\sqrt{S_{yy}}}\\ \hspace{20px}S_{xx}={{\small \sum}(x_i-\bar{x})^2}={{\small \sum} x_i^2}- n \cdot \bar{x}^2\\ \hspace{20px}S_{yy}={{\small \sum}(\ln y_i-\overline{\ln y})^2}={{\small \sum} \ln y_i^2}- n \cdot \overline{\ln y}^2\\ \hspace{20px}S_{xy}={{\small \sum}(x_i-\bar{x})(\ln y_i-\overline{\ln y})}={{\small \sum} x_i \ln y_i}- n \cdot \bar{x}\overline{\ln y}\\ \)