Frequency-Based Power Regression
Analyzes the entered frequency distribution table using power regression and plots a graph.
Power regression: y=AxB
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
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
| \(\normalsize\ Power\ regression\\ (1)\ mean:\ \overline{\ln x}={\large \frac{{\small \sum}{\ln x_i}}{n}},\hspace{10px}\overline{\ln y}={\large \frac{{\small \sum}{\ln y_i}}{n}},\hspace{10px}n={\small \sum}f_i\\ (2)\ trend\ line:\ y=Ax^B,\hspace{10px} B={\normalsize \frac{Sxy}{Sxx}},\hspace{10px} A=\exp({\overline{\ln y}-B\overline{\ln x}})\\ \\ (3)\ correlation\ coefficient:\ r=\frac{\normalsize S_{xy}}{\normalsize \sqrt{S_{xx}}\sqrt{S_{yy}}}\\ \hspace{20px}S_{xx}={{\small \sum}(\ln x_i-\overline{\ln x})^2 f_i}={{\small \sum} \ln x_i^2 f_i}-n \cdot \overline{\ln x}^2\\ \hspace{20px}S_{yy}={{\small \sum}(\ln y_i-\overline{\ln y})^2 f_i}={{\small \sum} \ln y_i^2 f_i}-n \cdot \overline{\ln y}^2\\ \hspace{20px}S_{xy}={{\small \sum}(\ln x_i-\overline{\ln x})(\ln y_i-\overline{\ln y}) f_i}={{\small \sum} \ln x_i \ln y_i f_i}-n \cdot \overline{\ln x} \hspace{10px} \overline{\ln y}\\ \) |
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