Log-frequency regression
This program analyzes the entered frequency distribution table using logistic regression and plots a graph.
Logarithmic regression: y = A + B ln(x)
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 correlation0-1:\normalsize\ Logarithmic\ regression\\
(1)\ mean:\ \overline{\ln x}={\large \frac{{\small \sum}{\ln x_i}}{n}},\hspace{10px}\bar{y}={\large \frac{{\small \sum}{y_i}}{n}},\hspace{10px}n={\small \sum}f_i\\
(2)\ trend\ line:\ y=A+B \ln x,\hspace{10px} B={\large\frac{Sxy}{Sxx}},\hspace{10px} A=\bar{y}-B\overline{\ln x}\\
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(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}(y_i-\bar{y})^2 f_i}={{\small \sum} y_i^2 f_i}- n \cdot \bar{y}^2\\
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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 correlation0-1:\normalsize\ Logarithmic\ regression\\
(1)\ mean:\ \overline{\ln x}={\large \frac{{\small \sum}{\ln x_i}}{n}},\hspace{10px}\bar{y}={\large \frac{{\small \sum}{y_i}}{n}},\hspace{10px}n={\small \sum}f_i\\
(2)\ trend\ line:\ y=A+B \ln x,\hspace{10px} B={\large\frac{Sxy}{Sxx}},\hspace{10px} A=\bar{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}(y_i-\bar{y})^2 f_i}={{\small \sum} y_i^2 f_i}- n \cdot \bar{y}^2\\
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