Linear Regression with Frequency Data

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

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