Quadratic Regression

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

\(\normalsize\ Quadratic\ regression\\ (1)\ mean:\ \bar{x}={\large \frac{{\small \sum}{x_i}}{n}},\hspace{10px}\bar{y}={\large \frac{{\small \sum}{y_i}}{n}}\hspace{10px}\overline{x^{\tiny 2}}={\large \frac{{\small \sum}{x_i^2}}{n}}\\ (2)\ trend\ line:\ y=A+Bx+Cx^2\\ \hspace{20px}B={\large\frac{SxySx^{\tiny 2}x^{\tiny 2}-Sx^{\tiny 2}ySxx^{\tiny 2}}{SxxSx^{\tiny 2}x^{\tiny 2}-(Sxx^{\tiny 2})^2}}\\ \hspace{20px}C={\large\frac{Sx^{\tiny 2}ySxx-SxySxx^{\tiny 2}}{SxxSx^{\tiny 2}x^{\tiny 2}-(Sxx^{\tiny 2})^2}}\\ \hspace{20px}A=\bar{y}-B\bar{x}-C\overline{x^{\tiny 2}}\\ (3)\ correlation\ coefficient:\\ \hspace{20px} r=\sqrt{1-\frac{{\small \sum}(y_i-(A+Bx_i+Cx_i^2))^2}{{\small \sum}(y_i-\bar{y})^2}}\\ \hspace{35px}S_{xx}={{\small \sum}(x_i-\bar{x})^2}={{\small \sum} x_i^2}-n \cdot \bar{x}^2\\ \hspace{35px}S_{xy}={{\small \sum}(x_i-\bar{x})(y_i-\bar{y})}={{\small \sum} x_i y_i}-n \cdot \bar{x}\bar{y}\\ \hspace{35px}S_{xx^{\tiny 2}}={{\small \sum}(x_i-\bar{x})(x_i^2-\overline{x^{\tiny 2}})}={{\small \sum} x_i^3}-n \cdot \bar{x}\overline{x^{\tiny 2}}\\ \hspace{35px}S_{x^{\tiny 2}x^{\tiny 2}}={{\small \sum}(x_i^2-\overline{x^{\tiny 2}})^2}={{\small \sum} x_i^4}-n \cdot \overline{x^{\tiny 2}}\overline{x^{\tiny 2}}\\ \hspace{35px}S_{x^{\tiny 2}y}={{\small \sum}(x_i^2-\overline{x^{\tiny 2}})(y_i-\bar{y})}={{\small \sum} x_i^2y_i}-n \cdot \overline{x^{\tiny 2}}\bar{y}\\ \)