## Analyzes the data table by quadratic regression and draws the chart.

 （input by clicking each cell in the table below） data
 6dgt10dgt14dgt18dgt22dgt26dgt30dgt34dgt38dgt42dgt46dgt50dgt
 Guidelines for interpreting 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$\normal\ Quadratic\ regression\vspace{10}\\(1)\ mean:\ \bar{x}={\large \frac{{\small \sum}{x_i}}{n}},\hspace{10}\bar{y}={\large \frac{{\small \sum}{y_i}}{n}}\hspace{10}\bar{x^{\tiny 2}}={\large \frac{{\small \sum}{x_i^2}}{n}}\\[10](2)\ trend\ line:\ y=A+Bx+Cx^2\\[10]\hspace{20}B={\large\frac{SxySx^{\tiny 2}x^{\tiny 2}-Sx^{\tiny 2}ySxx^{\tiny 2}}{SxxSx^{\tiny 2}x^{\tiny 2}-(Sxx^{\tiny 2})^2}}\\[10]\hspace{20}C={\large\frac{Sx^{\tiny 2}ySxx-SxySxx^{\tiny 2}}{SxxSx^{\tiny 2}x^{\tiny 2}-(Sxx^{\tiny 2})^2}}\\[10]\hspace{20}A=\bar{y}-B\bar{x}-C\bar{x^{\tiny 2}}\\[10](3)\ correlation\ coefficient:\\\hspace{20} r=\sqrt{1-\frac{{\small \sum}(y_i-(A+Bx_i+Cx_i^2))^2}{{\small \sum}(y_i-\bar{y})^2}}\\[10]\hspace{35}S_{xx}={\large \frac{{\small \sum}(x_i-\bar{x})^2}{n}}={\large \frac{{\small \sum} x_i^2}{n}}-\bar{x}^2\\\hspace{35}S_{xy}={\large \frac{{\small \sum}(x_i-\bar{x})(y_i-\bar{y})}{n}}={\large \frac{{\small \sum} x_i y_i}{n}}-\bar{x}\bar{y}\\\hspace{35}S_{xx^{\tiny 2}}={\large \frac{{\small \sum}(x_i-\bar{x})(x_i^2-\bar{x^{\tiny 2}})}{n}}={\large \frac{{\small \sum} x_i^3}{n}}-\bar{x}\bar{x^{\tiny 2}}\\\hspace{35}S_{x^{\tiny 2}x^{\tiny 2}}={\large \frac{{\small \sum}(x_i^2-\bar{x^{\tiny 2}})^2}{n}}={\large \frac{{\small \sum} x_i^4}{n}}-\bar{x^{\tiny 2}}\bar{x^{\tiny 2}}\\\hspace{35}S_{x^{\tiny 2}y}={\large \frac{{\small \sum}(x_i^2-\bar{x^{\tiny 2}})(y_i-\bar{y})}{n}}={\large \frac{{\small \sum} x_i^2y_i}{n}}-\bar{x^{\tiny 2}}\bar{y}\\$

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