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

 （input by clicking each cell in the table below） data 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit
 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$\normal\ Quadratic\ regression\vspace{10}\\(1)\ mean:\ \bar{x}={\large \frac{{\small \sum}{x_i}}{n}},\hspace{10}\bar{y}={\large \frac{{\small \sum}{y_i}}{n}}\hspace{10}\bar{x^{\tiny 2}}={\large \frac{{\small \sum}{x_i^2}}{n}}\\[10](2)\ trend\ line:\ y=A+Bx+Cx^2\\[10]\hspace{20}B={\large\frac{SxySx^{\tiny 2}x^{\tiny 2}-Sx^{\tiny 2}ySxx^{\tiny 2}}{SxxSx^{\tiny 2}x^{\tiny 2}-(Sxx^{\tiny 2})^2}}\\[10]\hspace{20}C={\large\frac{Sx^{\tiny 2}ySxx-SxySxx^{\tiny 2}}{SxxSx^{\tiny 2}x^{\tiny 2}-(Sxx^{\tiny 2})^2}}\\[10]\hspace{20}A=\bar{y}-B\bar{x}-C\bar{x^{\tiny 2}}\\[10](3)\ correlation\ coefficient:\\\hspace{20} r=\sqrt{1-\frac{{\small \sum}(y_i-(A+Bx_i+Cx_i^2))^2}{{\small \sum}(y_i-\bar{y})^2}}\\[10]\hspace{35}S_{xx}={\large \frac{{\small \sum}(x_i-\bar{x})^2}{n}}={\large \frac{{\small \sum} x_i^2}{n}}-\bar{x}^2\\\hspace{35}S_{xy}={\large \frac{{\small \sum}(x_i-\bar{x})(y_i-\bar{y})}{n}}={\large \frac{{\small \sum} x_i y_i}{n}}-\bar{x}\bar{y}\\\hspace{35}S_{xx^{\tiny 2}}={\large \frac{{\small \sum}(x_i-\bar{x})(x_i^2-\bar{x^{\tiny 2}})}{n}}={\large \frac{{\small \sum} x_i^3}{n}}-\bar{x}\bar{x^{\tiny 2}}\\\hspace{35}S_{x^{\tiny 2}x^{\tiny 2}}={\large \frac{{\small \sum}(x_i^2-\bar{x^{\tiny 2}})^2}{n}}={\large \frac{{\small \sum} x_i^4}{n}}-\bar{x^{\tiny 2}}\bar{x^{\tiny 2}}\\\hspace{35}S_{x^{\tiny 2}y}={\large \frac{{\small \sum}(x_i^2-\bar{x^{\tiny 2}})(y_i-\bar{y})}{n}}={\large \frac{{\small \sum} x_i^2y_i}{n}}-\bar{x^{\tiny 2}}\bar{y}\\$

 [1-10] /63 Disp-Num5103050100200
[1]  2019/04/21 05:35   Male / 60 years old level or over / An engineer / Very /
Purpose of use
Personal curiousity
Comment/Request
Give the formula to calculate R^2 in terms of Sxx, etc.
[2]  2019/04/12 01:05   Female / Under 20 years old / High-school/ University/ Grad student / Very /
Purpose of use
Math homework
Comment/Request
[3]  2019/04/10 10:08   Female / Under 20 years old / High-school/ University/ Grad student / Useful /
Purpose of use
Math homework
[4]  2019/04/09 08:28   Male / Under 20 years old / High-school/ University/ Grad student / Useful /
Purpose of use
math homework
Comment/Request
it would be very useful if the equation was ax^2+bx+c instead of a+bx+cx^2.
[5]  2019/03/21 10:49   Female / Under 20 years old / Elementary school/ Junior high-school student / Useful /
Purpose of use
Algebra 1 homework
Comment/Request
Add ability to make predictions from model.
[6]  2019/03/19 08:11   Female / Under 20 years old / High-school/ University/ Grad student / A little /
Purpose of use
Algebra 1 homework
[7]  2019/03/15 23:54   Male / Under 20 years old / High-school/ University/ Grad student / Useful /
Purpose of use
Pre-Calculus homework
Comment/Request
A+Bx+Cx² is not standard in anything I've seen, ax²+bx+c seems to be much more common
[8]  2019/03/08 10:18   Male / Under 20 years old / Elementary school/ Junior high-school student / Useful /
Purpose of use
Homework
Comment/Request
Make the results copy-pastable.
[9]  2019/02/13 10:12   Female / Under 20 years old / High-school/ University/ Grad student / A little /
Purpose of use
Algebra 2 homework
Comment/Request
Have the data table of the graph available. Also, the formula is not one proper order according to powers.
[10]  2018/11/30 02:33   Male / 60 years old level or over / A teacher / A researcher / Very /
Purpose of use
Best quadratic fit from noisy Doppler data.
Comment/Request
Superb.

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