## 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] /54 Disp-Num5103050100200
[1]  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.
[2]  2018/11/26 04:24   Male / Under 20 years old / High-school/ University/ Grad student / Useful /
Purpose of use
School Project
Comment/Request
Maybe show the Sxx, Sxy, Sxx2, Sx2x2, Sx2y values as well?
[3]  2018/11/02 20:06   Male / 50 years old level / An engineer / Very /
Purpose of use
curve fitting of power electronic converter manufacturer's power loss data to build a simple power loss compensation routine
[4]  2018/09/13 00:20   Male / 40 years old level / An engineer / Very /
Purpose of use
Used to find closest quadratic fit for the angle of swirl between jet engine combustion system and exhaust temperature as a function of power level.
Comment/Request
Loved that I could paste a 44 point data straight in from Excel. Nice. Worked perfectly.
[5]  2018/08/19 00:51   Male / 60 years old level or over / A retired person / Not at All /
Purpose of use
Seeing if Social Security benefits/age is a quadratic equation
Comment/Request
Gave me A=20,000 B=0 C=6. Nonsense results.
Perhaps your equations explode when B=0.
Maybe for small B, you need to expand the equation as a series.
[6]  2018/08/13 14:22   Male / 40 years old level / - / A little /
Purpose of use
research
[7]  2018/05/22 06:31   - / - / - / - /
Bug report
Every calculation that I have done with your site has given me mixed up data. Your a and c values are switched, other than that confusing part, your site is great. Please fix that one piece everything else is helpful.
[8]  2018/05/22 06:17   Female / Under 20 years old / Elementary school/ Junior high-school student / A little /
Purpose of use
Help on HW
Bug report
a =/= 12.9285... a = 0.5833...
c =/= 0.5833... c = 12.9285

Values of a and c are mixed up, b is correct.
[9]  2018/05/14 04:18   Female / 30 years old level / Others / Useful /
Purpose of use
Helping son with Advanced Algebra homework (calculator with regression analysis needed)
Comment/Request
The inputs were simple and it''s a great tool. If possible, please show the value of the max or min on the graph and the coordinating numbers below for more analysis. Keep up the good work!
[10]  2018/04/10 05:40   Male / Under 20 years old / High-school/ University/ Grad student / Useful /
Purpose of use

Sending completion

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