## 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] /51 Disp-Num5103050100200
[1]  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.
[2]  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.
[3]  2018/08/13 14:22   Male / 40 years old level / - / A little /
Purpose of use
research
[4]  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.
[5]  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.
[6]  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!
[7]  2018/04/10 05:40   Male / Under 20 years old / High-school/ University/ Grad student / Useful /
Purpose of use
[8]  2018/03/21 04:49   Female / Under 20 years old / High-school/ University/ Grad student / Very /
Purpose of use
Finding the correlation between musical notes and their wavelengths because I got bored in my engineering class.
[9]  2018/03/14 05:23   Male / - / An engineer / Very /
Purpose of use
Building a stepper motor based antenna elevation mechanism for aiming antennas for moon bounce communication. Formula is used to calculate number of steps required to achieve desired elevation angle. Platform movement is not linear so this is perfect for adjusting the number of steps to get from one angle to another.
[10]  2018/03/09 03:07   Male / 20 years old level / High-school/ University/ Grad student / Very /
Comment/Request
Do you have some kind of code for this? Would like to use it in python :)

Sending completion

Male or Female ?
Male Female
Age
Under 20 years old 20 years old level 30 years old level
40 years old level 50 years old level 60 years old level or over
Occupation
Elementary school/ Junior high-school student
High-school/ University/ Grad student A homemaker An office worker / A public employee
Self-employed people An engineer A teacher / A researcher
A retired person Others
Useful?
Very Useful A little Not at All
Purpose of use?