Steve's Junk » 3 point http://smackaay.com A showcase of Steven Mackaay's stuff Sun, 11 Mar 2012 20:11:37 +0000 en hourly 1 http://wordpress.org/?v=3.3.2 3 point quadratic regression formula http://smackaay.com/2009/04/29/3-point-quadratic-regression-formula/ http://smackaay.com/2009/04/29/3-point-quadratic-regression-formula/#comments Wed, 29 Apr 2009 22:01:05 +0000 smackaay http://smackaay.com/?p=572 While developing the in-process stormer viscometer, one of my goals is to allow the end user to calibrate the device with 3 fluids of known viscosity. With a bit of help from mathematica, I’ve found the formula and for whoever wants it, it’s posted, also for my own future edification. This formula is meant to convert 3 data points of the form {X1,Y1},{X2,Y2},{X3,Y3} into a form of ax^2+bx+c=y. This is probably the fastest way to do this kind of operation on a microcontroller. Here’s an image of the formula

Reverse Quadratic from data

Reverse Quadratic from data

also, here’s a dirty FreeBasic program using it. regress-3point.bas

Also, for fun I decided to do a cubic version. This is in the form of 4 data points {X1,Y1},{X2,Y2},… converting to ax^3+bx^2+cx+d=y

Cubic equation inverse

Cubic equation inverse

You gotta love Mathematica!!!

]]> http://smackaay.com/2009/04/29/3-point-quadratic-regression-formula/feed/ 2