Algebra, Excel, Statistics, and fan curves...Question.
It's been a while since I formally learned any algebra, and I've never really spent much time with statistics.
What I want to do, is take a set of about 5 points (pressure,flow) and create a 2nd order polynomial from them, just the same way that excel does it with the trendline function on a chart. I could just cut and paste the shown equation and use it to complete more points,but..
The application I have for this needs to use the equation as a function: ax^2+bx+c; where a, b, and c are stored as constants, after 'calibrated' by intrepreting a minimum number of points.
How does excel 'interpret' the points for a poly? Is it a proprietary combination of LINEST and LOGEST? Where's a good place to find out?
How many points would be a good minimum for accuracy?
How would I do it mathematically, without using excel?
Any points in the right direction (other sites would be fine too) would be much appreciated.
For a polynomial curve fit I believe you will be looking at a least squares problem, solving matrix equations, etc. This really is a computational suited task - I think it would take a long, long time by hand. I'm sure the math methods are out there if you plug a few your words into google.
there might be newer methods - I've been out of school for a lot of years.
After researching a bit, it seems to me you're right about the least squares polynomial fit, thanks for the pointer
It made an excellent search term for me.
I found what I'm looking for, and for anyone interested:
library of C++ routines, using double precision arithmetic, for constructing and evaluating spline functions.