Hi, I have the following points on a graph of X,Y, derived empirically, but I would like to have the formula for their relationship. They seem to lie on a reasonable curve, bearing in mind the Y values were empirically derived, to not many decimal places. [5,2.6],[6,2.35],[7,2.26],[8,2.18],[9,2.13],[10,2.1] I was hoping that there would be a web site somewhere, where i could enter the x/y values, and out would pop the formula, but so far not found one. It was a long time ago, if ever, when I had to derive polynomial formulae. Any help appreciated. Best wishes, Ray

Here is one that seems decent: https://arachnoid.com/polysolve/ Some example search terms: polynomial best fit calculator polynomial regression curve fitting etc. On Sun, Jan 23, 2022 at 8:48 AM Raymond West <raywest@raywest.com> wrote: > Hi, > > I have the following points on a graph of X,Y, derived empirically, but > I would like to have the formula for their relationship. They seem to > lie on a reasonable curve, bearing in mind the Y values were empirically > derived, to not many decimal places. > > [5,2.6],[6,2.35],[7,2.26],[8,2.18],[9,2.13],[10,2.1] > > I was hoping that there would be a web site somewhere, where i could > enter the x/y values, and out would pop the formula, but so far not > found one. It was a long time ago, if ever, when I had to derive > polynomial formulae. Any help appreciated. > > Best wishes, > > Ray > > _______________________________________________ > OpenSCAD mailing list > To unsubscribe send an email to discuss-leave@lists.openscad.org >

To work on your question, there is some physics that has to go on: 1) What were you measuring? 2) What were your error bars? i.e. how much should we trust each measurement? 3) This looks like it could be a parabola or a lens with the minima at 10, or it could be a x^-a kind of graph, again what is being measured? Desmos might be able to do this, but in University, I was taught to do it using Excel. On Sun, Jan 23, 2022 at 9:48 AM Raymond West <raywest@raywest.com> wrote: > Hi, > > I have the following points on a graph of X,Y, derived empirically, but > I would like to have the formula for their relationship. They seem to > lie on a reasonable curve, bearing in mind the Y values were empirically > derived, to not many decimal places. > > [5,2.6],[6,2.35],[7,2.26],[8,2.18],[9,2.13],[10,2.1] > > I was hoping that there would be a web site somewhere, where i could > enter the x/y values, and out would pop the formula, but so far not > found one. It was a long time ago, if ever, when I had to derive > polynomial formulae. Any help appreciated. > > Best wishes, > > Ray > > _______________________________________________ > OpenSCAD mailing list > To unsubscribe send an email to discuss-leave@lists.openscad.org >

Since this is the OpenSCAD list, how about a solution using OpenSCAD! Below is a quadratic least squares fit using BOSL2. Of course, whether this is the right thing to do depends on those questions Ari asked. include<BOSL2/std.scad> $fn=16; data = [[5,2.6],[6,2.35],[7,2.26],[8,2.18],[9,2.13],[10,2.1]]; // Solve least squares problem: x = column(data,0); y = column(data,1); const = repeat(1,len(data)); x2 = [for (a=x) a^2]; M = transpose([const, x, x2]); coef = linear_solve(M,y); // Here are coefficients, [const, linear, square] echo(coef); // It prints: [4.16429, -0.430071, 0.0225] // Visualize solution color("black") stroke([for(x=lerpn(3,12,100)) [x,coef*[1,x,x*x]]], width=.03); move_copies(data) circle(r=.05); On Sun, Jan 23, 2022 at 10:39 AM Ari Diacou <ari.diacou@gmail.com> wrote: > > To work on your question, there is some physics that has to go on: > 1) What were you measuring? > 2) What were your error bars? i.e. how much should we trust each measurement? > 3) This looks like it could be a parabola or a lens with the minima at 10, or it could be a x^-a kind of graph, again what is being measured? > > Desmos might be able to do this, but in University, I was taught to do it using Excel. > > On Sun, Jan 23, 2022 at 9:48 AM Raymond West <raywest@raywest.com> wrote: >> >> Hi, >> >> I have the following points on a graph of X,Y, derived empirically, but >> I would like to have the formula for their relationship. They seem to >> lie on a reasonable curve, bearing in mind the Y values were empirically >> derived, to not many decimal places. >> >> [5,2.6],[6,2.35],[7,2.26],[8,2.18],[9,2.13],[10,2.1] >> >> I was hoping that there would be a web site somewhere, where i could >> enter the x/y values, and out would pop the formula, but so far not >> found one. It was a long time ago, if ever, when I had to derive >> polynomial formulae. Any help appreciated. >> >> Best wishes, >> >> Ray >> >> _______________________________________________ >> OpenSCAD mailing list >> To unsubscribe send an email to discuss-leave@lists.openscad.org > > _______________________________________________ > OpenSCAD mailing list > To unsubscribe send an email to discuss-leave@lists.openscad.org