RE: How to use BestFitParameters?
- To: mathgroup at smc.vnet.net
- Subject: [mg24301] RE: [mg24274] How to use BestFitParameters?
- From: "David Park" <djmp at earthlink.net>
- Date: Fri, 7 Jul 2000 00:11:43 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
> -----Original Message----- > From: rob [mailto:piovere at pdq.net] To: mathgroup at smc.vnet.net > p is a list of data pairs { {x1,y1}, {x2,y2}, ....} and when I fit > this data to a function Mathematica does a pretty good job of > doing the fit: > > NonlinearRegress[p, a/Sqrt[d^2 + (x1 - w0)^2], {x1}, {a, d, w0}, > MaxIterations -> 200, RegressionReport -> BestFitParameters] > > gives this as an output: > {BestFitParameters -> {a -> 1.07061, d -> 0.300272, w0 -> 28.8068}} > > I know it is pretty a pretty good fit to the data because I can use > another program like Excel to plot the curve using these parameters > and display it next to the data. It sure would be nice to do this in > Mathematica without going to an outside program. I've tried things but I > can't seem to be able to get to the parameters a, d and w0. I can't > even list them. For example, I'd like to display the number > d/Sqrt[w0^2-d^2]. So I tried this: > > d/Sqrt[w0^2-d^2] /. % > > All I get is the formula in symbolic form. > > Can someone here provide some relief? > > Thanks, Rob > Rob, Follow the form given in In[4] and Out[4] in the NonlinearFit documentation. rules = BestFitParameters/. NonlinearRegress[p, a/Sqrt[d^2 + (x1 - w0)^2], {x1}, {a, d, w0}, MaxIterations -> 200, RegressionReport -> BestFitParameters] You should get: {a -> 1.07061, d -> 0.300272, w0 -> 28.8068} Then: d/Sqrt[w0^2 - d^2] /. rules 0.0104242 To plot your function: f[x_] = a/Sqrt[d^2 + (x - w0)^2] /. rules 1.07061/Sqrt[0.090163273984 + (-28.8068 + x)^2] Plot[f[x], {x, -5, 5}]; David Park djmp at earthlink.net http://home.earthlink.net/~djmp/