       Re: How to use BestFitParameters?

• To: mathgroup at smc.vnet.net
• Subject: [mg24289] Re: [mg24274] How to use BestFitParameters?
• From: Matt.Johnson at autolivasp.com
• Date: Fri, 7 Jul 2000 00:11:30 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```
Rob-

In:
answer = NonlinearRegress[p, a/Sqrt[d^2 + (x1 - w0)^2], {x1}, {a, d, w0},
MaxIterations -> 200, RegressionReport -> BestFitParameters]

Out:
{BestFitParameters -> {a -> 1.07061, d -> 0.300272, w0 -> 28.8068}}

In:

Out:
1.07061

In:
Do[ var[ i ] = answer[[ 1 , 2 , i , 2 ]], { i, 3} ]

will assign each part of answer to var[ i ].  Then just plot your function using
Plot with the variables var[ i ] in place of the parameters.  Use ListPlot to
plot the data.  Then use Show to combine the data plot and the function plot
into one graphic.

-matt

piovere at pdq.net (rob) on 07/05/2000 09:10:59 PM

Subject: [mg24289]  [mg24274] How to use BestFitParameters?

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

```

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