       Using Fit to interpolate data

• To: mathgroup at smc.vnet.net
• Subject: [mg127429] Using Fit to interpolate data
• From: Kris Carlson <carlsonkw at gmail.com>
• Date: Tue, 24 Jul 2012 04:15:18 -0400 (EDT)
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• Delivered-to: mathgroup-newout@smc.vnet.net
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```Hi,

Can someone enlighten me about how to fit a curve to data? These data are
of the density of axons of given diameters in the spinal cord. The density
of smaller fibers is dramatically larger than that of larger fibers. There
cannot be density < 0 of any diameter, so heuristically to prevent a fit
yielding an equation that dips below 0 I added an end point with fiber
diameter = 16 that is 0. Then using Fit I try to increase the exponent of x
until the curve doesn't yield negative values. The fit looks good in large
scale but when I plot the region of greatest interest, 8 < x < 14, it no
longer looks so good. Maybe I am simply ignorant about fitting a curve to
somewhat irregular data? Or can it be done?

Thank you.

Kris

fiberDataDensitiesFeierabend = {{16, 0}, {10.7, 0.11}, {10.4,
0.19}, {9.77, 0.41}, {8.29, 3.05}, {7.14, 19.86}};

fbddPlot =
PlotMarkers -> {Automatic, Medium}]

fbddFit = Fit[fiberDataDensitiesFeierabend, {1, x, x^-13}, x]

Show[Plot[fbddFit, {x, 4, 20},
PlotRange -> {{4.5, 20}, {-0.5, 25}}], fbddPlot]

Show[Plot[fbddFit, {x, 4, 28},
PlotRange -> {{8, 16}, {-0.5, 1}}], fbddPlot]

```

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