Re: Using Fit to interpolate data

*To*: mathgroup at smc.vnet.net*Subject*: [mg127457] Re: Using Fit to interpolate data*From*: "Kevin J. McCann" <kjm at KevinMcCann.com>*Date*: Thu, 26 Jul 2012 03:34:25 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*References*: <jullkd$ptc$1@smc.vnet.net>

One last go at it: fiberDataDensitiesFeierabend = {{16, 0}, {10.7, 0.11}, {10.4, 0.19}, {9.77, 0.41}, {8.29, 3.05}, {7.14, 19.86}}; model = A Exp[-a x + b]; params = FindFit[fiberDataDensitiesFeierabend, model, {A, a, b}, x] f[x_] = model /. params min = Min[fiberDataDensitiesFeierabend[[All, 1]]]; max = Max[fiberDataDensitiesFeierabend[[All, 1]]]; {min, max} p1 = ListPlot[fiberDataDensitiesFeierabend, PlotStyle -> {Red, AbsolutePointSize[7]}, PlotRange -> All]; Plot[f[x], {x, min, max}, Epilog -> p1[[1]], Frame -> True, FrameStyle -> AbsoluteThickness[2], GridLines -> Automatic, PlotRange -> All, BaseStyle -> {FontFamily -> "Arial", FontSize -> 12, FontWeight -> Bold} ] Cheers, Kevin On 7/24/2012 4:16 AM, Kris Carlson wrote: > 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 = > ListPlot[fiberDataDensitiesFeierabend, > 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] > >