Fitting a spline to data with FindFit?

Question

I am trying to find a function that fits my almost linear data. A high order polynomial model has too much residual. So I was hoping to use Mathematica to fit splines to the curve.

This is what I would like to see in an example.

• FindFit with a spline function
• How to get model stats like what LinearModelFit provides.
• How to dump the spline terms and control points so I can implement in "C"

I can then use the cubic spline on my embedded platform.

So can I get a symbolic representation of this function so I can implement it?

You can get the sample data here

Answer 1

Taking your data in account from link you provided:

data={{......}};

Find the model:

model = Fit[data, x^# & /@ Range[0, 10], x]

20.2513 + 43.3389 x - 0.208411 x^2 + 0.193888 x^3 - 0.0341689 x^4 + 
 0.00281455 x^5 - 0.000131003 x^6 + 3.64629*10^-6 x^7 - 
 6.01724*10^-8 x^8 + 5.43205*10^-10 x^9 - 2.06702*10^-12 x^10

Verify it is more or less correct:

Show[ListPlot[data, PlotStyle -> Directive[PointSize[.02], Opacity[.02], Red]], 
 Plot[model, {x, -7, 55}, PlotStyle -> Thickness[.005]], 
 Frame -> True, Axes -> False, ImageSize -> 500]

The blue line inside is your model. Red line is your data points blended together (too many of them) with applied opacity. I've chosen so many polynomial terms to take in account well little bent at the beginning. You can play with number of polynomial terms.

Export your model to C:

CForm[model]

20.251253486790134 + 43.33892854755122*x - 0.20841104603541305*Power(x,2) + 
   0.19388822209706186*Power(x,3) - 0.03416888859439315*Power(x,4) + 
   0.0028145533596680857*Power(x,5) - 0.0001310033312242676*Power(x,6) + 
   3.646291289683582e-6*Power(x,7) - 6.017238075935027e-8*Power(x,8) + 
   5.432049184033492e-10*Power(x,9) - 2.0670190082996488e-12*Power(x,10)