Re: How I can fit data with a parametric equation?

*To*: mathgroup at smc.vnet.net*Subject*: [mg91908] Re: How I can fit data with a parametric equation?*From*: Bill Rowe <readnews at sbcglobal.net>*Date*: Fri, 12 Sep 2008 05:29:02 -0400 (EDT)

On 9/11/08 at 6:14 AM, dinodeblasio at gmail.com wrote: >Hello and thanks for your collaboration, I read a little bit and I >wrote the following code: "when I try to do the FindFit command, the >parameters have to be positive, so i was searching for the optimal >values of the parameter that fit the data. How I can modify my code >in order to find the best parameters fitting the data?I tried to do >the Norm between the value of the data and the value of the equation >but i cant do more. Thanks. >Remove["Global`*"] data = {{1, 1}, {28, 0.719188377}, {54, >0.35746493}, {81, 0.182114228}, {117, >0.166082164}, {260, 0.132765531}}; >express = (1 - k*x)*(1 - k*x/q)*(1 - p*k*x/q) "this is the >equation with which i want to fit the data" When you want to place constraints on the parameters, using NMinimize is probably going to work for you better than FindFit. First create a function that computes the summed square error In[18]:= ss[x_, y_, k_, p_, q_] := Total[((1 - k*x)*(1 - k*x/q)*(1 - p*k*x/q) - y)^2] Here I've separated the x,y components to simplify the code In[19]:= {xx, yy} = Transpose[data]; Now, NMinimize can be used to find the desired parameters In[20]:= NMinimize[{ss[xx, yy, k, p, q], k > 0 && p > 0 && q > 0}, {k, p, q}] Out[20]= {0.0178264,{k->0.00204306,p->1.,q->0.348625}} In[21]:= Show[ ListPlot[data, PlotRange -> All, Frame -> True, Axes -> None, PlotMarkers -> Automatic], Plot[express /. Last[%20], {x, 0, 300}]] Shows the estimates give a reasonable fit to the data.