Re: Automate datafitting to a series of parameterized function

*To*: mathgroup at smc.vnet.net*Subject*: [mg70297] Re: [mg70277] Automate datafitting to a series of parameterized function*From*: Darren Glosemeyer <darreng at wolfram.com>*Date*: Thu, 12 Oct 2006 05:37:05 -0400 (EDT)*References*: <200610110553.BAA19424@smc.vnet.net>

The model is a linear model in the basis functions 1, x, x^2,..., so you can use Regress to easily get this information. This will give the fitted function and residuals for the model with n terms. << Statistics`LinearRegression` fittedAndResiduals[n_] := {BestFit, FitResiduals} /. Regress[data, x^Range[0, n], x, RegressionReport -> {BestFit, FitResiduals} ]; The mentioned results for a constant model can then be computed directly as follows, and for higher order models by choosing the appropriate value of n. res0 = fittedAndResiduals[0]; error0 = res0[[2]]^2; avererror0 = Total[error0]/Length[data] maxerror = Max[error0] If there is a maximum power for the terms, say 5, that you wish to allow, results for all those models could be obtained as follows. Table[Block[{res = fittedAndResiduals[n], error}, error = res[[2]]^2; {res[[1]], Total[error]/Length[data], Max[error]}], {n, 0, 5}] Other diagnostics could also be obtained from Regress or computed from results obtained from Regress if desired. Darren Glosemeyer Wolfram Research Peng Yu wrote: > Suppose I have some data x_i, y_i. Let us generated them by > > coef = Table[Random[Real, {-1, 1}], {i, 0, 4}] > poly = Table[x^n, {n, 0, 4}] > data = Table[{x, coef.poly}, {x, 0, 1, .01}] > > Let us forget how we generated the data. Now, we want to find an > function to fit the data. The simplest way to do is using Tayler > series. But the problem is I don't know how many terms I should keep. > One way I can do is to try for different number of terms. I start by > only 1 term (0th order). > > f[x_, a0_] := a0 > f[x_] := Evaluate@NonlinearFit[data, f[x, a0], {x}, {a0}] > error = Apply[(f[#1] - #2)^2 &, data, {1}]; > avererror = Apply[Plus, error]/Length[data] > maxerror = Apply[Max, error] > > If the above one doesn't work, I'll try 2 terms (0th and 1st order). > f[x_, a0_, a1_] := a0 + a1 x > f[x_] := Evaluate@NonlinearFit[data, f[x, a0, a1], {x}, {a0, a1}]; > error = Apply[(f[#1] - #2)^2 &, data, {1}]; > avererror = Apply[Plus, error]/Length[data] > maxerror = Apply[Max, error] > > I can try even higher orders. But the problem is that ever time I have > to define the function f[x_,a0_...] and supply the right function and > parameter list to NonlinearFit. I feel it is especially difficult to > parameterize the number of parameters to a function. > > Can some give some idea on how to do it if it is possible in > Mathematica? Of cause I could write a python program to generate the > mathematica code, and call math.exe in the command line mode. But that > is just to much, I just want to stick with mathematica. > > Thanks, > Peng >

**References**:**Automate datafitting to a series of parameterized function***From:*"Peng Yu" <pengyu.ut@gmail.com>