Questions on the use of Mathematica to construct models for approximating empirical data.

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1
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1answer
160 views

show fit information on plot

After performing a fit in Mathematica, I would like to show the fitted parameters in a box on the plot showing the fitted function. How would I go about achieving that? Here is a MWE: ...
0
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1answer
210 views

Fitting to a sigmoidal model

I am trying to fit a set of stochastic data to a sigmoidal function, but it's not working. Can you please help? Here is the function I am trying to fit to my data. ...
1
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1answer
193 views

NonLinearFit with “complicated” integral model

I have a set of data $y_i (z_i)$ with errors $\Delta y_i$ ...
8
votes
1answer
201 views

Inconsistent DistributionFitTest results?

In pondering this question, I used Mariana's function to generate the following data. ...
1
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1answer
179 views
17
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2answers
2k views

How to fit 3 data sets to a model of 4 differential equations?

I'm a biologist and a newbie in Mathematica. I want to fit three data sets to a model consisting of four differential equations and 10 parameters. I want to find the parameters best fitting to my ...
4
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1answer
266 views

Fitting triangular function with HeavisideTheta

I have a problem fitting a triangular function (like potential vs. time in cyclic voltammetry) with a HeavisideTheta function. I just want to get used to ...
2
votes
1answer
102 views

nonlinearnodelfit with a matrix as weights

I have to fit a non linear model to my data and I am trying to use nonlinearmodelfit. The problem is that I have systematic errors, so the ...
1
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1answer
252 views

FindFit (Jacobian Error) [duplicate]

I, like others before me, am struggling with FindFit. So, I tried a simple example. ...
-1
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1answer
62 views

How to fit one parametric array to another numerical array?

I have two arrays of length n. One of them is obtained by experiment, so every element of the array is a number. The other array is parametric, each element is a ...
6
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1answer
131 views

Why LinearModelFit is slower than NonlinearModelFit?

Why LinearModelFit is slower than NonlinearModelFit? ...
1
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0answers
285 views

Speeding up Nonlinearmodelfit by constraining parameters?

I have a complicated parametric PDE that can be fitted to some data with NonlinearModelFit, but takes several hours to estimate the best values of the four free parameters. Currently, the code ...
1
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1answer
265 views

dynamically set fit parameters and models with FindFit

I want to fit a gaussian profile by setting some values dynamically, but FindFit returns an error and i can't see the problem. with a given gaussian: ...
0
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1answer
202 views

Nonlinear fit with piecewise functions

I have an ensemble of data points $(x_i,y_i)$ and I need to fit them according to $y=F(a,b,x)$ if $x \leq x_{ref}$ and $y=G(c,d,x)$ if $x \geq x_{ref}$. The parameters I need to adjust are then ...
1
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1answer
246 views

Can ParametricNDsolve be used for coupled PDEs with 5 parameters?

I have a system of coupled PDEs with five parameters that I only know ranges for rather than explicit values, and I was wondering if I could define a parametric equation with ParametricNDSolve and ...
1
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1answer
145 views

Fitting data using a series of Sin and Cos

I have the following data representing the normal displacement caused by a normal load applied at the middle cross section of a cylinder: I've made the data available here. I am trying to fit ...
0
votes
0answers
80 views

Simultaneously fitting data sets with many variables as free parameters [duplicate]

I found a partial answer in the documentation centre, but would like to expand on it and know how can I fit multiple sets of data and extract the parameters from them. It is an eigenvalue problem - We ...
5
votes
1answer
365 views

Fit data with linear combinations of Cos and Sin

Recall that if $f$ is a piecewise continuous function on the interval $[-\pi, \pi]$, then the Fourier series of $f$ is $$f(x) = \sum_{n=0}^{\infty} (a_n \cos(nx) + b_n \sin(nx)).$$ See for example, ...
4
votes
1answer
668 views

NonlinearModelFit does not find a good fit

I am trying to fit my data to the following function, $$\frac{a b t \left(\log \left(\frac{-a d t+a t-1}{a d t}\right)-2\right)}{4 (a t-1)}-c$$ ...
1
vote
2answers
90 views

Minimizing the maximal residual in mathematica

With this: d1 = 10; d2 = 4; mat = RandomReal[{-1, 1}, {d1, d2}]; vec = RandomReal[{-1, 1}, d1]; LeastSquares[mat, vec] ...
0
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0answers
356 views

histogram fit for probability density

I am trying to fit the (probability density) histogram of some data with the exponential function, but I am having difficulties. My raw data are in file called ...
1
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2answers
178 views

FindFit giving weird values on a logistic equation

I was trying to fit a set of data onto a logistic equation, however it ended up telling me that the initial value when $t=0$ is greater than the maximum limit, thus I am led to believe that it isn't ...
12
votes
1answer
460 views

Does anyone have experience with performing symbolic regression using Mathematica?

I understand that there is at least one Mathematica package, DataModeler commercially available for symbolic regression. I'm seeking any observations with this or any other similar tool. I'm ...
2
votes
2answers
744 views

Line of best fit on LogLog plot

I have a LogLog plot, and i'm unsure about how to fit a line to it. The data represents a calibration curve. ...
0
votes
1answer
100 views

Replicating Excel output using Mathematica

I have 2 columns of data in Excel. One is inputs the other is outputs. I ask Excel to make a graph of that data and to fit the data to a power trendline. Excel does this and it's fine as far as it ...
1
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2answers
272 views

Can't find a fit for Erf

I have the following numbers ...
1
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2answers
93 views

How can I get a fully functional FittedModel when fitting data to a pointwise function?

When I am fitting data with a pointwise function using NonlinearModelFit, the produced FittedModel fails to calculate variances ...
0
votes
0answers
50 views

Supply parameter values in NormFunction of FindFit

As I understand the input to the NormFunction is a list of residuals. Is there a way to get parameter values into the NormFunction as well? I ran into a problem where the norm depends on the values of ...
20
votes
4answers
2k views

Mathematica envelope for the bottom of a plot, a generic function

I have the following set-up: xaxis = Table[x, {x, 0, 10, 0.01}]; yaxis = Table [Sin[x] + Abs[RandomReal[{-1, 1}]], {x, 0, 10, 0.01}]; ListLinePlot[Transpose[{ xaxis, yaxis}]] My ...
0
votes
2answers
159 views

Any other way to get a better FindFit for my data besides good initial parameters?

I fit some data with FindFit and NonlinearModelFit with some constraints and I am not getting a good fit with my data. I read ...
3
votes
2answers
190 views

Multi-Fitting with Nonlinear model

I want to fit experimental data by the H-N model. Here is the H-N model: $$\text{EHN}(T)\text{=}\text{E$\infty $}+\frac{\text{E0}-\text{E$\infty $}}{\left(1+\left(i \omega\tau(T_g)10^{-\frac{\text{C1} ...
8
votes
1answer
192 views

Least Square Data Fit /Design Matrix

I am trying to learn how to use the DesignMatrix function in Mathematica and how to perform a LeastSquares fit. I am at end of ...
0
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0answers
222 views

Non linear model fit mathematica

I want to fit experimental data (temp,alpha) to the following equation for calculating k and Ea -Log[alpha]^n = function(k,Ea,temp) However i do not know ...
-1
votes
2answers
243 views

Fitting a beta distribution to a probability density curve

If I have a spectral data set showing measured energy on the y-axis and frequency on the x-axis, how would I go about fitting this to a beta distribution? For example, lets say I had the data for the ...
2
votes
1answer
631 views

Nonlinear least squares

I have a typical nonlinear least square problem and it seems very similar to the example provided in the section on parameter fitting at the Wolfram website. Unfortunately I always get some error ...
-1
votes
1answer
1k views

How do I calculate RSquared in Mathematica 9? [closed]

I imported data from an Excel package and used LinearModelFit to return a FittedModel: FittedModel[6.90762 - 0.999573 x] How ...
1
vote
1answer
329 views

Fitting data using a differential equation

I have data generated from two functions given below. How can I go about finding a fit of the form: y'[x] == -(a + b/(c + d y[x] + e F[x] )) where a,b,c,d,e are ...
1
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1answer
383 views

Method used by FindFit

Using FindFit, Mathematica selects an optimal algorithm when Automatic is selected. I'd like to know the name of the method ...
6
votes
1answer
401 views

Mathematica vs Sigmaplot (Non LinearModelFit)

I asked a question in a previous post that was closed because "The title of the question is not correct and the issue here is too trivial to help anyone later". NonLinearModelFit It's possible ...
5
votes
3answers
307 views

Determing two Nonlinear model fits with 95% confidence bands from one data set

I have the following data which is postulated to have contributions from two different sources .....as can be seen from the confidence band, many points are out of the band. Question: How can I ...
2
votes
3answers
381 views

Estimating a distribution using binned data

I have data from which information has been irretrievably lost through binning and I am trying to find a plausible distribution from which it derives. There is an academic paper suggesting that the ...
17
votes
5answers
6k views

Problem with NonlinearModelFit

I'm having trouble with a non-linear fit: fit = NonlinearModelFit[data, y0 + A Sin[\[Pi] (x - xc)/w], {y0, xc, A, w}, x] where ...
1
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1answer
286 views
0
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2answers
196 views

How to solve this FindFit::nrlnum:

the following code show error message FindFit::nrlnum: "The function value {6.71759 -9.36268*10^-8\ I,6.51797 -8.42641*10^-8\ I,6.31789 -7.49014*10^-8\ I,6.1179 -6.55387*10^-8\ I,5.91794 ...
1
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1answer
181 views

How do I construct a non-linear model from experimental data?

I want to find a function $w=f(x,y,z)$ that fits experimentally determined values of w. For example, assume ...
4
votes
1answer
718 views

How does Mathematica estimate error on fit parameters?

When performing a fit using NonlinearModelFit (or any of Mathematica fitting functions, but I am particularly interested in nonlinear models), Mathematica makes a ...
0
votes
0answers
149 views

NonlinearModelFit with multiple parameters

I am now trying a slightly more complicated model which actually consists of finding the parameters of 2 particles in an Image (I attached an Plot of an image). Although I put very good initial values ...
2
votes
1answer
75 views

is there an option for FitResiduals in FindFit?

I know this option exists in NonlinearModelFit and probably in other fit models as well but for some reason the best result i get is with FindFit. Regards Doron
2
votes
1answer
177 views

Judging the quality of fitting an EventData object to a distribution using LogRankTest

I have $389$ data points defined in an EventData object and want to judge the quality of fit of this data to a fitted $3$-parameter Weibull distribution. This ...
4
votes
1answer
227 views

FindFit not giving a good fit despite good initial parameters

I'm having a problem with FindFit not giving a good fit to my data, even though the initial parameters I give look really good when plotted. The fitting function is ...