# Tagged Questions

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

2answers
4k 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 ...
6answers
11k views

### Estimate error on slope of linear regression given data with associated uncertainty

Given a set of data, is it possible to create a linear regression which has a slope error that takes into account the uncertainty of the data? This is for a high school class, and so the normal ...
4answers
8k views

### Simultaneously fitting multiple datasets

What is the proposed approach if one wants to simultaneously fit multiple functions to multiple datasets with shared parameters? As an example consider the following case: We have to measurements of ...
5answers
9k views

### How to perform a multi-peak fitting?

I am wondering how to implement the multi-peak detecting and fitting in Mathematica. Following is an example of fitting the data using three peaks (such that the data ~ peak1 + peak2 + peak3). The ...
5answers
10k 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 ...
3answers
3k views

### Fitting fractional complex data with NonlinearModelfit

I've difficulites with the NonlinearModelFit function. In principle Mathematica should be able to deal with complex data. E.g. if I define the following table <...
6answers
14k views

### How to determine the center and radius of a circle given some points in 3D?

I was wondering if anyone could give me a hand with this problem I have. I have six points on a plane, and I am trying to determine if they form a circle or not. I know that any three points in 2D ...
4answers
7k views

### Using FindFit to fit $a\,b^t$: how to avoid introducing complex numbers?

I'd like to find a model $f(t)=a\,b^t$ which matches the following data ...
4answers
2k views

### Implementation of smoothing splines function

I have some problems in writing a module for spline smoothing. Actually, I have been trying for about two weeks. My listing is here: ...
5answers
3k views

### Fitting points to tilted, off-center ellipse

I have 24 x-y points that are supposed to form an ellipse. ...
4answers
3k 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 ...
2answers
1k views

### Is it possible to use the LevenbergMarquardt algorithm for fitting a black-box residual function?

I have a black-box multiargument multiparametric function of the type SRD[dataPoint_List,params_List] which accepts experimental data along with the parameters of ...
1answer
744 views

### Difference between Fitting Algorithms

I am new to Mathematica, and I don´t quite understand, what the difference between the fitting algorithms Fit, FindFit, ...
1answer
2k views

### Methods for NonlinearModelFit

I am using NonlinearModelFit for a thesis project. I get quite different results if I change the Method to LevenbergMarquardt or QuasiNewton or ConjugateGradient ...
3answers
1k views

### Ηow to create an interpolated CDF from its samples?

I want to use a distribution I have only aggregate statistics on, namely its CDF sampled at certain points. I would like to keep it "nonparametric" (remain noncommittal on the parametric form), but I ...
1answer
1k views

### Fitting piecewise functions

I have several large data sets which follow the following pattern: A position is measured, a force is applied until a new equilibrium is found. I'd like to find a fit for the position, at least at the ...
1answer
2k views

### NonlinearModelFit does not find a good fit

I am trying to fit my data to the following function, $$\frac{a b t \left(\log \left(\frac{-a d t+a t-1}{a d t}\right)-2\right)}{4 (a t-1)}-c$$ ...
3answers
244 views

### Removing background from peak function

Let's say I have a a very large list of data in the format {{n,f[n]}} so something like {{1,600},{2,700},{3,1100}...} and if this data is plotted, then it will look like a sum of Gaussian functions+a ...
1answer
2k views

### Combined fitting via NonlinearModelFit

I am trying to fit my data to a combined function model. Say I have two functions with some common parameter(s) f[x_]:= a*x^2 + b*x + c g[x_]:= d*x^2 + e*x + c ...
4answers
1k views

### Generating an “average curve” from a dense set of “semicontinuous curves” which clear trends

This question is related to a previous one of mine: Partitioning a superset of coordinates into subsets that generate continuous curves, where the challenge was to partition a data set into two ...
1answer
2k views

### Finding the area, algebraic curve and jaggedness of an arbitrary shape

I start with a photograph of a shape (physically made by the flow of a liquid into another), of which I can extract the border, manually or using Mathematica's feature detect feature : Using the ...
3answers
3k views

### How to use FindFit to fit an implicit function?

Now I am trying to fit some data with a implicit model function. Firstly, I tried a toy example. Toy example with input and output ...
1answer
1k views

### How does Mma compute Confidence Intervals?

I am trying to understand how Mma computes the Confidence Intervals after a NonlinearModelFit. Consider the following example: ...
2answers
773 views

### Does FindFit support complex numbers or doesn't it?

Inspired by this previous question: Findfit doesn't give the good fit; Changing the starting values will not change the results. Consider the following complex-valued dataset. ...
2answers
2k views

### FindFit returns Infinity::indet error when data contains {0,0}

Let's consider the following data: data = Table[{q, 2*q^2}, {q, 0, 2}]; and then, do a very simple fitting to this data: ...
2answers
1k views

### Detecting an ellipse in a glaucoma photo

For glaucoma diagnosis it is common to determine a "cup to disk ratio" which compares the diameter of the optic disk (VDD) and optic cup (VCD). The optical disk is visible as a circular red feature (...
2answers
297 views

### Unable to fit function convolved with NIntegrate with FindFit even with NumericQ

I am attempting to fit to the convolution of a simple function with a Gaussian. (I realize this could be done with Convolve also, but I thought I could make it go faster this way). I am able to ...
1answer
611 views

### Fitting data to a circle with FindFit

I'm currently trying to use the Mathematica's FindFit command to fit a curve of some data to the bottom half of a circle. The data is of the form ...
2answers
960 views

### What is the difference between FindFit and NonlinearModelFit

I cannot get the difference between these two fitting functions in Mathematica. I even read in MMA that the result of these two are the same.
5answers
3k views

### How to plot Fit functions?

If I do something like this f[x_]:=x^2 Plot[f[x],{x,1,10}] Mathematica plots the function $f(x)=x^2$, as expected. However, ...
2answers
1k views

### How can I consistently get a good logistic regression fit?

I'm executing the command NonlinearModelFit[data, c/(1 + a Exp[-b x]), {a, b, c}, x] with the data being ...
2answers
544 views

### Can't find a fit for Erf

I have the following numbers ...
1answer
277 views

### how to find curve fitting parameters without an explicit relation between x and y?

Let's say I have some experimental data (x,y) and I want to find some fitting parameters. But in my mathematical model, the fitting parameter are not in a simple equation that relates x and y. For ...
5answers
3k views

### Mathematica Implementations of the Random Forest algorithm

Is anyone aware of Mathematica use/implementation of Random Forest algorithm?
3answers
2k views

### Data fitting with Image processing feature detection

I have some 2D data that once plotted looks like the following ...
3answers
817 views

### What is behind experimental function: FindFormula?

In version 10.2 there is a new experimental function: FindFormula[]. I suspect that a genetic programming algorithm (symbolic regression) is behind this new ...
0answers
894 views

### Nonlinear least squares on a GPU with Mathematica 9

Update: A Mathematica wrapper for (https://github.com/zitmen/cuLM) should allow for us to directly implement the Levenberg-Marquardt algorithm in CUDA for nonlinear least squares fitting. In a ...
3answers
469 views

### Disentangling the data

An experiment yields a functional dependence on two variables $F(x,y)$, can be imagined as a 2D map. It is known that the function can be factored as follows $F(x,y)=fx(x) gy(y) +gx(x) fy(y)$. Given ...
1answer
330 views

### Fittting data with combination of an unknown number of Gaussians

I have data that I want to fit with a constant plus a combination of Gaussians, with their actual number being one parameter of the fit (besides the average and the variance of every one of them). ...
3answers
2k views

### Fitting ellipse to 5 given points on the plane

Five points are required to define a unique ellipse. An ellipse has five degrees of freedom: the $x$ and $y$ coordinates of each focus, and the sum of the distance from each focus to a point on the ...
4answers
10k views

### Fitting a two-dimensional Gaussian to a set of 2D pixels

Imagine I have a set of data like the following: ...
1answer
371 views

### Inconsistent DistributionFitTest results?

In pondering this question, I used Mariana's function to generate the following data. ...
1answer
530 views

### Model fitting to noisy data with a custom minimization function

I'm looking into fitting some data with Mathematica. I've got my head around how NonlinearModelFit works (I've been using the Levenberg-Marquardt algorithm for some ...
2answers
3k views

### FindFit returns worse result when putting constraints on parameters

I want to fit some data to a model of exponential decay using the FindFit function: ...
1answer
428 views

### Using perpendicular offsets in FindFit

I want to use perpendicular offsets in the built-in FindFit function. Are there any possible ways or do I have to code everything by myself?
1answer
327 views

### Findfit does not find the best fit

I am working on a project that needs curve fitting. The experimental data should be fitted with a model that calculated with an integration equation. At first, I enter my experimental data ...
0answers
989 views

### ParametricNDSolveValue or NDSolve + fitting

I have been trying to find the value for the parameter kestim that yields the best fit of a model to some data points. datac has ...
0answers
219 views

### Using FindFit to fit nonlinear ODE parameters, subject to a constraint (an inverse problem) [duplicate]

Similar to this post I am finding that constraints tend to make FindFit poor at finding a good fit. However, unlike the previous post, the constraints are required ...
1answer
536 views

### Test Goodness of fit for FindFit

Is there any way to get an estimate of the goodness of fit from FindFit, for instance getting the final error? The documentation doesn't provide any hints, and a quick Google search didn't return any ...
1answer
168 views

### Saving data from NonlinearModelFit

If you use NonlinearModelFit the results are put into some sort of output package. How do you save these packages so that you can go back to them later? My particular problem is that I generating ...