All Questions
Tagged with linearmodelfit or fitting
307 questions
33
votes
2
answers
8k
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 ...
- 333
52
votes
5
answers
15k
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 ...
- 7,733
58
votes
6
answers
22k
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 ...
- 2,317
43
votes
2
answers
5k
views
What are some common issues with fitting functions to data?
Mathematica has numerous functions designed to, or capable of, fitting known functions, and finding unknown functions to match data sets. What are some common issues that come with finding those fits?
- 8,667
35
votes
6
answers
19k
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 ...
- 353
28
votes
6
answers
23k
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 ...
- 281
22
votes
3
answers
5k
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
<...
- 221
50
votes
8
answers
9k
views
Fitting points to tilted, off-center ellipse
I have 24 x-y points that are supposed to form an ellipse.
...
- 5,191
27
votes
4
answers
6k
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:
...
- 391
27
votes
6
answers
16k
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 ...
- 11.5k
31
votes
3
answers
5k
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.
- 3,886
21
votes
5
answers
10k
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
...
- 959
31
votes
5
answers
6k
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 questions is how can ...
- 1,257
25
votes
1
answer
2k
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, ...
- 449
9
votes
1
answer
6k
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
...
- 763
4
votes
1
answer
972
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 ...
- 363
20
votes
2
answers
817
views
Adding Regularisation to Built-in Interpolation Function
tl;tr; How to improve performance of regularised Interpolation?
Context
Since Version 12, Mathematica now incorporates a range of (underrated IMHO) regularisation ...
- 23.1k
18
votes
3
answers
3k
views
2D smoothing spline interpolation
Does Mathematica have 2D smoothing spline interpolation built in?
I requires an interpolation method with smooth first derivatives and cubic bivariate splines fulfill this nicely. In python I would ...
- 13.8k
15
votes
1
answer
8k
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 ...
- 1,201
15
votes
2
answers
2k
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 ...
- 62.3k
15
votes
1
answer
1k
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).
...
- 815
25
votes
3
answers
2k
views
Sensitivity of NonlinearModelFit to model
I have come across a circumstance where NonlinearModelFit is very sensitive to the model used. I am aware that NonlinearModelFit ...
- 16.8k
19
votes
3
answers
5k
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
...
- 191
14
votes
2
answers
1k
views
Fit a function to data so that fit is always equal or less than the data
I have a set of measurement data and I try to fit there a function (a Exp[b x] + c Exp[d x] - o). I have two problems:
The fit function does not converge nor after ...
- 143
10
votes
1
answer
5k
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 ...
- 8,667
9
votes
1
answer
8k
views
NonlinearModelFit does not find a good fit
I am trying to fit my data to the following function,
$$\frac{a b t \left(\log \left(\frac{-a d t+a t-1}{a d t}\right)-2\right)}{4 (a t-1)}-c$$
...
- 253
4
votes
2
answers
682
views
Fourier Transform to help guess with NonLinearModelFit
I imported some data in Mathematica which I cleaned a bit. This process went well. I also managed to plot it, and tried to take the Fourier transform of the data and plot it again. I'm not sure if I ...
- 41
21
votes
2
answers
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:
...
- 6,715
17
votes
3
answers
5k
views
Finding distribution parameters of a gaussian mixture distribution
Short version: how to estimate the parameters of a mixture of multivariate normal distributions (i.e.: Gaussian mixture model)?
Long version.
I am trying to estimate the parameters of a mixture of ...
- 273
15
votes
1
answer
2k
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:
...
- 2,188
13
votes
2
answers
2k
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 (...
10
votes
1
answer
2k
views
ODE fitting to dataset
So, I have a ODE system, it is a complex biochemical kinetic mechanism with six species changing over time.
...
- 101
8
votes
1
answer
3k
views
Find a Fourier series from discrete data
I am trying to fit a Fourier cosine series to discrete data. I read through this, but I was not able to understand it. The data should be periodic with a period of $0.2 \text{ m}$, and it is the ...
- 105
8
votes
3
answers
2k
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 ...
- 277
6
votes
3
answers
968
views
Multi-peak fitting for peak position
I have a {x,f} data-set featuring multiple peaks. The peaks evolve with a second variable y. I would like to fit the multiple ...
- 81
6
votes
1
answer
2k
views
Finding NonlinearModelFit of multiple data sets with the same parameters and in two dimensions
I have multiple sets of data (between 3 and 6 depending on the cases) dependent of space, time, and some parameters. The data are the response of a harmonic oscillator under a non-trigonometrical ...
5
votes
3
answers
4k
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
...
- 321
5
votes
2
answers
2k
views
Mathematica Interpolation or approximation
I have lists of points X and Y.
{1212,1216,1217,1219...}, {1,2,3,4,5,6...}
I combine ...
- 161
5
votes
3
answers
715
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 ...
- 3,268
4
votes
3
answers
797
views
Applying an exponential decay fit with uncertainties
I have some data from a radioactive decay experiment that I'm trying to fit an exponential decay curve on that will take account of the uncertainties on the data, and then ideally return the data for ...
- 505
1
vote
1
answer
262
views
NonLinearFit with data
i've data looking like this:
ListPlot[data]
Now I want to make a NonLinearFit
...
- 13
26
votes
4
answers
2k
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 ...
- 1,133
20
votes
1
answer
3k
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 ...
- 303
18
votes
4
answers
27k
views
Fitting a two-dimensional Gaussian to a set of 2D pixels
Imagine I have a set of data like the following:
...
- 761
15
votes
2
answers
3k
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.
...
user484
15
votes
4
answers
929
views
How to split data into clusters based on fitting to function
I have data which looks somewhat like this:
On the picture, you can see that the data can be described by 2 linear functions - if you manage to split it into 2 groups, each can easily be fitted with <...
- 513
9
votes
1
answer
4k
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 ...
- 369
7
votes
1
answer
1k
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
...
- 71
7
votes
5
answers
8k
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, ...
- 697
7
votes
1
answer
502
views
How to derive SinglePredictionBands from a NonlinearModelFit model
I have found NonlinearModelFit to be extremely useful in my work. Here I have fit 4 points to a function and am being asked to explain how the 95% SinglePredictionBands associated with the plot below ...
- 1,417