Questions on the use of Mathematica to construct models for approximating empirical data. (FindFit[], Fit[], LinearModelFit[], NonlinearModelFit[], etc.)
30
votes
4answers
828 views
How to visualize 3D fit
I have a data set of x,y,z values and I fit a function of x,y to the data. This works, but I can't come up with a nice way to ...
24
votes
4answers
2k 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 ...
16
votes
3answers
845 views
Data fitting with Image processing feature detection
I have some 2D data that once plotted looks like the following
...
15
votes
2answers
620 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 ...
15
votes
1answer
506 views
Compact Rational Function Fitting
I have some data from a study that I am trying to fit with a rational function of arbitrary form:
$y(x) = \frac{\sum_{i=n}^m A_ix^{i/q}}{\sum_{j=o}^p B_jx^{j/r}}$
where $i$, $j$, $k$, $l$, $m$, $n$, ...
14
votes
2answers
576 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:
...
14
votes
3answers
771 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 ...
13
votes
5answers
2k 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 ...
12
votes
3answers
577 views
Finding a fit to a multi-dimensioned function
I have a model function $f:\mathbb{R}^2\rightarrow\mathbb{R}^2$, and a bunch of data points for which I'd like Mathematica to fit for me. Unfortunately FindFit ...
11
votes
4answers
2k 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
votes
4answers
2k 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
...
11
votes
2answers
409 views
Trying to fit an unknown extreme distribution
First up, I'm quite new to Mathematica so any hints on better code would be greatly appreciated.
I have some histogram frequency data from an unknown distribution that I'm trying to fit. Here's the ...
10
votes
4answers
607 views
Mathematica Implementations of the Random Forest algorithm
Is anyone aware of Mathematica use/implementation of Random Forest algorithm?
10
votes
3answers
690 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
...
10
votes
2answers
256 views
Unexpected differences with various uses of NormFunction
I would expect all of the following to give the same answer (2.12467) but only half of them give this answer. The others seem to be using the default ...
10
votes
2answers
350 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 ...
10
votes
1answer
733 views
Fitting a spline to data with FindFit?
I am trying to find a function that fits my almost linear data. A high order polynomial model has too much residual. So I was hoping to use Mathematica to fit splines to the curve.
This is what I ...
10
votes
0answers
130 views
9
votes
3answers
810 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
...
8
votes
3answers
442 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 ...
7
votes
4answers
823 views
Can one force a linear regression fit to go through the origin?
As the question says, can one force a fit through the origin $(0,0)$ as one can when fitting a trendline to your data in MS Excel? If so, how do you do that?
6
votes
6answers
2k views
How to determine the center and radius of a circle given three 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 ...
6
votes
2answers
491 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:
...
6
votes
1answer
136 views
Obtaining standardised regression coeffiecients
Regression coefficients are the constant that indicate the rate of change in one variable as a function of change in another. Standardised regression coefficients are the same, but refer to a change ...
6
votes
1answer
116 views
Smoothing/Averaging 2D Vector Fields
I have a list of 2D vectors defined by {{x,y},{u,v}} and would like to smooth or average the vectors. For example here are 2 vector fields, the second has noise ...
6
votes
1answer
193 views
Fix end point in smooth kernel distribution density
I am using some extreme value fitting method which results in a parametric distribution for values exceeding some threshold, all values $\geq 0$.
For smaller values I'd like to use a smooth kernel ...
5
votes
2answers
609 views
NonlinearModelFit Problem
I have some problems with the NonlinearModelFit:
NonlinearModelFit[data,
A (1 + Cos[a x]) + B (1 + Cos[b x]) + c , {A, B, a, b, c}, x]
The model should fit my ...
5
votes
3answers
538 views
Finding the linear regression of data and plotting it
This is for a physics report that I have to hand in. I have a list of two-dimensional data points that approximately form a linear line.
I want to:
calculate the best linear fit.
put both data ...
5
votes
1answer
142 views
LinearModelFit with millions of rows
I'd like to do a simple regression with millions of rows of (x,y) data. It seems to be too long for Mathematica. Is there a way to speed it up? It shouldn't be that hard to do, I am not sure what ...
5
votes
2answers
232 views
How to find Matano plane
I have discrete collection of data points (10 to 10^4). I want to describe them by a continuous function and find a x value z, ...
5
votes
2answers
330 views
In finding a logarithmic fit for some data (of the form a*Log[b*x]), WolframAlpha succeeds where Mathematica 7.0 fails, why?
I would like to fit a function of the form: $a \log(b x)$ to a set of data:
...
5
votes
1answer
135 views
Specify a constraint on an interval under FindMinimum
I have an interpolated function that looks like this:
$\hskip1.2in$
and, based on extreme and critical points, I want to use a polynomial to approximate the function. The points in question are:
...
5
votes
0answers
64 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?
5
votes
0answers
194 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
0answers
227 views
NonlinearModelFit weights
I would like to know how to perform a nonlinear regression on a table with measurement errors. The table consists of two columns, and both have errors. I've been watching some tutorial and it is very ...
4
votes
3answers
385 views
Output of NonlinearModelFit differs from the correct result
I'm having a bad time dealing with the NonlinearModelFit in Mathematica 8, since the result given is a bit imprecise. An example is given on potential regression, ...
4
votes
1answer
470 views
NonlinearModelFit::cvmit: Failed to converge to the requested accuracy or precision within 100 iterations
I have got a problem in my program with NonlinearModelFit:
...
4
votes
1answer
135 views
Multinomial logistic regression
Has anyone done multinomial logistic regression in Mathematica?
The binomial case is essentially done on the LogitModelFit documentation page and works fine.
I am ...
4
votes
2answers
162 views
What can I do to eliminate the error FindFit::nrjnum:?
I am testing the "Power Law with finite-time singularity" hypothesis for world population growth for a project.
The data I'm using (same behaviour should also be exhibited by the stock market, thats ...
4
votes
1answer
231 views
Time approximation of decrypting RSA algorithm
I've written a function that encrypts a text using the RSA algorithm. It then decrypts it using prime factorization, and takes the time it took to decrypt it and puts it in a vector together with the ...
4
votes
0answers
457 views
Analytical model fitting
I have a special type of model fitting problem that I am trying to solve in Mathematica. Any insight how to attack it using available tools of Mathematica will be great to hear.
We have a variable
$$
...
3
votes
4answers
163 views
Remove linear trend from data
I have a large data set with 150k lines and two data columns. I noticed that there is a linear trend, which I want to remove. So, I do the following:
first fit with a linear model
...
3
votes
1answer
144 views
Getting slightly different results in fitting a logit model in R and Mathematica
I'm fitting some data to a Logit model in both Mathematica and R and I'm getting slightly different results.
R code:
...
3
votes
5answers
416 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, ...
3
votes
2answers
121 views
Linear regression in a chosen range of points
Hi I'm absolutely newbie in Mathematica and have following problem:
My list looks like {{50, 0.75}, {51, 0.76}, ..., and I want to choose a range out of my ...
3
votes
1answer
86 views
Does LinearModelFit perform an ordinary linear regression (least squares)?
Does LinearModelFit give an ordinary linear regression? I see lots of options, but nothing like "least squares" or OLR.
3
votes
1answer
401 views
How do I find the best parameter to fit my data if the model is a interpolating function?
Hi I have a question regarding to find the best parameters for my model to fit my data.
I have 3 ordinary equation, and I now just picked some parameters (...
3
votes
1answer
119 views
NonlinearModelFit returning nonsense for very simple data
In fitting the following data, if I first log transform the y-values and use LinearModelFit I get a set of parameters that fits the data:
...
3
votes
1answer
296 views
Why FindFit could not exactly fulfill condition?
I tried to fit some data with boundary conditions, but FindFit just could not work. Does anyone know the reason?
Details:
The function to be fitted is ...
3
votes
1answer
128 views
Error message from evaluating NonlinearModelFit
I am trying to fit data to a Morse potential using NonlinearModelFit as follows:
...
