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

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5
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1answer
217 views

FindFit returns “tensors have incompatible shapes”

I'm trying to fit experimental data with FindFit and implicitly calculated function. It seems, that function works fine and satisfactorily approximates data when parameters are fed manually. However ...
5
votes
1answer
234 views

Forcing NonLinearModelFit through a point

Like the title says, is there a way to make an NLM fit pass through a specific point.
5
votes
3answers
386 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 ...
5
votes
2answers
604 views

How to fit one distribution to another?

I have a custom distribution created to model some experimental observations. While too complicated to include in this question, I can provide an example and some illustrations to convey a sense of ...
5
votes
1answer
189 views

How are p-values in fittings estimated?

I am trying to understand how p-values retrieved in a ParameterTable estimated but I couldn't find any specific information in the documentation about this. For instance, considering ...
5
votes
3answers
2k views

How can I obtain a smooth curve from my data but preserve two inversion points

I have a list of data points, {x, y}, my data. When I plot them, the curve is jagged. I want to smooth the curve and preserve the two sharp corners. This is a plot ...
5
votes
1answer
309 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
439 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
1answer
362 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 ...
5
votes
2answers
180 views
5
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1answer
843 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.
5
votes
3answers
141 views

Better output for NonlinearModelFit “ParameterTable”

The Standard table fo parameters of NonlinearModelFit is obtained from NonlinearModelFit[{{0, 1}, {1, 2}, {3, 3}}, a + b*x, {a, b}, x] %["ParameterTable"]] I ...
5
votes
2answers
3k 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

What does LinearModelFit depend on except for its arguments?

I thought this would be always true, but most likely it returns false. ...
5
votes
1answer
605 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, ...
5
votes
2answers
100 views

Linear fit with conditional noise distribution

I need to fit a linear model of the form $y_i = a · x_i + b + e_i$. The $e_i$ are independent noise from a distribution that depends on $x$ as well as on global parameters of the data; however, the ...
5
votes
1answer
216 views

Intersection of a ListPlot3D surface with a plane

I'm trying to use Mathematica to analyze some physics data from an experiment, more precisely, I have to fit a 2D data series with a one dimension function. At the moment I'm able to load and plot ...
5
votes
1answer
366 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
2answers
770 views

Numerical Integration as Model for Nonlinear Fit

I'm trying to do a fit for parameters of a function within an integral but I'm getting errors when I try and run it. Essentially I want the following fit to work out: ...
5
votes
1answer
495 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 ...
5
votes
1answer
272 views

ODE fitting to dataset

So, I have a ODE system, it is a complex biochemical kinetic mechanism with six species changing over time. ...
5
votes
1answer
937 views

Linear regression with x and y errors

I have a question about finding a linear regression weighted with x and y errors. I found the answer provided by 0x4A4D in Estimate error on slope of linear regression given data with associated ...
5
votes
0answers
92 views

Multivariate Adaptive Regression Splines (MARS) - Mathematica implementation?

Does anybody have or know of a Mathematica implementation of the Multivariate Adaptive Regression Splines (MARS) algorithm?
5
votes
0answers
129 views

Custom Methods for NMinimize/NonLinearModelFit

Is there a way to write custom methods for NonLinearModelFit or NMinimize? To give background, I currently have a batch of code ...
5
votes
0answers
89 views

Third syntax version of LogitModelFit: unexpected result of “BestFit”

The third listed syntax version of LogitModelFit allows one to specify input in a simple way: Only a design matrix (with a row of values of the explanatory input ...
5
votes
0answers
738 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 $$ ...
4
votes
3answers
755 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
2k views

NonlinearModelFit does not find a good fit

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

Problem with fit on a numerical function

My question is related to a previous one: Problem with simple fit, where I had a problem to fit a simple analytic function $\dfrac{a}{\sqrt{b^2-x^2}}$. The solution proposed in Problem with simple ...
4
votes
1answer
1k views

How to make a multi-peak histogram fitting

I got a multipeak histogram from my data and want to fit it using a Gaussian Distribution function. ...
4
votes
4answers
694 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 ...
4
votes
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, ...
4
votes
2answers
701 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 ...
4
votes
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 ...
4
votes
2answers
152 views

How to find analytical expresion for data from image

I need to find an analytical expression for the data collected from an image. I found a relevant topic on how to extract the data in here. But there are some differences in my question. I have this ...
4
votes
2answers
92 views

Problem with a simple Fit

I have defined two functions to fit $\dfrac{a}{\sqrt{x^2-b^2}}$ and $\dfrac{a}{\sqrt{b^2-x^2}}$. ...
4
votes
1answer
922 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 ...
4
votes
1answer
116 views

Mystifying failure of NonlinearModelFit

Fitting the following two time-series (two repeats of the same exponential growth process) ...
4
votes
1answer
257 views

Removing Linear drift from an oscillating data

I have an array of 800,000 data measured at 1.1s time gap. It is oscillating data but has clear linear drift. I want to remove this linear drift. But the estimates by ...
4
votes
1answer
672 views

How do I draw a credible velocity vs. time graph using Locators?

This is partly a math question, partly a Mathematica question. For educational purposes, I'm making a simple demonstration to create a velocity over time graph from six locators. On the basis of ...
4
votes
1answer
595 views

How to get confidence bands of parameters from a fitting procedure?

I have done fitting of data points with a given model that has two parameters (A and B), using NonlinearModelFit. The result of the fit is the maximum of the ...
4
votes
2answers
124 views

FindFit and NMinimize to fit a parametric model (minimize the distance of two curves)

I am trying to find a fit to the cumulative distribution of a set of points using FindFit or NMinimize. In particular, I would like to find the parameters of the cdf of the Beta Distribution that ...
4
votes
2answers
259 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 ...
4
votes
1answer
3k 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
2answers
89 views

How to use Evaluation Monitor in conjunction with NonlineaModelFit?

I am trying to find out how many function, gradient and hessian evaluations are made when i run NonlinearModelFit for example in this case ...
4
votes
3answers
262 views

How to fit parameters in a system of coupled differential equations

Problem description: I'm studying a chemical reaction that can be modeled by a system of coupled differential equations, and I want to use measured data to determine the parameters that appear in the ...
4
votes
1answer
374 views

Fitting numerical model to experimental data

I have diffusion equation with the initial/boundary conditions: ...
4
votes
1answer
392 views

Using a user defined NormFunction in FindFit or NDSolve

I would like to use a different norm instead of the 2-norm in FindFit (Mathematica 9). For example, instead of using $$\sqrt{\sum (x_{\mathrm{model}} - ...
4
votes
1answer
640 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 ...
4
votes
1answer
75 views

Proper command to fit a distribution with data incomplete in a known way

Here is my scenario: got some data that I have to fit to a specific parametric family of probability distributions (cannot be changed). Data consist of several bunches of integers between, say, 0 and ...