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

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9
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1answer
1k views

Measure length and diameter of objects in an image

I am new to Mathematica, and I am trying measure length and diameter of rectangular objects in an image. I wanted to fit rectangles in the objects, and then get the values. Can I do that with ...
8
votes
4answers
4k 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?
8
votes
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 ...
8
votes
4answers
9k views

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

Imagine I have a set of data like the following: ...
8
votes
1answer
338 views

Inconsistent DistributionFitTest results?

In pondering this question, I used Mariana's function to generate the following data. ...
8
votes
1answer
281 views
8
votes
1answer
333 views

How can I improve my prediction for the end time of the Reddit button game?

There is an April Fools game on Reddit where users with accounts can press a button (once) to reset a 60 second countdown timer: https://www.reddit.com/r/thebutton ...
7
votes
3answers
166 views

Make NonlinearModelFit return continuous function

Suppose I want to fit the dataset ...
7
votes
3answers
3k 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 ...
7
votes
2answers
356 views

Maxwell fit in 2 dimensions

The histogram below shows the 2D-velocities v of a micrometer sized particle in a plasma measured from image to image (60 Hz) over 33,33 sec. I would like to fit ...
7
votes
3answers
184 views

Fitting data with interdependence

I have an issue, of which I'm not sure it can be solved, with or without Mathematica. I feel as if it should be possible, but I'm quite clueless as to how. Some introduction is required. I'm working ...
7
votes
4answers
869 views

How to fit a surface to 3D data in Mathematica?

I have a set of data coordinates which is mostly compatible with an Ellipsoid: {{x1,y1,z1},{x2,y2,z2}, ... , {xn,yn,zn}} Now I want to find the best 3d volume ...
7
votes
2answers
110 views

Behaviour of RegionDistance with Ellipse?

The data is: data = {{13, 60}, {36, 35}, {70, 29}, {106, 41}, {118, 72}, {94, 94}, {49, 99}, {24, 85}}; When I try to find a fit circle,So my method is work ...
7
votes
1answer
337 views

Computing launch parameters for hitting a point in 3D with projectile under influence of wind

The end goal of this problem is to compute functions which describe the launch parameters which are needed to hit a specified goal in 3D in the presence of wind disturbances. This is as far I have ...
7
votes
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 ...
7
votes
2answers
1k views

How can I compute and plot the 95% confidence bands for a fitted logistic regression model?

I have a set of binary data that I' d like to fit a logistic regression model to and show the 95% confidence band around the fitted function. I can produce the regression model but how do I compute ...
7
votes
1answer
1k 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 ...
7
votes
1answer
172 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 ...
7
votes
1answer
590 views

Fitting a numerical integral via NonLinearModelFit to magnetic data

I'm new to Mathematica and I'm currently trying to fit $$m_T (H,T) = N_T \int\limits_0^{\infty} \frac{x k_\text{B} T}{\mu_0 H} \mathcal{L}(x) \text{pdf}(D_\text{mag}) \text{d}D_\text{mag}$$ with ...
7
votes
1answer
830 views

What exactly is “ParameterErrors” of NonlinearModelFit?

I am trying to get what I call a "$\chi^2$ fit". This means taking a function $f(x,p)$ of the variable $x$ with a parameter $p$ and finding the value of $p$ that minimizes the "distance" from a data ...
7
votes
0answers
104 views

FindFormula Control [closed]

FindFormula is great start on the path to full symbolic regression and I realize it's level of development is only experimental at this stage. But if I happen to ...
6
votes
2answers
3k 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 ...
6
votes
3answers
229 views

Looking for ideas for handling a complicated fitting problem

I have the following data: ...
6
votes
1answer
246 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 ...
6
votes
2answers
240 views

Implement planar correction for skewed 3D profilometric data

I have some data that represents small-scale surface topography. The data is planar but not flat because it's impractical to level this microscope to a tolerance of microns. It looks like this: I'd ...
6
votes
3answers
2k views

Find a best fitting curve for some data with no regular pattern

Suppose some data with no regular pattern is given, so common patterns of functions all fail to fit it. Then how can one find the best fitting curve? I believe there will be some data for which we can ...
6
votes
2answers
239 views

Transforming noisy multivariate data

I’ve been racking my brain all afternoon on trying to solve this… I have a set of noisy co-ordinate data data = {{x1,y1,z1}…..{xn,yn,zn}} that forms an ...
6
votes
2answers
350 views

Find fit of an experimental PDF

After quite some struggle, I managed to put up a code that is syntaxically correct. The goal is to find the parameters for a gamma distribution that best match experimental data. The data is a set of ...
6
votes
1answer
302 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
2answers
206 views

Fitting does not work

I have a set of points, which is basically one minus a Lorentz curve. And the NonlinearModelFit ...
6
votes
1answer
751 views

Having trouble fitting data using NonlinearModelFit

I'm trying to fit data = {{2002, 45000}, {2004, 90000}, {2005, 120000}, {2013, 211000}}; to an exponential function ...
6
votes
1answer
1k 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 ...
6
votes
1answer
172 views

Default algorithm in NonlinearModelFit

Does anyone know the default algorithm used in NonlinearModelFit? The documentation gives several possible algorithms, but I can't figure out what it uses if you do not specify the algorithm. Thanks. ...
6
votes
1answer
90 views

Extracting fit weights directly from a FittedModel object

Suppose I have the following data: ...
6
votes
1answer
1k 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 (...
6
votes
1answer
160 views

FindFormula can't deal with the population data from Wolfram server

Bug introduced in 10.2 and fixed in 10.3 In the documentation of FindFormula, the first application of it is to predict the population of Poland. ...
6
votes
2answers
366 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 ...
6
votes
1answer
149 views

Why LinearModelFit is slower than NonlinearModelFit?

Why LinearModelFit is slower than NonlinearModelFit? ...
6
votes
2answers
667 views

RSquared: LinearModelFit vs NonlinearModelFit

I'm trying to understand the differences between LinearModelFit and NonlinearModelFit. One thing I notice is that the ...
6
votes
1answer
346 views

Using Manipulate to dynamically correct the baseline of a signal

i have data with a baseline and will correct it with a polynomial fit using Manipulate to see immediatly the changes in the resulting spectrum. It works so far, but ...
6
votes
2answers
252 views

how recover lost data of coordinates from contourplot of mention data?

I have made Contour Plot for a lot of data, like this ...
6
votes
1answer
471 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 ...
6
votes
1answer
442 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 ...
6
votes
1answer
68 views

Simulated Annealing, SearchPoints and InitialPoints options set at the same time

I have a function that needs to be minimized. Since the function depends on real-time data (which is fetched every few hours, and the function is redefined according to the new data), I have to run ...
6
votes
2answers
791 views

Find parameters of ODEs to fit solution data

Problem How to find the initial conditions x[0],y[0] and the optimal value of parameters ...
6
votes
0answers
284 views

Problems extending NelderMeadMinimize into 2D

Update The eventual route I followed was to adapt a version of the NM-simplex written in C and link to it with MathLink. Once I've tested this out fully I'll post it here. I've been playing around ...
5
votes
3answers
757 views

Finding exponential model from data [duplicate]

I'm trying to find an exponential model from data for a homework problem. There is an accompanying video explaining how to do the bigger problem but it omits any instructions on the step where the ...
5
votes
3answers
200 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 ...
5
votes
1answer
266 views

Is there any strategy to have a compiled version of FindFit or NonlinearModelFit?

Disclaimer: This is not a precise question with a definite answer. I know that neither FindFit nor NonlinearModelFit is in the ...
5
votes
4answers
813 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 ...