# Tagged Questions

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

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### How does Mma compute Confidence Intervals?

I am trying to understand how Mma computes the Confidence Intervals after a NonlinearModelFit. Consider the following example: ...
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### What is the best distribution for my histogram?

I defined a security bound for a random walk (cube with 15 lengh) and i have this code to obtain a sample of the random times at which the random walk crosses the boundary for the first time: ...
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### 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. ...
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### 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 ...
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### Least Square Data Fit /Design Matrix

I am trying to learn how to use the DesignMatrix function in Mathematica and how to perform a LeastSquares fit. I am at end of ...
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### 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 ...
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### 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?
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### 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 ...
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### Fitting a two-dimensional Gaussian to a set of 2D pixels

Imagine I have a set of data like the following: ...
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### 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 ...
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### Using StepMonitor/EvaluationMonitor with DifferentialEvolution in NMinimize

My question about tracking the progress of a minimisation/fitting process is two-fold: 1. The first part of my question can be considered a slight duplicate/follow-up of this question. There the OP ...
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### Inconsistent DistributionFitTest results?

In pondering this question, I used Mariana's function to generate the following data. ...
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### 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 ...
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### 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 http://www.redditblog.com/2015/04/...
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### Make NonlinearModelFit return continuous function

Suppose I want to fit the dataset ...
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### 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 ...
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### 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 ...
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### 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 ...
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### Locally Weighted Linear Regression

I am following the online Stanford Course in Machine Learning and I am trying to implement the algorithms on the fly in Mathematica. Currently, I have issues with minimizing the Locally Weighted ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 \$x=\...
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### 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 ...
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### 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 ...
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### How to measure accuracy of prediction distribution?

I have been trying to come op with a way to test if my dataset follows a Poisson distribution. Normally one would use the DistributionFitTest function, but here is ...
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### Looking for ideas for handling a complicated fitting problem

I have the following data: ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### Fitting does not work

I have a set of points, which is basically one minus a Lorentz curve. And the NonlinearModelFit ...
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### 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 ...
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### 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 ...
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### 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.
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### Having trouble fitting data using NonlinearModelFit

I'm trying to fit data = {{2002, 45000}, {2004, 90000}, {2005, 120000}, {2013, 211000}}; to an exponential function ...
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### Extracting fit weights directly from a FittedModel object

Suppose I have the following data: ...
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### 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. ...
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### 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 (...
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### 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 ...
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### Why LinearModelFit is slower than NonlinearModelFit?

Why LinearModelFit is slower than NonlinearModelFit? ...
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### RSquared: LinearModelFit vs NonlinearModelFit

I'm trying to understand the differences between LinearModelFit and NonlinearModelFit. One thing I notice is that the ...
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### 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 ...