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

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30 views

How to make an equation to fit measured data [on hold]

I want to make an equation based on my measurements and I have no idea where to start from. I have measured 3 parameters(x1,x2,x3) and calculated the 4th(y). How can I make an equation that can ...
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1answer
35 views

Multiple Linear Regression - obtaining equation with constant term

I am trying to use the LinearModelFit function to obtain a linear regression of my 5 inputs for my single output. I have the input data: ...
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0answers
34 views

Fitting data involving units

I want to fit some data to a model. However, if the data involves units in the independent variable, fitting seems not to work. As an example, consider the code ...
3
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1answer
83 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 ...
0
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0answers
42 views

Fit a 2 variable ODE to data and estimate parameters [on hold]

I am trying fitting on mathematica for the first time. I can do the one variable ones using the sample code. But here I cannot. Can someone help me fit to the data to get answers. I am trying to fit ...
1
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2answers
76 views

How to fit exponential function which is not converging

I performed an experiment where I measured diffusion in a lipid bilayer. I performed the measurement by fluorescently labeling some molecules in the bilayer, and the irradiating them with light ...
11
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1answer
278 views

Fit two intersecting straight lines in Mathematica

I am trying to do a Kurie analysis of the double beta decay of Strontium-90. Here we have two straight sections, and I need to obtain a value for the intersection along with an error for it. I ...
7
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1answer
179 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 ...
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0answers
24 views

fitting system of ODEs - “part2 of {} does not exist” errod

I'm trying to fit my data to a system of ODEs: x'[t]==a*x[t]+b*y[t] y'[t]==c*y[t]+d*x[t]+e*z[t] z'[t]==f*z[t]+g*y[t] having t,x[t],y[t],z[t]. I followed the code ...
1
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1answer
109 views

show fit information on plot

After performing a fit in Mathematica, I would like to show the fitted parameters in a box on the plot showing the fitted function. How would I go about achieving that? Here is a MWE: ...
0
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1answer
88 views

Fitting to a sigmoidal model

I am trying to fit a set of stochastic data to a sigmoidal function, but it's not working. Can you please help? Here is the function I am trying to fit to my data. ...
0
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1answer
94 views

Non-linear fit incorporating the error bar information

I make a non-linear fit to a data set. All my data have some error bars. Is it possible to do a fit to the data incorporating the error bar information? (I am not talking about the ...
7
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1answer
102 views

Inconsistent DistributionFitTest results?

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

NonLinearFit with “complicated” integral model

I have a set of data $y_i (z_i)$ with errors $\Delta y_i$ ...
5
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2answers
465 views

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: ...
1
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1answer
36 views

FindFit::nrlnum What am I doing wrong?

I have a model called qobs: ...
2
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1answer
56 views

nonlinearnodelfit with a matrix as weights

I have to fit a non linear model to my data and I am trying to use nonlinearmodelfit. The problem is that I have systematic errors, so the ...
1
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1answer
44 views

FindFit (Jacobian Error) [duplicate]

I, like others before me, am struggling with FindFit. So, I tried a simple example. ...
-1
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1answer
38 views

How to fit one parametric array to another numerical array?

I have two arrays of length n. One of them is obtained by experiment, so every element of the array is a number. The other array is parametric, each element is a ...
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0answers
37 views

Speeding up Nonlinearmodelfit by constraining parameters?

I have a complicated parametric PDE that can be fitted to some data with NonlinearModelFit, but takes several hours to estimate the best values of the four free parameters. Currently, the code ...
0
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1answer
74 views

Nonlinear fit with piecewise functions

I have an ensemble of data points $(x_i,y_i)$ and I need to fit them according to $y=F(a,b,x)$ if $x \leq x_{ref}$ and $y=G(c,d,x)$ if $x \geq x_{ref}$. The parameters I need to adjust are then ...
1
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1answer
88 views

Fitting data using a series of Sin and Cos

I have the following data representing the normal displacement caused by a normal load applied at the middle cross section of a cylinder: I've made the data available here. I am trying to fit ...
1
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1answer
81 views

Can ParametricNDsolve be used for coupled PDEs with 5 parameters?

I have a system of coupled PDEs with five parameters that I only know ranges for rather than explicit values, and I was wondering if I could define a parametric equation with ParametricNDSolve and ...
0
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0answers
48 views

Simultaneously fitting data sets with many variables as free parameters

I found a partial answer in the documentation centre, but would like to expand on it and know how can I fit multiple sets of data and extract the parameters from them. It is an eigenvalue problem - We ...
5
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1answer
146 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, ...
3
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1answer
251 views

NonlinearModelFit does not find a good fit

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

Minimizing the maximal residual in mathematica

With this: d1 = 10; d2 = 4; mat = RandomReal[{-1, 1}, {d1, d2}]; vec = RandomReal[{-1, 1}, d1]; LeastSquares[mat, vec] ...
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0answers
97 views

histogram fit for probability density

I am trying to fit the (probability density) histogram of some data with the exponential function, but I am having difficulties. My raw data are in file called ...
1
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2answers
131 views

FindFit giving weird values on a logistic equation

I was trying to fit a set of data onto a logistic equation, however it ended up telling me that the initial value when $t=0$ is greater than the maximum limit, thus I am led to believe that it isn't ...
0
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1answer
99 views

Exporting tables of interpolating functions

A few weeks ago I asked a question about manipulating parameters in NDSolve (Looping with NDSolve?) , and received some very helpful advice about the manipulate environment; now I want to take the ...
2
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2answers
182 views

Line of best fit on LogLog plot

I have a LogLog plot, and i'm unsure about how to fit a line to it. The data represents a calibration curve. ...
0
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1answer
75 views

Replicating Excel output using Mathematica

I have 2 columns of data in Excel. One is inputs the other is outputs. I ask Excel to make a graph of that data and to fit the data to a power trendline. Excel does this and it's fine as far as it ...
16
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5answers
555 views

Finding the intersection of a curve with an interpolation function

There are no issues trying to find the intersection points of two defined curves. ...
1
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2answers
137 views

Can't find a fit for Erf

I have the following numbers ...
1
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2answers
76 views

How can I get a fully functional FittedModel when fitting data to a pointwise function?

When I am fitting data with a pointwise function using NonlinearModelFit, the produced FittedModel fails to calculate variances ...
0
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0answers
34 views

Supply parameter values in NormFunction of FindFit

As I understand the input to the NormFunction is a list of residuals. Is there a way to get parameter values into the NormFunction as well? I ran into a problem where the norm depends on the values of ...
0
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1answer
45 views

Constraining some rows from LeastSquares to lines

For two matrices, A and B, with dimensions {n,p} and ...
0
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0answers
47 views

Find Numerical Derivatives (With Errors) given some data

I have a question. Suposse I have some data with their respective errors: ...
7
votes
1answer
128 views

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 ...
3
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2answers
128 views

Multi-Fitting with Nonlinear model

I want to fit experimental data by the H-N model. Here is the H-N model: $$\text{EHN}(T)\text{=}\text{E$\infty $}+\frac{\text{E0}-\text{E$\infty $}}{\left(1+\left(i \omega\tau(T_g)10^{-\frac{\text{C1} ...
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0answers
121 views

Non linear model fit mathematica

I want to fit experimental data (temp,alpha) to the following equation for calculating k and Ea -Log[alpha]^n = function(k,Ea,temp) However i do not know ...
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2answers
149 views

Fitting a beta distribution to a probability density curve

If I have a spectral data set showing measured energy on the y-axis and frequency on the x-axis, how would I go about fitting this to a beta distribution? For example, lets say I had the data for the ...
-1
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1answer
587 views

How do I calculate RSquared in Mathematica 9? [closed]

I imported data from an Excel package and used LinearModelFit to return a FittedModel: FittedModel[6.90762 - 0.999573 x] How ...
1
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1answer
189 views

Fitting data using a differential equation

I have data generated from two functions given below. How can I go about finding a fit of the form: y'[x] == -(a + b/(c + d y[x] + e F[x] )) where a,b,c,d,e are ...
2
votes
3answers
188 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 ...
0
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2answers
108 views

Any other way to get a better FindFit for my data besides good initial parameters?

I fit some data with FindFit and NonlinearModelFit with some constraints and I am not getting a good fit with my data. I read ...
1
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1answer
194 views

Curve fitting data to model

Example Assumptions: ...
2
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3answers
210 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 ...
4
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1answer
173 views

Fitting triangular function with HeavisideTheta

I have a problem fitting a triangular function (like potential vs. time in cyclic voltammetry) with a HeavisideTheta function. I just want to get used to ...
1
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1answer
141 views

How do I construct a non-linear model from experimental data?

I want to find a function $w=f(x,y,z)$ that fits experimentally determined values of w. For example, assume ...