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

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1
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1answer
53 views

Trouble fitting with NonlinearModelFit

I'am having a bit of a headache comparing the results from the NonlinearModelFit to a particular dataset. I have the following dataset, ...
2
votes
1answer
89 views

Find the best fitting function for some experimental data

I am almost new in Mathematica, and so I have some problems that may appear basic for you. I am given a set of data taken from an experiment. I am supposed to find the curve that best fits them. The ...
2
votes
1answer
108 views

FindDistributionParameters and Hypothesis Testing

Please excuse me if I am making any logical error in posting this question since I am not a math major. However, let me post my question. I am trying to fit multivariate parametric distribution to ...
1
vote
1answer
190 views

how to find curve fitting parameters without an explicit relation between x and y?

Let's say I have some experimental data (x,y) and I want to find some fitting parameters. But in my mathematical model, the fitting parameter are not in a simple equation that relates x and y. For ...
0
votes
0answers
80 views

How to make a twice-differentiable function that approximates some data?

I have some time series data that I would like to approximate with a twice-differentiable function. Each time series has ~10,000 datapoints, so I definitely do not want a function that passes through ...
0
votes
1answer
230 views

Fitting a theoretical density function with log-return sample

I am working on a exercise to fit a theoretical density function,presented below, with log-return series of a stock. $\frac{1}{2}a e^{a(x-\mu)} \quad \text{if x } < \mu $ or $ ...
6
votes
2answers
289 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 ...
0
votes
1answer
75 views

How to determine a function that fits a geological model

I have a problem. I am currently working on a code that works by comparing data (real or synthetic) to an earth model (described by earth layers, or in this particular, velocity (...
27
votes
5answers
2k views

Fitting points to tilted, off-center ellipse

I have 24 x-y points that are supposed to form an ellipse. ...
1
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1answer
79 views

Apply NonlinearModelFit to an image

I have several images (in FITS format), which I want to fit with a 2D-Gaussian distribution. The problem is that NonlinearModelFit expects data in the form of a ...
1
vote
0answers
35 views

Fit linear data with weights for y and x in LinearModelFit

I am quite new using Mathematica, I hope someone could give me some help. I have a set of {x, y} data and I have a list of {deltaX, deltaY} standard deviation. I would like to fit my data taking into ...
1
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2answers
216 views
20
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2answers
3k views

How to fit 3 data sets to a model of 4 differential equations?

I'm a biologist and a newbie in Mathematica. I want to fit three data sets to a model consisting of four differential equations and 10 parameters. I want to find the parameters best fitting to my ...
5
votes
1answer
211 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
2answers
551 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 ...
2
votes
2answers
74 views

FindDistributionParameters gives an error for a mixture of user defined sinh-arcsinh distributions

I have some data (1593 values). I first binned it using the Knuth rule and fitted a function that is a linear combination of two sinh-arcsinh functions. I then ...
1
vote
1answer
86 views
3
votes
0answers
77 views

Fitting data to plot using errors as weights

I have some enzyme kinetics data that I want to fit to the Michaelis-Menten curve in order to obtain the kinetic parameters of the enzyme. Is it meaningful, statistically and functionally speaking, ...
0
votes
0answers
49 views

Solve an integral equation: to fit the given data with an integral of two functions?

I am trying to find an efficient way to solve the following equation $$h\left(b\right)=\int_{0}^{b}f\left(\frac{b-c}{1-c}\right)\frac{g\left(c\right)}{1-c}dc$$ where for $h(b)$ I have the data ...
6
votes
4answers
411 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 ...
5
votes
1answer
125 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 ...
1
vote
1answer
259 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: ...
1
vote
2answers
187 views

Is it possible to monitor the sum of squared errors in a NonlinearModelFit or FindFit procedure during the process?

Since fitting procedures using NonlinearModelFit (or FindFit) sometimes take very long, I would like to monitor the sum of ...
9
votes
1answer
240 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 ...
10
votes
0answers
215 views

Implementation of Partial Least Squares (PLS)?

I'm looking for a PLS implementation for Wolfram Mathematica. I just can't seem to find any implementation for it - do you know one? In general, I'm a bit confused that there exist only so few ...
1
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2answers
95 views

Does FindFit use symbolic differentiation?

Does FindFit use symbolic differentiation when optimizing by least squares a non-linear function?
0
votes
2answers
171 views

Least Square Fitting

stuck on a mathematica assignment and could really use some help. A) Fit a function with the shape log(Y) = a0 + a1log(U) to the datapoints (log(Ui), log(Yi) with an least square fitting. Show this ...
0
votes
0answers
43 views

FindFit returning Power::infy: Infinite expression

So, I'm having an issue trying to fit some data to a function with a 2nd order pole. I know there are other functions that fit the data, just fine ... but the model is from the literature, however the ...
16
votes
1answer
519 views

Difference between Fitting Algorithms

I am new to Mathematica, and I don´t quite understand, what the difference between the fitting algorithms Fit, FindFit, ...
0
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0answers
57 views

Investigating the correlation between this 2 set of data

The picture below shows the growth of the traffic and the total number of published articles on that website. Which functions can I use to investigate if there is a correlation between them? Both ...
1
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1answer
60 views

How can I plot more regression trend line in the same graph?

I would like to do something like the example I drawed manually: ...
1
vote
1answer
70 views

Traffic growth forecast: showing the change of linear regression

The following picture shows a changement in the trend of data. (The data used are available here). Is there any tool that can show this change of trend? Until now I managed to show even more ...
1
vote
2answers
226 views

How to Fit experimental data with 4D ParametricNDSolve?

Let me first explain the background problem. I'm trying to solve a problem with a projectile motion in 4D such that the position vector is: $\boldsymbol{r}(t)=\boldsymbol{r}[x(t),y(t),z(t)]$ I have ...
4
votes
1answer
162 views

TimeSeriesModelFit incorrect?

I am trying to determine the optimal model for time series data (1592 observations). When I run TimeSeriesModelFit, Mathematica selects $AR(1)$ model, the estimated ...
1
vote
2answers
105 views

NonlinearModelFit and plot with multiple parameters function

i ve got quite simple function: $f(t) = x1 * a(t) + x2 * b(t)$ and table of results like this one: t | f(t) | a(t) | b(t) ---------------------- 1 | 2 | 5 | 3 ---------------------- 2 | 4 ...
1
vote
0answers
54 views

Fitting a vector-valued model using Mathematica

I'm wondering if there is a way within Mathematica to perform some kind of parameter fitting on a vector-valued model function (in this case a model of electric field vectors). Essentially what I want ...
2
votes
1answer
81 views

Computing a Gamma function-Gaussian integral

I would like to compute the following function: Integrate[Gamma[k,0,Exp[-2 e x^2]],x] k is an integer and ...
0
votes
1answer
79 views

How to do linear fit for 2D data points [closed]

I am very much new to Mathematica, and facing several difficulties. I used the following code Fit[{2, 4, 6, 8}, {1, x}, x] The output is ...
-2
votes
2answers
57 views

How can I use NonlinearModelFit with multiple variables? [closed]

I am trying to find the coefficients for following equation: $\quad \quad f(x,\,y,\,z) = a (x^2)\, exp(b x + y^2) + c z^2 y$ using NonlinearModelFit. But I can't ...
0
votes
2answers
156 views

Log Linear Fitting of a data: e.g. {xi,Log [yi]} and plotting the fit

I have a Log-Linear plot, and i'm unsure about how to fit a line to it. The data represents a I (current) vs V (voltage) curve. The exponential portion of this curve (linear in a Log-Linear plot) is: ...
1
vote
1answer
91 views

Interpreting P-Value on ParameterTable

When using LinearModelFit[] we can generate a table of parameter values and statistics for the corresponding model using the property "ParameterTable". Looking in the documentation I can't find an ...
5
votes
1answer
207 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 ...
4
votes
3answers
182 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 ...
2
votes
1answer
95 views

How can I get the coefficient of the exponent from a nonlinear model fit?

I have been trying for over an hour now to get the numeric value for "HalfLifeN" from the code in the screenshot below. Not to mention mathematica simplifies ...
0
votes
1answer
41 views

Using Check[] on multiple statements

I am using a loop to run run multiple fits. If a fit fails, I don't want it to either appear in my data or to affect later fits so I am using the Check[] function to catch if any errors occurred (I'm ...
2
votes
1answer
44 views
21
votes
4answers
2k 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 ...
3
votes
1answer
300 views

FindMaximum of loglikelihood in Gaussian Process

I am trying to implement a Gaussian Process and have problems to maximize the loglikelihood because the function consists of a determinant of a matrix that is dependent of 2 variables and the product ...