Questions on the use of Mathematica to construct models for approximating empirical data. (FindFit[], Fit[], LinearModelFit[], NonlinearModelFit[], etc.)
-7
votes
0answers
54 views
General linear model, multiple dependent variables? [closed]
Is there a way to use LinearModelFit with multiple y variables for each observation?
1
vote
0answers
64 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 ...
0
votes
0answers
39 views
Interpolating function as a model in Mathematica's procedures for fitting
Is it possible to use interpolating function with parameters as a model for NonLinearModel fit (and other integrated methods for fitting)?
Similar question was already posted earlier - How do I find ...
0
votes
0answers
67 views
FindFit for dimension reduction?
Given an n-dimensional function, can I use FindFit to produce an approximate (n-k)-dimensional function?
Here is a simplified illustration of what I am trying to do. I have
$$f(x,a,b,\mu,\sigma) = ...
-3
votes
0answers
66 views
I need to find the standard error for the predicted variable in NonLinearModelFit
Lets say my data is as follows:
...
3
votes
1answer
84 views
Using a user defined NormFunction in FindFit or NDSolve
I would like to use a different norm instead of the 2-norm in FindFit (Mathematica 9). For example, instead of using
$$\sqrt{\sum (x_{\mathrm{model}} - ...
3
votes
1answer
120 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 ...
0
votes
0answers
60 views
Fitting data representing the displacement of a cylinder with a normal load at the middle
I have the following data representing the normal displacement caused by load applied at the middle cross section of a cylinder, normal to the cylinder surface. Only the middle cross section cut is ...
2
votes
1answer
68 views
making a function of fit results
I have 13*25 datasets consisting each of around 40 points.
They are all linear I can easily fit them using fit function but my problem is when I want to call them I want them to be functions. I want ...
13
votes
5answers
358 views
How to perform a multi-peak fitting?
I am wondering how to implement the multi-peak detecting and fitting in Mathematica. Following is an example of fitting the data using three peaks (such that the data ~ peak1 + peak2 + peak3).
The ...
3
votes
0answers
62 views
NonLinearModelFit with Two Dimensional List of Weights
I'm currently trying to fit Planck's law (B[λ, T]) to measurements, thereby determining Planck's constant.
I have a list of triplets containing wavelength, ...
0
votes
0answers
60 views
1-norm minimization [closed]
I am fairly new to Mathematica and I'm having trouble running a 1-norm minimisation of the following function, g(x) = f(x) - c where c is the data to be fitted to and f(x) is some function. I know how ...
1
vote
1answer
63 views
Combined NonlinearModelFit [duplicate]
I'm trying to fit a number of data sets. Each of the sets should evaluate to a simple linear solution.ax+b.
The problem is, all data sets have interference from a ...
2
votes
3answers
125 views
Plotting a list along with its trend line
Say I have these data:
data = {{1, 3}, {2, 4}, {3, 6}, {4, 7}};
I want to fit these data with a quadratic equation, like this:
...
0
votes
1answer
44 views
Solving one equation, then inputting the values into another for NonlinearModelFit
Considering the equation
a*x^3 + a*x^2 + x + b == 0
I'm looking to find the best value for a and ...
-1
votes
1answer
88 views
How to define a pure function with a Module?
I was not able to use a self defined (using Module and For loops) piecewise function to fit data. It seems that the problem is that I have to define a pure function. I would like to learn how to ...
0
votes
1answer
68 views
Using NonlinearModelFit to fit data with errors
Assume we have some data of measurements
SeedRandom[9];
data = Table[{i,2*(1 + 5*RandomReal[])*Exp[-0.01*(1 + RandomReal[])*i]}, {i, {0, 100, 200, 400, 700}}];
...
2
votes
1answer
278 views
non-linear trend reduction using thresholds
Doing some mappings of the earth magnetic field results in the left-hand figure below (which consists of 181 profiles):
To improve this I tried a non-linear trend reduction using, for example,
...
12
votes
0answers
156 views
10
votes
2answers
366 views
Is it possible to use the LevenbergMarquardt algorithm for fitting a black-box residual function?
I have a black-box multiargument multiparametric function of the type SRD[dataPoint_List,params_List] which accepts experimental data along with the parameters of ...
1
vote
0answers
103 views
Performance in parameter estimation from ParametricNDSolve using varied initial conditions
I have 250 data points from a timecourse exeriment in a list, with columns specifying (1) time, (2-4) initial conditions, (5) absorbance reading. I want to fit 4 parameters (k1, k2, k3, k4) in a DAE ...
1
vote
1answer
105 views
How to adjust parameters to experimental data on a NDSolve problem
I have 2 differential equations with 2 variables, x and y,which are a function of t and I have the parameters k1, k2 y k3.
...
3
votes
2answers
135 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 ...
3
votes
4answers
170 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
...
0
votes
3answers
245 views
Fit line similar to power of trendline in Excel
Is there a way to fit a line similar to power trendline in Excel?
Something in this fashion: Fit[data, {1, x, x^(-n)}, x]
...
2
votes
2answers
74 views
Putting a matrix inside function
I want to fit a function to some data and inside the function there's a list
here's my data
...
14
votes
5answers
2k views
Estimate error on slope of linear regression given data with associated uncertainty
Given a set of data, is it possible to create a linear regression which has a slope error that takes into account the uncertainty of the data?
This is for a high school class, and so the normal ...
5
votes
0answers
77 views
Using perpendicular offsets in FindFit
I want to use perpendicular offsets in the built-in FindFit function.
Are there any possible ways or do I have to code everything by myself?
3
votes
1answer
103 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.
1
vote
1answer
64 views
How can I nicely overlay fits for multiple arrays with ListPlot or ListLogPlot?
I'm plotting multiple lists with ListPlot[] or ListLogPlot[]:
ListLogPlot[{ListA, ListB, ListC, ListD, ListE}, PlotRange -> {{0, 100}, Automatic}]
I also have ...
2
votes
2answers
84 views
FindFit: Fit that is always lower - Change of Norm?
I am trying to find a fitting function for a multidimensional set of data. I will have to find a fitting function that is always lower (conservative) than the data fitted.
The easiest way is to look ...
1
vote
1answer
151 views
How can I fit a matrix function with multiple variables to given eigenvalues?
I have a 5x5 matrix function H[kx]
...
1
vote
0answers
205 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 ...
6
votes
1answer
129 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 ...
2
votes
2answers
115 views
How can I consistently get a good logistic regression fit?
I'm executing the command
NonlinearModelFit[data, c/(1 + a Exp[-b x]), {a, b, c}, x]
with the data being
...
2
votes
0answers
90 views
Is it possible to marginalize one or several parameters obtained from fitting procedure?
Statistical model analysis package has a few fitting functions. Their arguments are data points, fitting model and parameters in the fit. The result is a set of best values for parameters, which ...
2
votes
1answer
111 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 ...
1
vote
0answers
71 views
Method used by FindFit
Using FindFit, Mathematica selects an optimal algorithm when Automatic is selected.
I'd like to know the name of the method ...
1
vote
0answers
68 views
Fitting a set if data to a 'plane'
I have a set of data ({{1,4,2},{1,-1,2},{-1,2,4},{2,1,5},{-1,1,4},{1,1,2},{5,2,2}}) that I am some how supposed to fit to "the plane, that is with the function ...
7
votes
6answers
2k views
How to determine the center and radius of a circle given three points in 3D?
I was wondering if anyone could give me a hand with this problem I have.
I have six points on a plane, and I am trying to determine if they form a circle or not.
I know that any three points in 2D ...
4
votes
1answer
166 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 ...
0
votes
1answer
109 views
Problem using NDSolve
This might be some simple mistake, but I am running out of ideas.
I am trying to fit an ODE system to some data. This error keeps appearing
NDSolve::nlnum: "The function value {0.299812 - ...
5
votes
1answer
153 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:
...
0
votes
0answers
76 views
FindFit and NIntegrate with dependency between integration variables
I am trying to use FindFit and NIntegrate in this situation:
...
1
vote
1answer
102 views
FindFit: getting confidence intervals for the returned parameters
I'm using FindFit[] to fit a function to some experimental data. I'd like to know what error bars are on the fitted parameters.
Scipy's ...
0
votes
0answers
130 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
$ ...
-1
votes
1answer
64 views
FindFit and Integration errors
First off, appologies for what may sound like a newbie question, as I am very new to using Mathematica.
I am trying to find a way to get Mathematica to give me an expression that would describe the ...
4
votes
2answers
182 views
What can I do to eliminate the error FindFit::nrjnum:?
I am testing the "Power Law with finite-time singularity" hypothesis for world population growth for a project.
The data I'm using (same behaviour should also be exhibited by the stock market, thats ...
0
votes
0answers
168 views
NonlinearModelFit and NMinimize [closed]
I'm doing a non-linear fit on some data. The calculation residual is low, but I prefer to minimize another objective function such as:
...
2
votes
2answers
262 views
Finding a best fit curve and plotting it [closed]
I have a list as shown below:
m01 = {{250, 0.083121}, {200, 0.0888446}, {150, 0.0992422}, {100, 0.121567}, {50, 0.186825}}
I'm new to Mathematica, and would like ...
