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

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1
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1answer
62 views

Fitting bivariate data using FindFit [on hold]

I am trying to fit the following bivariate data set using the FindFit function: ...
5
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2answers
102 views

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 ...
3
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2answers
55 views
2
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1answer
96 views

Find a family of curves

I have a diagram with seven curves (each with a different parameter). My goal is to find a function for the family of curves (i.e. a single function not just for the seven parameters, but for all ...
0
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1answer
71 views

How can I calculate the root of any order of power series

How can I calculate the root of any order of power series with Mathematica. Here I insert every quantity by hand. But I want to give a, ...
1
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0answers
44 views

x and y axis nonlinear error fit possible? [duplicate]

I have a set of datapoints with x (position) errors as well as y (measurement) errors. Is there a way in Mathematica to fit a nonlinear function through this points, with weighting both, the x and y ...
12
votes
2answers
380 views

Fitting a curve to an image object: not a superellipse, not an egg curve.. what else?

I'm facing the problem of quantifying the morphology of objects with such a shape (nannoconids... they are fossils). One of the final goals is to produce a solid of revolution and compute ...
21
votes
3answers
757 views

Exponential fitting - isn't actually a BUG there?

There are many questions on this site about wrong exponential fitting in Mathematica but no one considers this well-known problem as a potential bug. Usually people suggest well-known workarounds ...
6
votes
1answer
244 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 ...
0
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1answer
90 views
2
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0answers
39 views

How to realize Global Fitting with shared parameters, same as OriginPro9.0?

I have an experimental data from Michelson interference and I can fit the envelope in OriginPro9.0 using Global Fitting with shared parameters. The figure by OriginPro9.0 is like this: However, I ...
1
vote
1answer
51 views

Paramter Scans and $\chi^2$ Test in Mathematica

Is there any in-built function or a recommended package that enables one to find, say, 10 Parameters, which are used as boundary conditions in NDSolve, that minimize $\chi^2$? ...
7
votes
1answer
823 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 ...
0
votes
2answers
60 views

Getting image data values with coordinates in circular region

I have a number of gray level images (600, with size: 2400x2400 pixel, small instance see above). In this image there is a circular region of interest. The aim is to fit a function to the gray value ...
2
votes
1answer
48 views

Fitting data in Log-Log scale

I want to fit my data from a txt file to a curve in log-log scale. What I tried to do was this: ...
4
votes
0answers
85 views

Fitting data with unique variable per measurement

Imagine we are in the following situation, we have a nonlinear system of functions $f$ with coördinates $x_i$, and unknown parameters $\delta_i$'s and $t$. Let this system be defined as, ...
0
votes
0answers
31 views

How to calculate a required definition only once for each iteration of NonlinearModelFit

This is my first post here. I've been using Mathematica for about 4 years now to analyze data, but am still very new and have no background in formal programming. This is the first question I couldn't ...
1
vote
1answer
68 views
0
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2answers
70 views

Find the linear combination of two functions to fit to a third

I have been trying to solve a simple enough problem, but I can't seem to find the proper method. The problem is given as, Find 0 < x < 1 for which, h(t) $\approx$ (1-x) f(t)+x g(t), where is ...
0
votes
0answers
88 views

Find the (gaussian) function to fit a series of points?

I have a series of measurements for concentration of pollutant on a river C(x,t) where x is the location on the river and t is the timestamp. When plotted these data suggests a bell curve like Gauss ...
1
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0answers
44 views

Multivariate FindFormula?

I am using Mathematica Online and want to do FindFormula with two independent variables, but I cannot figure out if it's possible and if so what the syntax is. Here's my dataset: ...
1
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2answers
122 views

Use NMinimize instead of FindFit for constrained search (of coefficients)

(My problem is more complex, but let us formulate it through this example) I am trying to find the best polynomial approximation to the following function ...
1
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0answers
48 views

Fitting with constraints including the independent variable

I would like to write the following statement: data2fit = NonlinearModelFit[data2, {a Sqrt[b x + c] + d, b x + c > 0}, {a, b, c, d}, {x}] However, it returns ...
2
votes
2answers
134 views

Multiple regression curve fitting

I've got some data with 2 independent variables and 1 dependent variable I'm trying to fit a curve to. I'm really kind of a dummy with Mathematica except for the most basic things, so I looked ...
1
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0answers
57 views

Deriving ordinary least squares (OLS) in matrix form

How can I instruct Mathematica to derive the OLS in matrix form with respect to $\beta$ and obtain the result ${-2X}^{T}(y-X\beta)$? The matrices have the following dimensions: $y_{n \times 1}$, ...
5
votes
0answers
92 views

Multivariate Adaptive Regression Splines (MARS) - Mathematica implementation?

Does anybody have or know of a Mathematica implementation of the Multivariate Adaptive Regression Splines (MARS) algorithm?
3
votes
1answer
117 views
1
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0answers
101 views

Fitting data to an Normal Inverse Gaussian distribution

I am using data which I suspect is distributed according to the Normal Inverse Gaussian distribution (NIG). The literature says that the 4 parameters of the NIG can be estimated from the sample mean, ...
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 ...
1
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0answers
45 views

polar form of generalized superellipse (not Gielis formula!)

I am looking for the polar form of the following generalized superelliptic shape such that I can use it with NonLinearModelFit for curve fitting to data: $$ \left ...
3
votes
1answer
100 views

Why is TimeSeriesForecast linear?

When I use FinancialData with TimeSeriesForecast, the resulting graph is always linear and thus not very accurate. ...
0
votes
1answer
72 views

FindFit and log norm function

I'm trying to fit a function to data using FindFit, but I can't find a way to replace norm function RMSE with a RMSE in log space: ...
1
vote
0answers
66 views

How do I add custom deviation when using LinearModelFit?

I have a set of data in the form a list S1={{x,y},{x,y}} etc. I also have a function that calculates a corrected standard deviation in the y direction for ...
3
votes
0answers
51 views

Fitting real and imaginary parts of a function

I have an analytic form of a function G[w_] = -I*z0*w/(1 + I*z0*w*a) I know this function can be obtained (up to some overall normalization) from solving a ...
1
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0answers
435 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 NonLinearModelFit (and other integrated methods for fitting)? Similar question was ...
1
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0answers
184 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 ...
1
vote
1answer
60 views

Boundary parameter in Beta Distribution

I use EasyFit to find the probability distribution of my data. It turns out the data follows BetaDistribution with 0.54022,0.70601 shape parameters and 1.33,6.83 continuous boundary parameters I am ...
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 ...
2
votes
1answer
77 views

Fitting a set of functions using same basis functions

I am trying to fit the functions in the plot below, but I need them to be fitted using the same basis functions. I want to interpolate between the functions by interpolating between their ...
0
votes
0answers
47 views

Iterative process of least squares solution

I'm doing an inversion of gravity data in which the least squares solution is: V^(k+1) = V^(k) + Inverse[W].(Transpose[A.(Inverse[W])]).α; where ...
6
votes
2answers
661 views

RSquared: LinearModelFit vs NonlinearModelFit

I'm trying to understand the differences between LinearModelFit and NonlinearModelFit. One thing I notice is that the ...
4
votes
1answer
928 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 ...
1
vote
1answer
71 views

Data fitted by two linear fits [duplicate]

can anybody help me please and tell me how to fit my set of points by two linear fits? It is always exactly two of them and are always linear and should cover all the data. The second line should ...
3
votes
1answer
47 views

Displacement around the x axis, how to change a function location

While plotting a function I want to change the location of x. I am doing a regression with the logistic function ...
0
votes
1answer
56 views

problems of Lorentizan fit with Nonlinear fit model [closed]

I tried to do a Lorentzian fit for a Spectroscopy data.I found that I have to actually give the precise value for this fit.[i do not like to call this as fit ,if that is the case]? Am I missing ...
0
votes
1answer
79 views

What´s wrong with my FindFit

I updated the data which is a table I deleted the first coordinate as it was the quote from the document. ...
0
votes
1answer
72 views

Invert and fit implicitly defined curve

I need to fit an implicitly defined curve. I thought I could get some data out of Solve, and then using FindFit. Therefore, I ...
1
vote
0answers
76 views

Fitting in Mathematica: Which function? [closed]

in other programs, there is a possibility to take a data set and to find the function which fits best. Is there also such a possibility in Mathematica? I only could find ...
2
votes
2answers
91 views

NonlinearModelFit gives imaginary numbers [duplicate]

I am having trouble using NonlinearModelFit to fit to data generated by the equation I am trying to fit to. ...