What is Fitting: Definition and 242 Discussions

Curve fitting is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, possibly subject to constraints. Curve fitting can involve either interpolation, where an exact fit to the data is required, or smoothing, in which a "smooth" function is constructed that approximately fits the data. A related topic is regression analysis, which focuses more on questions of statistical inference such as how much uncertainty is present in a curve that is fit to data observed with random errors. Fitted curves can be used as an aid for data visualization, to infer values of a function where no data are available, and to summarize the relationships among two or more variables. Extrapolation refers to the use of a fitted curve beyond the range of the observed data, and is subject to a degree of uncertainty since it may reflect the method used to construct the curve as much as it reflects the observed data.

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  1. Y

    Fitting data to complicated model

    1) For standard non-linear least squares, the standard approaches are to either a) to use the jacobian to linearize, and proceed with linear regression, or to b) linearize the raw data 2) When data needs to be "fit" to a complicated model (e.g. some non-linear differential equation) that...
  2. A

    Integral equivalent to fitting a curve to a sum of functions

    Hello, I am searching for some kind of transform if it is possible, similar to a Fourier transform, but for an arbitrary function. Sort of an inverse convolution but with a kernel that varies in each point. Or, like I say in the title of this topic a sort of continuous equivalent of fitting a...
  3. carllacan

    Wrong width when fitting a gaussian with SciPy

    Hi. Has anybody here any experience with SciPy? I'm trying to get SciPy to adjust a gaussian function to some data. For more details its the photopeak of Co60. This is what I do: import numpy as np from scipy.optimize import curve_fit # counts is a numpy array which...
  4. CuppaMuons

    What should I choose as the error on x? (Curve Fitting Matlab)

    Homework Statement So I've done an experiment by scanning over a range of angle and measuring the intensity of X-Rays. There are peaks where I have X-Ray diffraction occurring and in order to do analysis I need to identify the values of angle and an error (as in the plus/minus) on this value...
  5. ElijahRockers

    MATLAB DSP: Best curve fitting approach via MATLAB?

    I am doing an experiment that generates data in three 1-hour-blocks. Each block has a different number and timing for acquisitions. (The first hour is more frequent and numerous, while the last hour is only 6 acquisitions) The reason for breaking it up into 3 hours is to give the subjects a...
  6. S

    How Do I Use Functions for Curve Fitting in Origin Software?

    I plotted a graph on Origin software and need to do curve fitting to get accurate results. From my understanding, I need to provide a function for the fitting. So how do I derive the function? I am actually provided with the function I(x)=I0-I1cos(x-x0) and this function will fit the lowest...
  7. kandelabr

    A Least-squares - fitting an inverse function

    I have a set of data points that I must fit to an inverse function like this: y(x) = a/(x+b) + c My problem is that least-squares fitting using this equation is extremely unstable and heavily dependent on initial guess. No matter how accurate parameters I start with, the algorithm often goes...
  8. Y

    Nonlinear Regression Curve Fitting

    This isn't a precise homework question, but this seemed like the most reasonable place to post. If not, please feel free to move it. I have a large set of data points that should fit to a known equation (the Drude-Smith model for conductivity) The equation the data should fit to is: σ(ω) =...
  9. W

    Fitting a (Very) Large Random Number To A Formula

    It has been a very long time since I have done any calc or hard math, I hope this question is in the right place. I have a HUGE number, that is random and big. What do I need to study/look at to create a formula that will generate just it?
  10. QuantumCurt

    Fitting data to a Gaussian Distribution in Excel

    Hey everyone, I'm hoping I can get some input on this. As some of you may recall, I'm currently in an internship at Fermilab, and I've hit a snag in plotting my data. I'm measuring the intensity of the NuMI neutrino beam at multiple different points to look for discrepancies in the measured...
  11. C

    What is the Purpose of Fitting Supernova Remnant Spectra?

    PF, I work as a researcher at my undergraduate institution. I have to give a presentation in a week and this question always gets me. What does learning the properties of these SNRs contribute to the overall body of knowledge? What does the scientific community gain from this knowledge...
  12. Buzz Bloom

    Fitting a model to astronomical data

    I have several questions about the process of determining the value of cosmological parameters by LMS fitting tunctions of the form z = f(DL) (where DL is the luminosity distance to astronomical data points), for example, as shown in the following diagram: The five cosmological parameters I am...
  13. H

    Quick-Release Fittings for Wood Supports on Walls

    Hi all, Does anyone know of a quick release fitting that can replace a screw thread? I'm thinking along the lines of a bayonet fitting but any other ideas would be great. Looking to put pieces of wood sticking out perpendicularly from a wooden wall (railway sleepers) to act as supports for...
  14. R

    4 parameter logistic model for fitting PCR data

    I have a question about the logistic fit they used on this paper: http://online.liebertpub.com/doi/pdf/10.1089/cmb.2005.12.1047. Its PDF page 5, or journal page 1051. They define all the variables and then say x0 and b define the shape of the model. If I am fitting 30 cycles of PCR data how am I...
  15. S

    Fitting an ellipse through 3-d data

    Hey, sorry if this is not the right section to post in, the topic is a bit ambiguous. I've generated a set of coordinate points for the orbit of Mercury (3d cartesian) and now I want to fit an ellipse through it so I can get an accurate estimate of the location of the perihelion. I am using...
  16. deccard

    Fitting distribution to histogram with low number of counts

    I have one dimensional binned data that has a peak to which I need to fit a distribution, such as Gaussian or Lorentzian, that is described with four parameters, height, width, centroid position and the background. The problem is that the counts per bin are low and the peak is only 5-6 bins wide...
  17. P

    Integral curve fitting in origin

    Dear users, I deal with following problem. I've got a data of Intenzity of chemiluminezcence as a function of temperature. The data should be fitted by following equation: I found that in origin one can fit also data with integral function, with fittin parameters P, A, i, E. The beta and...
  18. E

    How to Perform Murnaghan Equation Fitting for Determining Bulk Modulus?

    Hello, I am going to determine the bulk modulus of Silicon by using Murnaghan equation. Anyone can tell me how to do Mrnaghan equation fitting? If u kindly give me an example of code, it will be great!
  19. A

    Model Fitting to Data - Scaling x Values & Shifting Parameters

    I have some (x,y) data with x in the range of 1e10 and 1e13, y is between 0 and 1. I am fitting this data using several theoretical models to gain an understanding of underlying mechanisms (by which model fits best). Using NonlinearModelFit in Mathematica, I get memory failures and cannot...
  20. B

    MHB Fitting a function to a sinusoidal curve

    Hi Folks, I have a curve that varies sinusoidally calculated from a numerical program as attached "Trace.png". I would like to fit this amplitude modulation expression to it. f(t)=A[1+B \cos(\omega_1 t+ \phi)] \cos(\omega_2 t+ \theta) I managed to adjust the parameters manually to get a very...
  21. A

    MATLAB [Matlab] Which is the good solution My vs. School - curve fitting?

    Hy, I wonder which is the good solution for this problem: Nonlinear least square problem: function: y = x / (a + b.x) linearization: 1/y = a/x + b substitution: v = 1/y , u = 1/x >> model v = b + a.u What we did in school: x = [1 2 4 7]; y = [2 1 0.4 0.1]; v=1./y; u=1./x; n = length(x)...
  22. L

    Free Curve Fitting Software for 4 Parameter Equation

    Is there a software(preferably free) that can fit data into a 4 parameter equation? like the generalised logistic function
  23. D

    Multidimensional fitting of two sets of data

    Hello, my problem is the following: A lasers gives out a bunch of data points which are reflected off a metal surface and recorded by a camera attached to the side of the laser. The image the camera receives is however distorted. In order to calibrate the camera I need to find a function...
  24. C

    Fitting experimental data with exponential curve

    Hello! :-) I' have a problem... I fitted experimental data with a second order exponential theoretical curve: y = A1*exp(-x/t1)+ A2*exp(-x/t2) + y0 and I have these data for 4 repetitions of the same experiment: first time: Reduced Chi-Sqr = 6,81066E-4 Adj. R-Square = 0,41005...
  25. T

    Fitting a mixture model when component priors are known

    I have a list of scores between 0 and 1 generated by an information retrieval system - 1 being very relevant and 0 being completely non-relevant. I do not know whether the scores correspond to relevant or non-relevant items or not but I do know that the distribution of scores is generated by a...
  26. T

    Can a Beta Distribution Model Scores in the Interval [0,1] for Ranked Retrieval?

    I have a set of scored items with the scores in the interval [0,1]. Roughly speaking the distribution of scores is about 50% equal to 0 and then sloping steeply downward all the way toward one or near to one. I want to fit this data to a distribution and use that down the road in some...
  27. D

    MOND : Help with fitting procedure

    I am looking for pedagogical guides to fitting rotation curves with MOdified Newtonian Gravity. I want to study how to fit the luminosity data as well as the kinematic data. I have studied some published papers on MOND fits(Sanders, Mcgaugh, blok etc). But, they are not sufficiently elaborate...
  28. A

    Fitting Correlation Function w/ Igor Pro | Paid Help Avail.

    Hello I am working with fluorescence correlation spectroscopy. I want to fit the correlation function on Igor pro. Does anyone know how to fit the correlation function with Igor? I am willing to pay for the help.
  29. D

    Fitting a curve to data with error bars on curve parameters

    I have several data points with error bars, and these error bars are different sizes for each of the data points. I'd like to fit a model function to them which has non-linear parameters, and be able to get error bars on the model parameters, ie. if my model is something like f(x) = A +...
  30. N

    Nonlinear Least Squares Fitting

    Hello, So I was hoping to get some help implementing a nonlinear least squares fitting algorithm. Technically this is an extension of my previous thread, however the problem I am having now is correctly computing the algorithm So the problem definition is this: Given two sets of n 3D points...
  31. R

    Exponential least-squares fitting and initial parameters

    Dear All, I would like to do an exponential function least-squares fitting, but having two or more exponents. For example the function looks like this: y (x) = A \exp (-x/a) + B \exp (-x/b) where A, a, B and b are the least-squares fitted parameters. My question is how to obtain the...
  32. N

    Modified least squares fitting?

    Hi, I wonder if someone could give me some guidance on this problem please. I'm not a mathematician and I'm not even sure what the title of this problem should be - curve fitting, regression, function minimization? It started with something fairly simple, least squares fitting with 3...
  33. Y

    Sellmeier's equation & Least-squares Fitting

    Homework Statement Determine the values of Sellmeier's coefficients (S and λ0) using the least-squares method and Sellmeier's dispersion equation: n2=1+Sλ2/(λ2-λ02)Homework Equations n2=1+Sλ2/(λ2-λ02) The Attempt at a Solution I understand how to use the least-squares method with a simple...
  34. A

    Three equations and three unknowns: fitting a function.

    Hi! I'm doing a project with sound, and exploring modulation. I got stuck on an intermediate step ... and can't solve a simple algebra problem. I have a wave, which I know the envelope is a perfect sine wave, and fits the following three equations: A * cos( ph1 ) = knownSlope1 A *...
  35. P

    Curve fitting with errors-in-variables

    Hi, I need some directions to target a problem that is bothering me quite a lot, even some links or small explanation if possible, thank you in advance! I have a huge dataset Ω (unknown) of experimental values {e_i} that should approximate (with noise both in the value and in the...
  36. N

    Fitting bacterial growth curve in Prism

    Hello, I'm in need of someone to show me how to fit a bacterial growth curve to data in Prism, preferably using the Gompertz function. I also need someone to show me how to assess the goodness of this fit. I have many different growth curves and I need to compare the parameters. Hopefully...
  37. S

    How to do circular curve fitting?

    If I was given some n(very large) points, and if I want to fit a curve circularly, I think I should go for least squares method. What is the optimal way to do it? can someone explain me clearly how to proceed using least squares method? I don't how to proceed. But I know I should do least...
  38. C

    Fitting the 'tightest' rectangle to a set of three dimensional points

    I have a group of 8 3-D points which all sit on an arbitrary plane (The points were generated by projecting the corners of a axis aligned cube, box, onto the plane) I wish to group all the points in a rectangle with the smallest surface area - so a tight fit rectangle. What I am doing at...
  39. L

    Data analysis: 2D Surface fitting from raw data

    Hey everybody I've got a question for the programming savvy. I'm generating data which can generally be described by.. f(x,y) = Ʃn(an * xn)*Ʃn(bn * yn) Basically what I'm looking at is a data set which shows a surface which looks like about 1/4th of a wonky bowl. My trouble is...
  40. P

    Fitting a sine curve that isn't a perfect sine curve?

    For my 3rd year project, I have a set of data which is the variation within an interference pattern. The outcome has clear sine curve properties (Alternating peaks and troughs of intensity) but the positions aren't regular (i.e. the peak-to-peak distance between peak1 and peak2 is larger than...
  41. M

    What Type of Curve Uses Sequential Control Points from A0 to A6?

    If I construct a curve such start from point A0, A3, to point A6 where A1-A2 and A4-A5 are control points, is called a Bezier curve. What is it called by and what its equation if I construct and fit a curve start from point A0 > A1 > A2 > A3 > A4 > A5 > A6 such as below image?
  42. J

    Fitting a curve using a spline, Fourier transform, etc.

    Homework Statement Just wondering if my output seems wrong. The interpolating polynomial looks like it's way off, though I've looked over my code many times and it seems right (?). clc clear all format long x1=[1:1/10:4]; y1=zeros(1,length(x1))...
  43. MarkFL

    MHB Zero's question at Yahoo Answers regarding polynomial fitting

    Here is the question: Here is a link to the question: Write a function for the polynomial that fits the following description.? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.
  44. D

    Sigma Plot, Non-linear regression, fitting a line to a set of points

    I model arterial baroreflex data that I have collected in humans using the Kent equation which is: y=p1/(1+exp((x-p3)*p2))+p4; where Y=heart rate, X= estimated carotid sinus pressure, p1=range of Y, p2=slope coeff, p3=centerpoint on X, p4 = minimum Y. I use Sigma Plot to do a best fit line...
  45. K

    A problem on polynomial fitting

    I encounter a problem on the fitting ability of a special class of multi-variable polynomials. To be specific, I need find whether a special class of multi-variable polynomials, denoted by p(m), where m is the number of variables, can universally and exactly fit all member in another special...
  46. C

    Finding primes fitting a certain algebraic relation.

    Homework Statement Find all the primes p and q such that p^2-p-1=q^3 The Attempt at a Solution Trying out the first prime number 2, it is clear that p>q and that the difference is larger than 1. Then when factorizing it p^2-p=q^3+1 \Rightarrow p(p-1)=(q+1)(q^2-q+1), I get that p must...
  47. P

    Fitting Pulsed NMR Data for Spin-Lattice Relaxation Time (T1)

    Hello, I didn't know where else to post this so here it goes ... I have collected data from a pulsed NMR experiment to calculate the value of the spin-lattice relaxation time (T1). Now I'm asked to fit the data using a function of the form V(t) = V_0*(1 - 2*exp(-t/T1)). But I'm not really...
  48. G

    Deriving the equation of points for exact fitting and shape analysis

    Hello, I would like to ask you some questions. 1) I've a closed curve (for example an ellipse, which may represent the contour of an object) represented by the set of its (known) points. I need to find the equation of that curve to pass through all and every point (exact fit). I think that...
  49. T

    How can I achieve a tighter fit for my aluminum pipe in a clamp-on tee?

    Hello, I am currently doing a project and have ran into a problem. I have a structural fitting (clamp-on tee) that fits around a fixed structure. I am trying to fit an aluminum pipe into it, but the pipe's outer diameter is much smaller than the clamp-on fitting. I'm attach 2 images that show...
  50. A

    Finding the Best fitting curve for a graph?

    Hi, I m unsure whether or not this should perhaps be in the homework forum, however one might say this is more of a technical issue. I recently conducted an experiment for a report I intend to write up promptly, and I wanted to find the best fitting curve for these values. I tested how different...
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