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. J

    Problem with fitting simple quadratic function to 3 data points

    Hello PF, Ok so here is my problem. I have an array of data points which are the chi^2 values for a fit I have performed. I wish to calculate the 1-sigma error for this fit, so I figure I could find the lowest chi^2 value, and the two points either side that value, and fit a quadratic...
  2. C

    Universal joint/ball bearing controlled rotating arm for a furniture fitting

    Universal joint/ball bearing... controlled rotating arm for a furniture fitting Hello forum, I need your help on a furniture project we are developing in the office. its basically a floor standing lamp which needs to have a user regulated rotating arm. We are right now looking at different...
  3. K

    Accurately fitting curve to data

    Hi everyone, I want to find a function to fit a two arrays data (X,Y=f(X)) with high precision, but I am not succeed. Can anyone help me. These are my data: X={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32...
  4. H

    How to Linearize and Fit Data Points in MATLAB?

    Homework Statement For the given set of data, find the least-square curve: A) f(x)=Ce^Ax, by using the change of variable X=x, Y=ln(y), and C=e^B to linearize the data points. B) f(x) = 1/(Ax+B), by using the change of variable X=x and Y = 1/y to linearize the data points. x : [ -1 0 1...
  5. f95toli

    Shape preserving fitting algorithms

    "Shape preserving" fitting algorithms Does anyone know if there is such a thing as a "shape preserving" fitting algorithm? Now and then I run into the following problem: I have a set of rapidly varying data and try to fit it using an equation with e.g. 5 unknowns; I know that I can make it...
  6. S

    Maximum Likelihood Fitting normalization (Bevington)

    Hi, I'm posting this in this particular forum because, though this's a statistics question, my application is in high energy. My question is regarding a problem in Bevington's book (Data Reduction and Error Analysis..., Page 193, Ex. 10.1), but I'll give a general description here... Say...
  7. V

    EndStyles of Tube fitting Parts

    Dear All, I have received 2D drawings of Tube Fitting Parts. I need to create the model and assign the properties. I like to know how to assign the end styles for different Tubing Parts and how to define the connector (tubing) points. Any help is highly appreciated. Thanks in...
  8. C

    MATLAB Curve Fitting Question?

    Homework Statement Given: clear n = 100; x = 1:n; err = randn(1,n); mean(err); std(err); y = x + err; cftool Q - Relate your fitted to the data in y to the mean, S and SE values. You should also compare the fit results to the 95% point on the curve of the integral of the normal...
  9. T

    Curve fitting using (r, f(r), f'(r), f''(r))

    Hi! I know the value of a function f and its first and second derivatives at different point r (1D). I know how to fit it using only f(r) and r, but I'm sure its is possible to improve the quality/speed of the fitting by using also f'(r) and f''(r). Is anybody have in mind a fitting algorithm...
  10. N

    Helping in using linear fitting

    Hi everybody, I hope to find someone can help me, What are the equations of linear fitting? Are my equations right? n.Er + R-\sumI =\sumV \sumI.Er + R \sum(I.I) =\sum(IV) Please help me I need it today.:cry: If there is any website can help me please put it here:confused:
  11. B

    Is There a Way to Fit Lines of Worst Fit Using Statistical Packages?

    I recently completed an experiment for university level physics and am currently doing the analysis of the data. This data has been transformed to fit a linear model and it fits this very well, with the line of best fit lying within all error bars. I need to provide estimate of the gradient...
  12. V

    Curve-to-curve fitting trouble

    I'm currently working on a MATLAB program which, given two sets of data each representing curves, will transform (through rotations about the origin and x-y shifts) the first curve so it fits the second one best (so far in terms of sum of squares). I have been able to create a program...
  13. N

    Fitting Highly Non-linear Data

    Hi all, At the moment I am trying to find a best fit equation to radial velocity data vs. time of a planet HD17156b. The paper with the Authors fit parameters (I am trying to mimic the fit) has the arXiv ref number of :0704.1191v2 From this paper I extract their data, which is on the final few...
  14. M

    How to Apply Curve Fitting Algorithms for Magnetization Analysis in Origin 7?

    hi, there my question is let's suppose we have the magnetization (M) versus the applied field (H) as M(H,T)= \sum _{n=1}^{N} W(x_i ) (x_i ) Lang (H.A.x_{i}/T) here 'A' is a constant 'T' is the temperature of system Lang(x) is the Langevin function coth(x)-1/x , My problem is how to...
  15. M

    Langevin Curve Fitting for Magnetization and Applied Field Relationship

    hi, there my question is let's suppose we have the magnetization (M) versus the applied field (H) as M(H,T)= \sum _{n=1}^{N} W(x_i ) (x_i ) Lang (H.A.x_{i}/T) here 'A' is a constant 'T' is the temperature of system Lang(x) is the Langevin function coth(x)-1/x , My problem is how to...
  16. R

    Hydraulic Fitting - Max Temperature

    Customer of mine is wanting me to confirm that a hydraulic fitting I am selling him will withstand 800F. The fitting is a standard issue hydraulic fitting (#12 BPP Female Coupling) that will be welded to 6" SHD 80 pipe. The pipe is on the exhaust side of a diesel engine onboard a cruise ship...
  17. H_man

    MATLAB Curve Fitting in Matlab: Harry's Experience

    Hi, I've just been trying unsuccessfully to fit a polynomial to a large set of data in Matlab (1301 points). I want to fit a polynomial to the data so that I have a function with which to try and manipulate the data in different ways. I have no problem fitting polynomials to much smaller sets...
  18. N

    What are some freeware options for fitting radial velocity data?

    Hi all, I am attempting to find the best Keplerian fit to the Radial velocity data vs. Time such as this plot: http://austral.as.utexas.edu/planets/hd37605/hd37605.html I was wondering whether anyone could suggest some freeware that might be able to help me out. Any information would be...
  19. N

    Mathematica Mathematica, fitting an arbitrary number of parameters

    Let's say I have some data, as a function of a variable x. I want to fit this to the real part of the function \frac{A}{1-ix}\left(1+\sum_{n=1}^\infty\frac{c_n}{(1-ix)^n}\right) by numerically fitting the first N of the c_n's (A is fixed). I tried something like A = 1; N = 100; fit...
  20. N

    Data points and fitting functions

    Homework Statement I have made an experiment with a Hall-meter and I have got some data. I know have an expression on the form B(a) = \mu IN\frac{{a^2 }}{{2\left( {a^2 + z^2 } \right)^{\frac{3}{2}} }} where z = 0.02 m and a is my only parameter varyring. I have plottet these data, and I...
  21. D

    Find Fitting Function for Plot Without Data Points

    Hi there, This might be a sort of vague question, but if I have a plot say that I don't know the data points for, how can I go about trying to find a fitting function (basically a functional form) for the curves I'm looking at? Basically I have a figure I got from a journal paper that I want to...
  22. E

    How do I use Least Square Fitting to Calculate the Best Line of Fit?

    Hey I need to use the Least Square Fitting approach to calculating the best line of fit. I have read loads, and can't seem to figure out how to get passed the Inverse matrix part? Anyone know any good links, or can guide me on how to do least square fitting? Thanks
  23. D

    Curve fitting and least squares method.

    Homework Statement I have an equation as a function of time. (eq1) C(t) = Css + a(e^.5t) + b(e^.9t) t>0 Where, Css is a constant. then I have 6 data points of time and C (Concentration of a liquid) 1. I have to find an equation to find the maximum time and contains a, b and Css...
  24. deccard

    Measurement error analyses, fitting min/max slopes to data with error bars.

    I have measurement dataset (x_i,y_i) -pairs with error for each value \Delta x_i and \Delta y_i so that I can plot datapoints with vertical as well as horizontal errorbar. I want to fit linear regression line y=a_1 x + a_0 and also error lines to the data. But how I take into account as...
  25. R

    MATLAB Curve Fitting with Matlab: Solving Waveform Division using Invfreqz

    hi, I am trying to do a curve fitting for a waveform obtained from the division of 2 FFT data. So, I used invfreqz in Matlab so that I can obtain the transfer function of the waveform, and at the same time, find an estimated waveform for the curve obtained. However, I can't seem to do it...
  26. B

    Fitting quadratic curve to three constraints

    This should be easy but I've not done this in years and I'm feeling dense: I need to fit a quadratic curve to three constraints, two of which are points, the third is an angle. I've found examples to do this but only if all three constraints are points, so if someone would kindly explain...
  27. A

    MATLAB Fitting a Curve to Data: MATLAB vs Excel

    I have a set of data and I need to fit a curve to it. The equation of the curve is: y=20-a*10*log(x) My problem is just getting a curve fit to this equation. What function in MATLAB should I be looking for? How do I get the value of 'a'? Is it easier to achieve this in Excel? How?
  28. B

    Least-Squares fitting of King's Equation

    Homework Statement A hot wire is placed in a region of mass air flow. There is a current on the wire causing it (wire) to heat up. The current is regulated such that the wire temperature is constant. Measurement of current on the wire is related to the mass airflow by King's Equation...
  29. D

    Method of Least Squares Linear Fitting

    Homework Statement An experiment was conducted on a liquid at varying temperatures and the volume obtained at the differing temperatures are as follows: V/cm3 θ/oC 1.032 10 1.063 20 1.094 29.5 1.125 39.5 1.156 50 1.186 60.5 1.215 69.5 1.244 79.5 1.273 90 1.3 99 Assume that V...
  30. T

    Find Best Quadratic Bezier Curve Fit for Points

    hello having a set of points of a curve, how i can find the best quadratic bezier curve that fits this curve? (so we have start and end points of bezier curve, and only the position of control point is required.) THX.
  31. G

    What is the simplest curve that fits this data?

    I have a set of data points relating the width of an object in an image to its distance from the camera. I'd like to find the simplest curve that fits "pretty well". When I graph the points, it looks like a hyperbola would be a good fit. Is there a simple iterative method to find an equation...
  32. H

    Data Fitting with Bezier curve

    Does anyone know how to fit a cubic Bezier curve to a given set of data points? If so, I'd appreciate some coaching on the methodology. Bezier curves have separate equations for x and y in a parametric variable t that varies from 0 to 1: x = at3 + bt2 + ct + d y = et3 + ft2 + gt + h...
  33. A

    Aerospace: Banjo Fitting and Its Uses

    Hi, What is Banjo fitting?(In Aerospace) Application of it?
  34. S

    Fitting points from a straight line segment onto a circular segment

    Hello, I have a problem I need to solve quickly... basically, I have a set of points in 3D space that make up a straight segment of a nanotube, and I want to "bend" the points along a circle (to simulate what happens if you bend a nanotube into a torus). I basically want to do to all of my...
  35. C

    Equation Fitting: Seeking Insight to Meet Requirements

    I'm almost too embarrassed to post, but I thought someone might have insight that could help me here. I'm trying to fit an equation to data, but I'm just not sure what sort of equation I should use. I have some requirements on the form of the equation, and then I have points (yet to be...
  36. L

    Fitting an inverse quadratic curve

    If I know 2 points in the +x,+y quadrant, and I want to find the f(x) = a -------- (b*x)^2 curve that passes through both points (a and b are constants). This is probably either really simple or impossible. :rolleyes:
  37. Clausius2

    Optimal Function for Computational Mesh: Achieving Desired Shape and Flexibility

    I am seeking a function r=r(\eta) for a computational mesh. It has to have the same shape as the one shown in the figure attached. This figure has been achieved via polinomical approximation, but it doesn't give me many chances to change parameters of contractions. Maybe there is an analytical...
  38. C

    Can I Use a 60 Watt Bulb in a "40 Watt Max" Fitting?

    Gday, This is a very simple question and it should only take one sentence to answer. It's not worthy of these forums, lol, but despite my efforts I cannot find an answer through google. If a light fitting says '40 watt max' and I stick a 60 watt bulb in it, will that have any adverse...
  39. A

    Fitting a Sine Curve to Two Points

    I'm a web developer working on a bit of javascript code for a personal project. I took through Calc II and linear algebra in college, but haven't looked at any of it a couple of years, so I'm a little rusty on the details. Anyway, what I'm trying to work out is a way to scale/transform an...
  40. B

    Need help with polynomial fitting

    I have two polynomials fit to two different sets of data points. What I need to know is if there is a way to obtain a polynomial such that it will minimize the distance between all the points on both the other polynomials?
  41. A

    Men's Slim Fitting Suits - Where to Buy

    Guys.. Does anyone know where to find really slim fitting suits? (male)
  42. D

    Can 3D Bin Packing Algorithms Optimize Box Packing?

    Hello, I'm writing some code that will check if an array of products with given dimensions (length, width, height) can fit inside of a shipping box of given dimensions (length, width, height). Is there an algorithm to do this, or could someone point me in the right direction of where to go...
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