Curve fitting Definition and 59 Threads

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. 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...
  2. C

    How Do You Relate Fitted Curve to Mean, Standard Deviation, and Standard Error?

    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...
  3. 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...
  4. 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...
  5. 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...
  6. 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...
  7. 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...
  8. 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...
  9. 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.
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