Curve fitting for non-linear data
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I am trying to fit some data using lsqcurvefit in MATLAB but I am fairly new to this area.
xdata1 = [0 60 660 1250];
ydata1 = [0 18 23 31];
In the image below, the red line is the fit I want to achieve. Sadly, Polyfit does not provide suitable results.
How can I achieve this fit? Thank you in advance!
More Answers (2)
Chaoyu Zhang on 11 Oct 2018
Edited: Chaoyu Zhang on 15 Oct 2018
You can use the method described below,
The target equation (3rd order or maybe higher) is
y = a*x.^3 + b*x.^2 + c*x + d;
A * p = y;
p is the parameters of the equation,
p = [a;b;c;d]
A is the matrix made of x.^3,x.^2,x,1,
A = [x(1).^3 x(1).^2 x(1) 1; ... ; x(n).^3 x(n).^2 x(n) 1]
y is the vector made of y,
y = [y(1); ... ;y(n)];
p = (A.'*A)^(-1)*A.'*y;
Now you get the parameters you need.
Image Analyst on 11 Oct 2018
You cannot get that unless you put in a model curve for that shape. Otherwise functions are not going to know that it's a piecewise linear fit or some sharply kinked log function or whatever. And having more data points would help too. Then you can use fitnlm.
I'm attaching several examples for piecewise linear fit and non-linear fits.