# curve of best fit from a few points

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Tom on 6 Mar 2013
Commented: JoaquinB on 15 Nov 2019
I have these points: -
x=[1 1.5 2 2.5 3];
y=[19.74 14.26 12.34 11.45 10.97];
and I know I can do a very rough approximation of a curve of best fit simply by "joining the dots" using: -
plot(x,y)
but is there a way to get MATLAB to join them using a curve of best fit?
I'm not sure exactly how to define 'curve of best fit', but I suppose an example might be if one had a string of x-values (+ & -) and each one had a corresponding y-value that was just x^2, then a curve of best fit for those points would show the get close to showing the curve y=x^2.
I obviously don't know the equation of my curve, which I guess is one of the issues that requires a certain method to be adopted over another.

Jan on 6 Mar 2013
There is an infinite number of "good" fits and you can decide arbitrarily, which is the best one. E.g. you could prefer a line, a parabola or another polynomial of a certain degree. You could want a taylor series or Legendre polynomials, SIN or E functions, piecewise continuously differentiable curves, splines, b-splines, etc. How do you define "best"?
Tom on 6 Mar 2013
Well I suppose some assumptions need to be made, i.e. guessing at the nature of the curve. My curve looks like it might be a hyperbola (it's similar to a positive section of y=1/x). If I assumed that then how would I proceed from there?
amberly hadden on 16 Jun 2014
I would suggest you in put your data in terms of x and y. next type cftool. you will get a new window which will ask you to input x and y. then creat data and next step go to fitting option and click new fitting you will see lots of curves. Fit them one by one and see which one is best fit for your data.You will get equation as well.

Azzi Abdelmalek on 6 Mar 2013
Edited: Azzi Abdelmalek on 6 Mar 2013
x=[1 1.5 2 2.5 3];
y=[19.74 14.26 12.34 11.45 10.97];
xi=1:0.2:3
method='spline'
yi=interp1(x,y,xi,method)
plot(xi,yi)

Tom on 6 Mar 2013
Many thanks for this - I think I'll end up using this solution.
Azzi Abdelmalek on 6 Mar 2013
If you have a curve fiting toolbox, you can use fit function

Daniel Shub on 6 Mar 2013
The title of your question says line, bu the body of the question says curve. If you really interested in a straight line, then lsline will do the job.
x=[1 1.5 2 2.5 3];
y=[19.74 14.26 12.34 11.45 10.97];
plot(x,y, '*')
lsline
The source of lsline is available:
type lsline
and you can see it does all the work with polyfit, so it should be possible to create a enhanced version that fits higher order polynomials or your own custom curve.

Tom on 6 Mar 2013
Thanks Daniel. Sorry yes I did want a curve of best fit. Do you know how to do that?
Daniel Shub on 6 Mar 2013
Please edit the question to explain how you are defining the curve of best fit.
Tom on 6 Mar 2013
Okay - done that.

Shashank Rayaprolu on 21 Oct 2017
I took the points and formed a curve using spline function (using spline method and interpl command). But now I want to get the equation of the curve generated.
How should I go about that???

Alex Sha on 20 Oct 2019
The equation below is good enough:
y = p1+p2/(p3-x)^2;
Root of Mean Square Error (RMSE): 0.000924797017843405
Sum of Squared Residual: 4.27624762106028E-6
Correlation Coef. (R): 0.999999958196234
R-Square: 0.999999916392469
Determination Coef. (DC): 0.999999916392469
Chi-Square: 1.87530479087576E-7
F-Statistic: 11960644.0637016
Parameter Best Estimate
---------- -------------
p1 9.87104884862438
p2 9.88400654611518
p3 -0.000758647151949232 #### 1 Comment

JoaquinB on 15 Nov 2019
How did you do that? Curve Fitting Toolbox?