curve of best fit from a few points

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]

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]

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]

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.

Answer 1

[Azzi Abdelmalek]

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]

Many thanks for this - I think I'll end up using this solution.

[Azzi Abdelmalek]

If you have a curve fiting toolbox, you can use fit function

[Ghada Bakaraki]

this method can be used with any set of points?or only with the given set of points in the question?

Answer 2

[Daniel Shub]

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]

Thanks Daniel. Sorry yes I did want a curve of best fit. Do you know how to do that?

[Daniel Shub]

Please edit the question to explain how you are defining the curve of best fit.

[Tom]

Okay - done that.

Answer 3

[Shashank Rayaprolu]

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???

Answer 4

[Alex Sha]

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

Adjusted R-Square: 0.999999832784938

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

[JoaquinB]

How did you do that? Curve Fitting Toolbox?