# curve of best fit from a few points

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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.

##### 3 Comments

amberly hadden
on 16 Jun 2014

### Accepted Answer

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)

##### 3 Comments

Ghada Bakaraki
on 3 Jan 2021

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

### More Answers (3)

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.

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???

##### 0 Comments

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

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

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