CODEWITHSUNDEEP
algorithmmatlabnumericalcurve-fittingleast-squares
dr_rk
dr_rk

Reputation: 4565

Fitting a line that passes through the origin (0,0) to data

I have a set of points (x,y) and I need to find the line of best-fit that passes through the origin using MATLAB.

Upvotes: 10

Views: 15939

Answers (3)

David Chandler
David Chandler

Reputation: 21

The best fit line, in general, passes through the centroid of the data (average the x's and average the y's). So find the centroid and plot the line from the origin through the centroid.

Upvotes: 2

Andrey Rubshtein
Andrey Rubshtein

Reputation: 20915

In short: Your function must be in the form of y=ax+0, which makes polyfit useless. But you can use the least squares method:

 a = x(:)\y(:);

Explanation:

You have n equations and one variable a that is needed to be found:

 a*x1 = y1;
 a*x2 = y2;
 ...
 a*xn = yn;

The operator \ finds the least squares solution.

Alternatively, you can find the solution manually:

 a = (x'*x) \ (x'*y);

or in Pseudo code:

     (x1*y1 + x2*y2  + ... xn*yn)
a =  ----------------------------
     (x1*x1 + x2*x2  + ... xn*xn)

This is useful if you are not using Matlab - for example in C code.

Example and code snippet:

enter image description here

function FindLSSolution()
    a = 2.5;
    x = rand(100,1)*10;
    y = a*x + randn(100,1);
    figure;scatter(x,y);

    A = x(:)\y(:);
    hold on;plot(x, A*x,'g');
end

Upvotes: 15

Daniel
Daniel

Reputation: 104

if you have the "Curve Fitting Toolbox" you can use 

f = fit( x, y, 'a*x' );

Upvotes: 3

Related Questions