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

Question

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.

How do you define your criterion for a "best fit"? Least square error? — Eitan T, Sep 19 '12 at 14:13
Yes that's right - thanks for pointing that out as its important. — dr_rk, Sep 20 '12 at 05:27

Andrey Rubshtein · Accepted Answer · 2012-09-19T14:47:37.510

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

@dr_rk, Yes, but it is not recommended because it is slower and less stable numerically — Andrey Rubshtein, Sep 19 '12 at 13:29

score 3 · Answer 2 · answered Sep 19 '12 at 13:27

3

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

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

answered Sep 19 '12 at 13:27

Daniel

104
4

score 2 · Answer 3 · answered Feb 27 '21 at 22:28

2

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.

answered Feb 27 '21 at 22:28

David Chandler

21
2

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

3 Answers3