MATLAB: 3D line of best fit

Question

I have about 50000 points with x,y,z data spread in 3 coloumns in excel. I have managed to create a plane of best fit. (by creating a comma delimited file, importing it, setting each column as a variable, then using the SFTOOL function. This gives me a plane of best fit through the data when I select the plane to be polynomial with degrees x=1 and y=1).

What I cannot seem to do is create a line of best fit through this data. This line must be a straight line and I would like to know the parametric equation of this line.

I would be most grateful if someone could advise me (a complete matlab beginner) how to go about this.

Many thanks

regards

kanai

Answer 1

Suppose the rows of xyz are your data points,

 r0=mean(xyz);
 xyz=bsxfun(@minus,xyz,r0);
 [~,~,V]=svd(xyz,0);

The parametric equation is

 r(t) = r0 + t*V(:,1);