Does this help?

with(LinearAlgebra):
 

X := Vector[row]([x1(x),x2(x),x3(x)]);

Dot product:
 X.X;

differentiating every component by x:
map(f -> diff(f,x),X);

multiplying every component by x
map(f -> f*x,X);

adding one to every component of X:

X + Vector[row]([1,1,1]);

Thank you John. Thank you Robert.

Thanks for the help!

The example given in the link fits a plane to a set of 3D points. Is there a way to fit a line to them? And to calculate the least squares error?

(At the moment my points in x, y and z coordinates are in matrix form, with one point per row, but I could write a function to change it to lists of coordinates.)

I've been searching through least squares and fit and couldn't find out how...

PS. Sorry. I accidentally pressed flag thinking it was something else (i thought it meant it'll notify me when someone replies) and now I don't know how to unflag it...