3-D line of best fit from origin to cloud of data points

I'm trying to get a line of best fit for a 3-D set of data points. This line of fit should go from the origin to the "cloud" of points, and I'd like to know the equation for that fit. Any ideas?

Thanks

Answer 1

[Matt J]

The equation is t*u where u is 3D line direction vector obtained by,

[V,d]=eig(A.'*A,'vector');
[~,i]=max(d);
u=V(:,i);

and A is an Nx3 matrix whose rows are your cloud points.

[Wes Anderson]

Thank you. What does t represent in this equation? I'm trying to find a regression to use for future data for an axis shift based off of this data...if that makes sense.

[Matt J]

t is an arbitrary scalar. For different choices of t, you get different points along the line.

[Wes Anderson]

Thank you for replying. So, for new data, when I want to use this transformation/line fit, where do I plug the new data in? Or is that not how this works...I'm sorry if that is a dumb question.

Thank you again

[Matt J]

Not sure what you mean by "new data" nor what you mean by "use this transformation". You haven't described what you plan to do with the line fit once you have it. But what I can say is, the steps I showed do indentify the best fit line and give you a way to calculate different points along the line (by evaluating t*u for different t).

https://math.oregonstate.edu/home/programs/undergrad/CalculusQuestStudyGuides/vcalc/lineplane/lineplane.html

[Chang hsiung]

wow, thanks a lot Matt !!!

[Matt J]

@Chang hsiung You're quite welcome. Please accept-click the answer if it helped you.