This question is purely for curiosity's sake:

Suppose I have a collection of points on a 2D plane {P1, P2,..., Pn}

How would I find the point X such that the sum of the magnitude of all vectors (||PnX||) is the smallest possible.

- June 1st 2010, 11:12 AMBigCPoint that is at the shortest total distance from multiple points
This question is purely for curiosity's sake:

Suppose I have a collection of points on a 2D plane {P1, P2,..., Pn}

How would I find the point X such that the sum of the magnitude of all vectors (||__PnX__||) is the smallest possible. - June 1st 2010, 11:34 AMdwsmith
- June 1st 2010, 12:05 PMBigC
- June 1st 2010, 12:44 PMdwsmith
The line of best fit uses least-squares. If your points are in a linear fashion, you can come up with a line, y=mx+b, where the magnitude is minimized. The line you achieve will be the line of best fit. Of course, we could do this for circles, quadratics, polynomials, etc.

- June 1st 2010, 12:59 PMBigC
- June 1st 2010, 01:07 PMdwsmith