# Proving the nonuniqueness of the intersection of minimal deviation lines (given a set of points)

Heres the problem that I have formulated based on my observation (of the result). I am trying to understand why such a result holds, and hopefully be directed to similar mathematical websites/literature that can help me understand.

Problem:

Given a set of points and a line with a slope of m, we want to find the y intercept that minimizes the deviation of the points from the line. This is the "minimal deviation line", given the slope of the line.

The deviation of a point from a line is the perpendicular distance of the point to the line, with a positive sign if the point is above the line, and a negative sign if the point is below the line.

Prove that the intersection of two such lines with different slope is always at the same point, regardless of which lines (of whatever slope) we choose.

I tire of searching wiki endlessly :) Thank you !

• The point is the mean of the data, but i was just wondering about the geometry of the situation. Taking the deviation is like reducing the data to one-dimension, and then the mean of all the data is the point through which any line has a residue of zero with respect to the points. – user1055563 Nov 18 '13 at 2:13