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6.3. Segmented Least Squares: Multi-way Choices
With this problem, at each step we have a polynomial number of possibilities to consider the structure of the optimal solution.
The Problem
Suppose our data consists of a set P of n points in the plane,:
(x1y1),(x2y2),…,(xnyn), where x1 < x2,…,< xn
Given a line L with equation y = ax + b, we say that an “error” of L with respect to P is the sum of all of its squared distances to the points in P:
Error(L,P) = ∑i =1n (yi - axi- b) 2
