Definition:Method of Least Squares
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Definition
Approximation Theory
Let there be a set of points $\set {\tuple {x_k, y_k}: k \in \set {1, 2, \ldots, n} }$ plotted on a Cartesian $x y$ plane which correspond to measurements of a physical system.
Let it be required that a straight line is to be fitted to the points.
The method of least squares is a technique of producing a straight line of the form $y = m x + c$ such that:
- the points $\set {\tuple {x_k', y_k'}: k \in \set {1, 2, \ldots, n} }$ are on the line $y = m x + c$
- $\forall k \in \set {1, 2, \ldots, n}: y_k' = y_k$
- $\ds \sum_n \paren {x_k' = x_k}^2$ is minimised.