\begin{definition}[Definition:Method of Least Squares (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.
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\end{definition}