Definition:Method of Least Squares

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 $y = m x + c$

$\forall k \in \set {1, 2, \ldots, n}: x_k' = x_k$

$\ds \sum_n \paren {y_k' - y_k}^2$ is minimised.

Statistics

The method of least squares, in the context of statistics, is a method to estimate parameters, particularly in regression models.