Category:Method of Least Squares (Approximation Theory)

This category contains results about the method of least squares in the context of approximation theory.
Definitions specific to this category can be found in Definitions/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 $y = m x + c$

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

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