The General Problem
Consider an overdetermined system
of m linear equations in n unknown coefficients, β1,β2,…,βn, with m > n. This can be written in matrix form as
where
Such a system usually has no solution, so the goal is instead to find the coefficients β which fit the equations "best," in the sense of solving the quadratic minimization problem
where the objective function S is given by
A justification for choosing this criterion is given in properties below. This minimization problem has a unique solution, provided that the n columns of the matrix X are linearly independent, given by solving the normal equations
Read more about this topic: Linear Least Squares (mathematics)
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