Least squares
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The method of least squares or ordinary least squares (OLS) is used to solve overdetermined systems.Least squares is often applied in statistical contexts,particularly regression analysis.
Least squares can be interpreted as a method of fitting data.The best fit in the least-squares sense is that instance of the model for which the sum of squared residuals has its least value,a residual being the difference between an observed value and the value given by the model.The method was first described by Carl Friedrich Gauss around 1794.[1] Least squares corresponds to the maximum likelihood criterion if the experimental errors have a normal distribution and can also be derived as a method of moments estimator.Regression analysis is available in most statistical software packages.
The discussion is presented in terms of polynomial functions but any function can be used in least-squares data fitting.For example,a Fourier series fit is optimal in the least-squares sense.