Feilkvadrater

Feilkvadrater, often translated as "least squares," is a fundamental method in mathematics and statistics used for solving systems of equations that are either inconsistent or have more equations than unknowns. The core idea is to find a solution that minimizes the sum of the squares of the differences between the observed values and the values predicted by the model. This minimization process is what gives the method its name.

When faced with an overdetermined system of linear equations, where there is no single exact solution that satisfies all equations simultaneously, the method of least squares provides a way to find the "best fit" solution. Instead of seeking an exact match, it aims to find parameters for a model that make the residuals, which are the differences between the observed data and the model's predictions, as small as possible when squared and summed.

The method is widely applied in various fields. In regression analysis, it's used to estimate the coefficients of a linear model by fitting a line or curve to a set of data points. This allows researchers to understand the relationships between variables and make predictions. In signal processing, it can be used for noise reduction and system identification. The mathematical derivation typically involves calculus, specifically finding where the partial derivatives of the sum of squared errors with respect to the model parameters are equal to zero.