jäännösneliöt

Jäännösneliöt, known in English as least squares, is a standard approach to the problem of finding the best fit for a set of data points by minimizing the sum of the squares of the offsets or errors. These errors are the differences between the observed values and the values predicted by the model. The method is widely used in regression analysis and signal processing.

The core idea is to define a function that quantifies the "badness of fit" for a given model and a set of data. This function is typically the sum of the squared differences between the observed data and the model's predictions. The goal then becomes to find the parameters of the model that minimize this sum of squares. This minimization is often achieved using calculus, by finding where the partial derivatives of the sum of squares function with respect to the model parameters are zero.

Jäännösneliöt has several desirable properties. It is statistically efficient under certain assumptions, meaning it provides the best possible estimates in terms of minimizing variance. It is also robust in the presence of some types of errors. The method is mathematically tractable and forms the basis for many statistical and machine learning algorithms, including linear regression. Applications range from fitting curves to experimental data to estimating parameters in complex systems.