middelkvadratisk

Middelkvadratisk, often translated as least squares, is a standard approach in regression analysis to approximate the solution of overdetermined systems or systems of equations in which the number of equations exceeds the number of unknowns. The principle behind the method is to minimize the sum of the squares of the differences between the observed values and the values predicted by the model.

In a typical regression scenario, one seeks to find a function that best describes the relationship between a set of independent variables and a dependent variable. When the observed data points do not perfectly lie on this function, the differences between the actual data points and the function's predictions are called residuals. Middelkvadratisk seeks to find the parameters of the function that make these residuals as small as possible, specifically by minimizing the sum of their squared values. This squared value is used because it penalizes larger errors more heavily and ensures that positive and negative errors do not cancel each other out. The solution derived from minimizing this sum of squares often provides the best linear unbiased estimator (BLUE) under certain assumptions, such as the errors being normally distributed with constant variance.

The method is widely applied in various fields including statistics, physics, engineering, and economics for tasks such as curve fitting, parameter estimation, and data smoothing. It forms the foundation for many statistical models and algorithms.