Koefficienter

Koefficienter are numbers that multiply variables in mathematical expressions and equations. In Danish, the standard plural is koefficienter; Koefficienter is sometimes used as a heading or topic name in glossaries and encyclopedias. They function as weights or scale factors that determine the contribution of each term in a model.

In algebra, a coefficient can be a constant or a parameter; in a linear expression such as y = a + b x1 + c x2, b and c are coefficients that determine how strongly x1 and x2 influence y, while a is the constant term. In a polynomial, each term has its own coefficient (the coefficient of x^k is the weight for x^k).

In statistics and machine learning, coefficients are estimated from data to describe relationships. For example, in linear regression y = β0 + β1 x1 + β2 x2, the βs are coefficients: β0 is the intercept, β1 and β2 measure the change in y per unit change in the predictors. Coefficients can be interpreted only within the context of the chosen model and variable scaling.

Calculation and interpretation: Coefficients are commonly estimated by least squares, maximum likelihood, or regularized methods. Their units depend on the units of the variables. Multicollinearity can complicate interpretation, as some coefficients become unstable.

See also: Coefficient, Linear regression, Polynomial, System of linear equations.