koefficiensét

Koefficiensét is a term used in mathematical modeling and statistics to denote the set of coefficients that determine the influence of each predictor in a model. The term reflects a Hungarian adaptation of the word coefficient, with the suffix -ét signaling a collective noun that names the whole set. In common notation, the koefficiensét is represented as a vector β in linear models.

In a standard linear model, y = Xβ + ε, the koefficiensét comprises the elements of β, with each component corresponding to a predictor’s partial effect on the response. The intercept is often included as the first element of the koefficients, sometimes denoted β0, together with the slope terms β1, β2, and so on.

Estimation and interpretation: The koefficiensét is estimated from data using fitting procedures. Ordinary Least Squares yields β̂ = (X^T X)^{-1} X^T y under typical assumptions. Regularization methods, such as ridge (L2) and lasso (L1), produce biased but often more stable koefficiensét estimates to address multicollinearity and overfitting. Each coefficient represents the expected change in the response per unit change in its associated predictor, holding other predictors constant. Feature scaling affects the numeric values and comparability of the koefficiensét across predictors.

Extensions and limitations: In generalized linear models, the koefficiensét links linear predictors to mean responses through a chosen link function. When interactions or polynomial features are included, the koefficiensét expands accordingly. Multicollinearity, model misspecification, and regularization choices can influence interpretation and stability of the koefficiensét.