Regressionsanteile

Regressionsanteil is a term used in statistics to describe the share of the total variability of a dependent variable that is explained by a regression model. It is the portion of the total sum of squares (SST) that is accounted for by the regression, quantified as SSR/SST, where SSR is the regression sum of squares and SSE is the residual sum of squares. In simple linear regression with an intercept, the regression share equals the coefficient of determination, R-squared, i.e., R^2 = SSR/SST = 1 - SSE/SST. In multiple regression, the concept generalizes to the same ratio SSR/SST. It is unitless and ranges from 0 to 1.

Interpretation and use: A higher Regressionsanteil indicates that the model explains a larger portion of the dependent variable’s variability. It is commonly used to assess model fit and to compare competing models. However it does not imply causality and can be influenced by adding predictors; adjusted R-squared provides a version that penalizes model complexity. Limitations include sensitivity to data range and outliers, and it is not a direct measure of predictive accuracy on new data. Calculation notes: SSR = sum (ŷ_i − ȳ)^2, SST = sum (y_i − ȳ)^2, R^2 = SSR/SST = 1 − SSE/SST.

Example: If SST = 800, SSR = 500, and SSE = 300, then Regressionsanteil = 0.625 (R^2 = 0.625), meaning 62.5% of the total variance in y is explained by the regression model.