Forklaringsgrad

Forklaringsgrad, or explained variance, is a statistical measure that indicates how well a regression model accounts for the variability of the dependent variable. In linear regression, it is commonly expressed as R^2, the proportion of the total variance of the dependent variable that is explained by the independent variables. R^2 takes values from 0 to 1 (0% to 100%); higher values suggest the model captures more of the variability in the data.

Calculation and interpretation: R^2 = 1 - SSE/SST, where SSE is the sum of squared residuals and SST is the total sum of squares. In multiple regression, R^2 tends to increase when more predictors are added, even if they do not improve predictive power. Therefore, adjusted R^2 is used to compare models with different numbers of predictors; it adjusts for model complexity and provides a more accurate comparison.

Limitations: A high forklaringsgrad does not imply causation, and the statistic can be influenced by outliers and the range of the data. It is also sensitive to model specification and cannot be directly compared across different datasets. It should be used along with other diagnostics.

Non-linear models and alternatives: For logistic regression or other non-linear models, traditional R^2 is not appropriate; researchers often report pseudo-R^2 measures (such as McFadden's or Nagelkerke's) that approximate explained variance but have different scales and interpretations.

Usage: The forklaringsgrad is commonly used to assess model fit and to compare alternative specifications on the same data. It is most informative when reported consistently and interpreted in the context of the data and modeling approach.