Gütemaßzahl

Gütemaßzahl, often translated as "goodness of fit" or "coefficient of determination," is a statistical measure used to assess the proportion of the variance in a dependent variable that is predictable from an independent variable or variables in a regression model. It is denoted by the symbol R² and is always between 0 and 1, or 0% and 100%.

An R² value of 1 indicates that the regression model perfectly predicts the dependent variable, while an R² value of 0 indicates that the model does not predict the dependent variable at all. In practice, R² values between 0.5 and 1.0 are considered good, while values below 0.5 are considered poor.

The Gütemaßzahl is calculated as the square of the correlation between the observed and predicted values of the dependent variable. It is an indicator of how well the regression model fits the data. However, it does not indicate whether the model is adequate, as it does not measure the bias of the model or the distribution of errors.

It is important to note that R² can increase artificially when unnecessary independent variables are added to the model, a phenomenon known as overfitting. Therefore, it is often used in conjunction with other statistical measures to assess the overall fit of a regression model.

The Gütemaßzahl is widely used in various fields, including economics, social sciences, and engineering, to evaluate the effectiveness of predictive models.