Restgröße

Restgröße is a term used in measurement science, statistics and related fields to denote the portion of a quantity that remains after subtracting the predicted or modeled part from the observed value. In practice, it corresponds to the residual or remainder of a measurement or calculation.

Calculation and interpretation

If y denotes an observed value and ŷ the value predicted by a model (for example a calibration curve or regression line), the Restgröße is R = y − ŷ. For a set of observations, the collection of Restgrößen describes the deviations of data from the model. These deviations can be analyzed to assess the quality of the model and the presence of systematic or random errors.

Relation to other concepts

Störgröße (disturbance or input error) are external factors that influence measurements. Restgröße refers to the portion of the measurement that remains unexplained after accounting for the modeled components; it is what the model does not capture. In regression and experimental analysis, examining the Restgröße (residuals) helps test assumptions like linearity, homoscedasticity and independence.

Applications

Restgrößen are used in residual analysis to evaluate model fit, in quality control to detect calibration issues, and in uncertainty assessment to quantify unexplained variance. They also inform model refinement, such as adding predictors or correcting for biases.

Example

In a calibration setting, measured values y_i are compared with predicted values ŷ_i from a calibration function. The Restgröße for observation i is R_i = y_i − ŷ_i. An analysis of the R_i distribution can indicate whether the model adequately describes the data.

See also

Residual (statistics), Residual analysis, Calibration, Measurement uncertainty.