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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

Relation to other concepts

Störgröße (disturbance or input error) are external factors that influence measurements. Restgröße refers to the portion

Applications

Restgrößen are used in residual analysis to evaluate model fit, in quality control to detect calibration issues,

Example

In a calibration setting, measured values y_i are compared with predicted values ŷ_i from a calibration function.

See also

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

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.
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.
and
in
uncertainty
assessment
to
quantify
unexplained
variance.
They
also
inform
model
refinement,
such
as
adding
predictors
or
correcting
for
biases.
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.