In univariate calibration the aim is to find a relationship which relates
a sample property to a peak area, a ratio of peak areas or a spectral
intensity at characteristic positions. This technique is widely accepted
for quantitative analysis in UV, IR and NIR spectroscopy, where the correlation
of the concentration of a sample and the spectral intensity is stated
by Lambert Beer's Law.
In regression the relationship which relates a sample property like
the concentration C and one or
more explanatory spectral variables X1, X2, ... Xn is defined by
a
polynomial function of nth
order. Thus the physical property is expressed
by spectral variables as shown in the following equation:
C
= c0
+ c1X1
+ c2X2
+ ... + cnXn
+ e
Legend:
C
Amount of an investigated sample property such as the concentration.
e
measurement error or random error
c0,
c1, ..., cn
usually unknown regression coefficients, which need to be determined
during construction of the calibration model.
X1,
X2, ..., Xn
explanatory variables taken from spectral data.
The simplest case is, when there is a single variable X1 and the relationship
is linear:
C
= c0
+ c1X1
+ e
Usually, the regression coefficients c0
and c1
are unknown and e is
some kind of measurement or random error.
In construction
of a calibration with suitable reference data and known property values,
the regression coefficients need to be calculated by polynomial regression
following one of the equations given above. The quality of regression
can be seen from the correlation coefficient and must be optimized by
the user.
Once a calibration model has been established,
the property C can also be calculated
for unknown samples. This procedure is called prediction.
