Chemometric methods application in pharmaceutical products and processes analysis and control - Computer-Aided Applications in Pharmaceutical Technology - page 66

adds additional variables one by one, depending on the maximum
reduction of the residual variance, whereas the backwards method
excludes variables one by one.
Once the MLR model is developed, its accuracy in prediction of the
dependent variable on the basis of knowledge of multiple independent
variables is assessed by calculation of the correlation coeffi cient, which is
calculated when true values are compared to predicted ones (predicted by
MLR model). Correlation coeffi cient R can be calculated with the
following formula:

[4.16]

with the values of R ranging from 0 (no correlation) to 1 (perfect
correlation). The reader should take care to never confuse coeffi cient of
determination with correlation coeffi cient.
Correlation coeffi cient is not reserved for MLR, as it is one of the most
frequently used statistic parameters for assessment of validity of the
developed model regardless of the model type. Except where x -variables
are controlled in designed experimentation, measured data in
pharmaceutical applications are typically multivariate and collinear and
MLR cannot be used (Rajalahti and Kvalheim, 2011). Therefore, in these
instances, other techniques should be applied.
In order to improve results of MLR modeling, LV regression methods
(LVR) are used where the new set of variables (latent, orthogonal) is
calculated from the original ones, thereby reducing dimensionality of
variables. Collinear variables can be combined and described by fewer
so-called factors or LVs, which describe the underlying structure in the
data (Rajalahti and Kvalheim, 2011).

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Principal Component Regression (PCR)

PCR is a combination of PCA and MLR. Once the PCs of the analyzed
data are identifi ed, MLR is performed on the scores of independent
(predictor) variables. If only the major PCs are used, noise is signifi cantly
reduced and error in predictions of dependent variables is very low. When
PCR is applied, it is important to note that derived PCs are not necessarily
directly infl uencing dependent properties. PCs are revealing variation in
independent (predictor) data that may or may not infl uence dependent