The occurrence of rotational effects (matrix effects proportional to the size of the analyte concentration) posses a severe analytical problem when separation of the analyte from any interfering species is not possible. Univariate calibration requires complete separation of the analyte from all interfering species, which is not always possible. Alternatively,Classical Least  Squares (CLS) assumes that the measurements are the weighted sum of linearly Independent signals. In spectroscopy, for example, the CLS model assumes that measured spectra are the sum of the pure component spectra weighted by the concentration of the analytes. The main disadvantage of CLS is that the pure responses must either be known a priori or estimated from the data. Furthermore, the pure component responses must be linearly independent.

Where either interferent free regions of the spectrum are unavailable, or pure spectra for all spectrally active species are unavailable, the use of interference rich spectral regions may enable multivariate calibration to be performed. By using more than one dependent variable it may be possible to determine the analyte of interest by modelling the changes in a series of calibration solutions that contain both the analyte and interferents. So-called inverse modelling eliminates the requirement of knowing or having to estimate the pure spectra of all spectrally active species by using an inverse least squares model. Inverse least squares (ILS) assume that a regression vector can be used to determine a property of the system (e.g. concentration) from the measured variables. There are many ways to perform ILS; perhaps the most common is multiple linear regression (MLR). Unfortunately, this approach fails in practice because of collinearity of the calibration matrix X, e.g. some of the columns of X (variables) are linear combinations of the other columns, or because X contains fewer samples than variables. For example, a spectroscopy calibration problem may be extremely ill conditioned due to a high degree of correlation between absorbencies at nearby wavelengths. It also typical that there are fewer calibration samples than the number of wavelengths in the model.

To help overcome these problems, Partial Least Squares (PLS) 1-4 uses a linear combination of the independent variables. In this manner collinearity is no longer a problem and the number of new variables (latent variables or principal components) is usually much fewer than the number of wavelengths used, hence accurate predictions can be made. It was for these reasons that PLS was used in this feasibility study.