Classical least squares calibration based

MLR is based on classical least squares regression. Since known samples of things like wheat cannot be prepared, some changes, demanded by statistics, must be made. In a Beer s law plot, common in calibration of UV and other solution-based tests, the equation for a straight line... 

Experience in this laboratory has shown that even with careful attention to detail, determination of coal mineralogy by classical least-squares analysis of FTIR data may have several limitations. Factor analysis and related techniques have the potential to remove or lessen some of these limitations. Calibration models based on partial least-squares or principal component regression may allow prediction of useful properties or empirical behavior directly from FTIR spectra of low-temperature ashes. Wider application of these techniques to coal mineralogical studies is recommended. 

The p and k matrix methods are two classical least squares approaches to multicomponent calibration. There are techniques based on factor analysis, however, that are increasingly popular these include the... 

Multiwavelength methods. Least squares curve fitting techniques may be used in the determination of multicomponent mixtures with overlapping spectral features. Two classical quantitation methods, the Classical Least Squares (CLS) mode and the Inverse Least Squares (ILS) model, are applied when wavelength selection is not a problem. CLS is based on Beer s law and uses large regions of the spec-tram for calibration but cannot cope with mixtures of interacting constituents. ILS (multivariate method) can accurately build models for complex mixtures when only some of the constituent concentrations are known. 

Because of peak overlappings in the first- and second-derivative spectra, conventional spectrophotometry cannot be applied satisfactorily for quantitative analysis, and the interpretation cannot be resolved by the zero-crossing technique. A chemometric approach improves precision and predictability, e.g., by the application of classical least sqnares (CLS), principal component regression (PCR), partial least squares (PLS), and iterative target transformation factor analysis (ITTFA), appropriate interpretations were found from the direct and first- and second-derivative absorption spectra. When five colorant combinations of sixteen mixtures of colorants from commercial food products were evaluated, the results were compared by the application of different chemometric approaches. The ITTFA analysis offered better precision than CLS, PCR, and PLS, and calibrations based on first-derivative data provided some advantages for all four methods. ... 

In the MCR framework, there are few cases in which the quantitative analysis is based on the acquisition of a single spectrum per sample, as is the case for classical first-order multivariate calibration methods, such as partial least squares (PLS), seen in other chapters of this book. There are some instances in which quantitation of compounds in a sample by MCR can be based on a single spectrum, that is, a row of the D matrix and the related row of the C matrix. Sometimes, this is feasible when the compounds to be determined provide a very high signal compared with the rest of the substances in the food sample, for example colouring additives in drinks determined by ultraviolet—visible (UV-vis) spectroscopy [26,27]. Recently, these examples have increased due to the incorporation of a new cmistraint in MCR, the so-caUed correlation constraint [27,46,47], which introduces an internal calihratimi step in the calculation of the elements of the concentradmi profiles in the matrix C related to the analytes to be quantified. This calibration step helps to obtain real concentration values and to separate in a more efficient way the information of the analytes to be quantified from that of the interferences. 

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