Multiple linear regression, analytical methods

If the system is not simple, an inverse calibration method can be employed where it is iKst necessary to obtain the spectra of the pure analytes. The three inverse methods discussed later in this chapter include multiple linear regression (MLR), jirincipal components regression (PCR), and partial least squares (PLS). Wlien using. MLR on data sees found in chemlstiy, variable. sciectson is... 

ILS is a least-squares method that assumes the inverse calibration model given in eqn (3.4). For this reason it is often also termed multiple linear regression (MLR). In this model, the concentration of the analyte of interest, k, in sample i is regressed as a linear combination of the instrumental measurements at J selected sensors [5,16-19] ... 

Most organic compounds when subjected to infra-red radiation present characteristic absorption bands. The spectral data are compared to those obtained for standard reference wines used to calibrate the instrument. The concentration of the analytes is calculated using multiple linear regression the apparatus is computerised and can be linked to an automatic sampler. The analyte should exhibit strong absorption bands for the method to be exploitable, and it is thus only suitable for major wine or must constituents, essentially ethanol and sugars. The major qualities of this technique are simplicity of operation, high sample throughput and the lack of necessity for sample preparation - the only required sample re-treatment is the removal of carbon dioxide from musts in fermentation. 

The method of standard additions has been used to suppress the influence of the bulk composition of solid samples. It requires that the analyte contained in the solid sample and the added analyte be identically affected by the matrix. This method can be used in three different ways in connection with solid samples. One involves adding increasing amounts of analyte to fixed amounts of sample. In the second, a single amount of sample is subjected to a single addition of analyte from a standard solution, which can lead to inaccuracy in the final result. In the third approach, both the amount of solid sample used and that of standard added are varied the instrumental signal is a function of two independent variables and can be extracted by multiple linear regression. 

These special cases of multiple linear regression analysis have been developed for the determination of the impact of individual molecular substructures (independent variables) on one dependent variable. Both techniques are similar yet, the Free-Wilson method considers the retention of the unsubstituted analyte as base, while Fujita-Ban analysis uses the less substituted molecule as reference. These procedures have not been frequently employed in chromatography only their application in QSRR studies in RP TLC and HPLC have been reported. 

Some application software programs use methods known as MLR multiple linear regression) that permits the statistical treatment of a large number of data points in order to establish a calibration equation. These chemiometric methods take advantage of all the absorptions measured at different wavelengths, irrespective of their origin analyte to be measured, matrix or artefacts of the instrument. 

The ultimate development in the field of sample preparation is to eliminate it completely, that is, to make a chemical measurement directly without any sample pretreatment. This has been achieved with the application of chemometric near-infrared methods to direct analysis of pharmaceutical tablets and other pharmaceutical solids (74-77). Chemometrics is the use of mathematical and statistical correlation techniques to process instrumental data. Using these techniques, relatively raw analytical data can be converted to specific quantitative information. These methods have been most often used to treat near-infrared (NIR) data, but they can be applied to any instrumental measurement. Multiple linear regression or principal-component analysis is applied to direct absorbance spectra or to the mathematical derivatives of the spectra to define a calibration curve. These methods are considered secondary methods and must be calibrated using data from a primary method such as HPLC, and the calibration material must be manufactured using an equivalent process to the subject test material. However, once the calibration is done, it does not need to be repeated before each analysis. 

The utilization of ion-selective membrane electrodes involves their prior calibration. It is necessary to make a regression to obtain good reliability of the analytical information. Because a linear relation between the independent and dependent variables cannot forced, sometimes the nonlinear calibration method is successful. The ion-selective membrane electrode linearization and subsequent calibration use multiple linear regression (MLR) and/or partial least-squares (PLS) when limited calibration data are available.219... 

Garrels and MacKenzie (1967) solved for these values using a sequential subtraction process. The more general multiple linear regression method used here distributes the rounding and analytical errors over the 4 estimates and is amenable to expansion to a much larger set of reactions. 

The generalized standard addition method of calibration reported by Saxberg and Kowalski is a combination of the standard addition method and multiple linear regression analysis. It develops calibration relations capable of determining analyte concentrations in the presence of interferents. This method is now built into commercial chemical instrumentation for on-line usage, and it is therefore practical to use in a routine way. 

Optical analysis can be done relatively fast. NIR analysis can be performed within a few seconds, depending on the magnitude of the analytical signal, sample absorbance, and overall error of the measurement. Simple analytes like moisture require only two to three wavelengths. On the other hand, more complex analytes may be calibrated best using up to six wavelengths. Multiple linear regression is the best calibration technique [125]. Near-infrared analysis is typically a secondary analytical method, i.e. it has to be calibrated with several samples of known concentrations. 

PG and BHA were simultaneously determined in food samples using stopped-flow mixing technique and a DAD [81]. The method was based on the different kinetic behavior of the analytes when reacted with 3-methylbenzothiazolin-2-one hydrazone in the presence of cerium(IV) and the measurement of the absorbance of each reaction product at a different wavelength. The determination was carried out using a system of two equations, which was resolved by multiple linear regression. 

This method is commonly known as inverse least-squares (ILS) regression, but it is also referred to as the P-matrix method or multiple linear regression (MLR) when the number of analytical wavenumbers is small. ILS is a multivariate technique that has some advantages over CLS, but ILS also has some shortcomings. 

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