Factor relation with regression parameters

Tab. 4.10 Comparison of regression equations (n, number of data points r, correlation coefficient s, standard error) relating pharmacokinetic parameters data (X) for P-adrenoceptor blocking compounds to retention factors (k) obtained using an esterIAM.PC.MG and IAM.PC.DD column. (Reprinted from Tab. 3 of ref. 41 with permission from Elsevier Science)...

In Table 5.1, where the statistical model is presented in a polynomial state, a rapid increase in the number of identifiable coefficients can be observed as the number of factors and the degree of the polynomial also increase. Each process output results in a new identification problem of the parameters because the complete model process must contain a relationship of the type shown in Eq. (5.3) for each output (dependent variable). Therefore, selecting the Ne volume and particularizing relation (5.5), allows one to rapidly identify the regression coefficients. When Eq. (5.5) is particularized to a single algebraic system we take only one input and one output into consideration. With such a condition, relations (5.3) and (5.5) can be written as ... 

NIR spectroscopy became much more useful when the principle of multiple-wavelength spectroscopy was combined with the deconvolution methods of factor and principal component analysis. In typical applications, partial least squares regression is used to model the relation between composition and the NIR spectra of an appropriately chosen series of calibration samples, and an optimal model is ultimately chosen by a procedure of cross-testing. The performance of the optimal model is then evaluated using the normal analytical performance parameters of accuracy, precision, and linearity. Since its inception, NIR spectroscopy has been viewed primarily as a technique of quantitative analysis and has found major use in the determination of water in many pharmaceutical materials. 

The first factor is related to steric bulk, the second to hydrogen bonding, the third may be interpreted in terms of volatility-related properties and the fourth in terms of solubility-related properties. By coincidence with simple regression, the p values, the dipole moments and the melting points separate into individual factors, indicating that their information is different from that of the other parameters. The possible mutual intercorrelations between... 

In addition to the set of adjustable coefficients and b contained in Eq. (13.7), the method CMF also requires ealeulation of a certain nmnber of adjustable parameters. Among them are the parameter v for the support vector regression method v-S VR and the ridge parameter y for KRR. Their values should be optimized with the aim to improve the predictive eapability of the model constracted. In addition, for each molecular field one can adjust the values of up to two parameters (attenuation factor, which is related to the width of the Gaussian function) and hj (mixing coefficient, which has the meaning of the relative contribution of molecular field of the ythtype). 

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