Predictions by PLS

Figure 3. Sweet score predicted by PLS model plotted against measured sensory score for 17 volatUe phenols.

The averaged absolute error of the data listed in Table 12.4 is slightly lower than those predicted by PLS. 

Figure 7.9 Correlation between the percentage of fat predicted by PLS and the measured value. The open circles and asterisks indicate, respectively, data for the calibration and prediction sets. (Source Adapted from Ref [14] with permission from Elsevier.)...

Fig.11 Phase diagrams for a PBut-b-PEO, b PBut-b-PEO-fr-PBut, and c PEO-b-PBut-b-PEC). Values of x were calculated for fluctuating melts and appropriate transition temperature. , , A, ODTs o, , 0 OOTs. , o L , C A S G 0 PL. Dashed lines boundaries predicted by exact SCFT with x = 0.6. The solid curves are freely drawn to indicate various phases. From [61]. Copyright 2001 Owner Societies...

Of course, aredk can be negative because P need not be reduced if the step bounds s are too large. To decide whether s should be increased, decreased, or left the same, we compare aredk with the reduction predicted by the piecewise linear model or approximation to P, Pl. This predicted reduction is... 

In Table II the sums of squared residuals (RSS) of Set I are found calculated by the TTFA type model solved by PLS. All 13 potential profiles were predicted from the 40 air samples, while in reality there were only 9 active. The first row contains the RSS s from PLS models predicting one source profile at a time, the second row from the PLS model predicting all the source profiles simultaneously. From the difference of the RSS s between the first nine and the last four profiles it is clear that in this data set there were only nine sources active. These results are Intended only to Illustrate what kind of information is provided by the PLS solution. 

Cd2+ and the Pb2+ and all electrodes display the two peaks but to different extents. Despite the peak overlap, the electrode array can be calibrated for each metal ion using a three-way partial least squares regression (AT-PLS) [53]. The electrode array was employed to analyse three test samples of known concentration of Cu2+, Cd2+ and Pb2+ and the concentrations of each analyte predicted by the calibrated electrode array are shown in Table 10.1. As can be seen from Table 10.1 there is reasonable agreement between the actual and predicted values despite the fact that all electrodes respond to all analytes and that the electrochemical responses to lead and cadmium overlap. Further improvements would be expected if the calibrations were performed with a box experimental design, which encompassed the linear range of all the sensors. 

Figure 9.2 Concentration profile of TFAA and activated lactol obtained by predicting the prediction run with the calibration model built from five PLS factors in the spectral range of 1780-1703 and 1551-1441 crrr1. Inside is the corresponding correlation plot of TFAA and activated lactol for prediction data set predicted by the same calibration model. Reprinted from Cameron etal. (2002)21 with permission from...

Figure 6.6. Illustration of the PLS methodology to relate two co-ordinate systems (X and YJ via score vectors (t and u, respectively). The upper left co-ordinate system contains the measurements X and the upper right co-ordinate system contains the external information, Y. The points in the two co-ordinate systems represent the same set of subjects. By fitting a line in each co-ordinate system to the points and then increasing the correlation between the t-scores and the u-score (lower middle plot) by tilting both lines, the PLS solution is obtained. The Y values of a new subject inside the tolerance region in X can be predicted by following the path indicated by the dotted line.

Fig. 1 Phase diagram of self-assembled structures in AB diblock copolymer melt, predicted by self-consistent mean field theory [31] and confirmed experimentally [33]. The MesoDyn simulations [34, 35] demonstrate morphologies that are predicted theoretically and observed experimentally in thin films of cylinder-forming block copolymers under surface fields or thickness constraints dis disordered phase with no distinct morphology, C perpendicular-oriented and Cy parallel-oriented cylinders, L lamella, PS polystyrene, PL hexagonally perforated lamella phase. Dots with related labels within the areal of the cylinder phase indicate the bulk parameters of the model AB and ABA block copolymers discussed in this work (Table 1). Reprinted from [36], with permission. Copyright 2008 American Chemical Society...

The noninvasive spectra collected from the rat skin can be assigned glucose concentrations on the basis of the reference measurements. They can then be subjected to a routine PLS multivariate analysis, as described above. The results of such an analysis are presented in Figure 13.11 where the concentrations of glucose predicted by the calibration model are superimposed on the measured arterial blood values as a function of time. The squares and circles are used to distinguish the spectra used to train the PLS model and those used for validation purposes, respectively. 

Entrainment flooding is predicted by an updated version of the Souders and Brown correlation. The most popular is Fair s (1961) correlation (Fig. 20), which is suitable for sieve, valve, and bubble-cap trays. Fair s correlation gives the maximum gas velocity as a function of the flow parameter (L/G)V(Pg/Pl), tray spacing, physical properties, and fractional hole area. 

As predicted by theoretical calculations <89AP(322)885>, the site of electrophilic attack on pyrazolo[3,4-c]pyridines is C-3. Reactions such as chlorination, bromination, and nitration of the parent compound (158) all give the 3-substituted derivatives (159) <73JCS(Pl)290l, 89AP(322)885>. 

Quantitative structure-activity/pharmacokinetic relationships (QSAR/ QSPKR) for a series of synthesized DHPs and pyridines as Pgp (type I (100) II (101)) inhibitors was generated by 3D molecular modelling using SYBYL and KowWin programs. A multivariate statistical technique, partial least square (PLS) regression, was applied to derive a QSAR model for Pgp inhibition and QSPKR models. Cross-validation using the leave-one-out method was performed to evaluate the predictive performance of models. For Pgp reversal, the model obtained by PLS could account for most of the variation in Pgp inhibition (R2 = 0.76) with fair predictive performance (Q2 = 0.62). Nine structurally related 1,4-DHPs drugs were used for QSPKR analysis. The models could explain the majority of the variation in clearance (R2 = 0.90), and cross-validation confirmed the prediction ability (Q2 = 0.69) [ 129]. 

The results with PCR and PLS regression include the number of PCs obtained by leave-one-out cross-validation procedure, the values of regression coefficients for X variables, the value of R, and the root mean square error of calibration (RMSE C ) and the root mean square error of prediction by cross-validation proce-... 

Fig. 6. 23. A Glucose profile of a single test person (comparable to that of Fig. 6.13), cgiuc reference value of glucose concentration, o, and the predicted glucose values of NIR measurements, , evaluated by PLS. B Recovery function and fitted calibration line of the PLS calibration (number of included wavelengths n = 56,6 factors). C Recovery function and fitted calibration line of the RBF calibration (number of included wavelengths n = 56,10 hidden layers), according to Fischbacher et al. [1995]...

Now we compare the variation of the brush thickness L with P, as predicted by Eq. (59), with the available data. The first experimental study of this problem [265], performed by SIMS for a series of very short (as compared to a standard depth resolution of this technique) (COOH)dPS (N=125-413) end-anchored chains annealed at different temperatures and with different matrices used (T= 108 °C for P=63, and 160 °C for P=4460), revealed identical unswollen brush conformation for both used matrix molecular weights. The variation of the brush height L with P, at a constant coverage other groups in experiments performed later [241,243]. On the basis of the cumulative data for the Pl-dPS (N=893) brush in the PS host matrix (P=88,495, and 3173), presented in Fig. 37, we were able to achieve an equi-o situation (o=3.7.10 3, see arrow in Fig. 37 and corresponding symbols (A, ) in Fig. 38 as described in... 

Predictions by the PLS model, as illustrated in Fig. 17.3, can be explained as foUows For an object "z", the corresponding x variables in the X matrix define a point in the X space. This point is projected on the first PLS(X) component to afford the score Zn. From the correlation, called the inner relation, the corresponding score, iZjj, along the PLS(Y) component of the Y block is determined. This score corresponds to a point in the Y space, and this point in turn corresponds to the predicted values of each response variable. These can then be compared to the observed responses in the Y matrix. 

Y block was augmented by the predicted optimum conditions from the response surface model, and the corresponding experimental yield. The model was recalculated and then used to predict the result with the bromo compound. Entry 7. Validation of the predictions by response surface modelling and experimental confirmation of optimum predicted by the response surface model is shown in Entry 7. Augmenting the X block and the Y block and recalculation of the PLS model afforded the predictions for p-methylthioacetophenone. An experimental yield of... 

Select an initial set of test systems to span the range of interest of the variation in the principal properties. Run the experiments, and adjust the experimental conditions for each of these systems towards an optimum performance. Fit an initial PLS model which relates the properties of the reaction systems to the optimum experimental conditions. Use the model to predict the optimum conditions for new reaction systems. Validate the predictions by experiments, and update the model by including the validation experiment. Continue the process until a sufficiently good mapping of the reaction space is obtained which permit reliable predictions. At this point, the questions posed to the reaction systems can very likely be adequately answered. 

---