Fitted contour plots

Figure 8 Fitted contour plots for percent C, D (temp = 50° and batch addition mode).

Figure Cl.3.6. Contour plot of the H6(4,3,2) potential for Ar—HF, which was fitted principally to data from far-...

Cornell discussed the significance of the component effects and nonlinear blending behavior by examination of the coefficients of the fitted model and by contour plots. No optimal formulation, however, was determined by this analysis. A minimization of the response by the Complex algorithm yielded the optimum response of -2.204 achieved at ... 

Fig. 1. TRJPES of azobenzene with 330nm excitation and 200nm ionisation (left) and global fit (right). The two-dimensional spectrum (contour plot) shows the photoelectron spectra along the x-axis (integrated spectrum shown at bottom) and the evolution with the pump-probe time delay on the y-axis (integrated decay trace shown on the left).

In addition to the nonlinear least square fittings, in order to visualize the variations of fitting as a function of contour plots of A(4>B, oc) = (F IeXp,v -Icai,v 2)1/2 have been generated, where IeXp,v are experimental current values at different bias and Icai,v are calculated ones using Eq. 3.2. Figure 3.12(b) is such a contour plot generated for the C12... 

FIGURE 3.12. (a) Measured C12 I(V) data (circular symbols) is compared with calculated one (solid curve) using the optimum fitting parameters of <1>b = 1-42 eV and a = 0.65. Calculated I(V) from the simple rectangular model (a = 1) with <1>b = 0.65 eV is also shown as dashed curve. Current is on log scale, (b) Contour plot of A (b, B and a, where the darker region corresponds to a better fitting. 

I(V) data (300 K). In this plot, darker regions correspond to a more accurate fitting. The best fitting condition from this contour plot was determined to be [Pg.57]

Fig. 8.9. Contour plot of the potential energy surface of H2O in the BlA state as a function of the H-OH dissociation bond Rh-oh and the HOH bending angle a the other O-H bond is frozen at the equilibrium value in the ground electronic state. The energy normalization is such that E = 0 corresponds to H(2S ) + OH(2E, re). This potential is based on the ab initio calculations of Theodorakopulos, Petsalakis, and Buenker (1985). The structures at short H-OH distances are artifacts of the fitting procedure. The cross marks the equilibrium in the ground state and the ellipse indicates the breadth of the ground-state wavefunction. The heavy arrow illustrates the main dissociation path and the dashed line represents an unstable periodic orbit with a total energy of 0.5 eV above the dissociation threshold.

Fig. 5.18. A contour plot of fitted yield when x3 = 1.75. (From Statistics for Engineering Problem Solving (1st Ed.) by S. B. Vardeman 1994. Reprinted with permission of Brooks/Cole, a Division ofThomson Learning www.thomsonlearning.com. FAX 800-730-2215.)...

One s understanding of fitted polynomial (and other) relationships often is enhanced through the use of contour plots made on coordinate systems such as that in Fig. 5.25. (This is even true forp > 3 component mixture scenarios, but the use of the idea is most transparent in the three-component case.) A plot like Fig. 5.25 can be a powerful tool to aid one in understanding the nature of a fitted equation... 

First, the presence of an additional minimum at r = 3 A along the reaction path is clearly discernible in the computer-simulated contour plot. The small energy barrier between this minimum and the minimum at r = 6 A is due to the molecularity of the solvent there is a free-energy cost associated with the making of the hole between the two fragments in order to fit in a water molecule. 

The regression analysis and the analysis of variance were performed using SAS package (SAS 9.1, SAS Institute, Cary, NC). The contour plots were developed using the fitted quadratic polynomial equation obtained from regression analysis [15-16]. 

Fig. 9 shows the fitted and CV-predicted production values and the corresponding residual normal probability plots of models 1-3. By cross-validation, the model 2, i.e. y = bg +b X +bj2 i 2 the best one. Finally, Fig. 10 shows the contour plot of the best model, model 2. 

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