Relative residual plots

Plots of data can be informative, for example parity plots and relative residual plots. Figure 2.7 shows parity plots, in which measured data are plotted against the data as cal-... 

For the basic evaluation of a linear calibration line, several parameters can be used, such as the relative process standard deviation value (Vxc), the Mandel-test, the Xp value [28], the plot of response factor against concentration, the residual plot, or the analysis of variance (ANOVA). The lowest concentration that has been used for the calibration curve should not be less than the value of Xp (see Fig. 4). Vxo (in units of %) and Xp values of the linear regression line Y = a + bX can be calculated using the following equations [28] ... 

Calibration Measurement Residual Plot (Model Diagnostic) The magnitude of the calibration spectral residuials shown in Figure 5.47 are large relative to the original preprocessed data (Figure 5-44), and they also have nonrandom features. These observations indicate a potential problem with the... 

Calibration Measurement Residuals Plot (Model Diagnostic) The calibration spectral residuals shown in Figure 5-53 are still structured, but are a factor of 4 smaller than the residuals when temperature was not part of the model Comparing with Figure 5-51, the residuals structure resembles the estimated pure spectrum of temperature. Recall that the calibration spectral residuals are a function of model error as well as errors in the concentration matrix (see Equation 5.18). Either of these errors can cause nonrandom features in the spectral residuals. The temperature measurement is less precise relative to the chemical concentrations and, therefore, the hypothesis is that the structure in the residuals is due to temperature errors rather than an inadequacy in the model. 

Figure 8. Fluorescence decay of Pr phytochrome (124 kDa) excitation at Aexc = 640 nm, emission measured at Aero — 680 nm. The semilogarithmic plots of the measured decay (curve with signal noise) and the decay function calculated from best-fit kinetics parameters obtained by single-decay analysis (thin line superimposed on measured decay) are shown. In the inset the calculated lifetimes xf 3 and relative amplitudes Rf 3 of the decay components are given. On top, a weighted residuals plot (sigma) indicates the deviations of these computer-fitted parameters from the measured decay, with the value of the squared reduced error (y2) in the inset. The fluorescence decay of the red-light adapted Pr + Pfr mixture exhibited a comparable triexponential behaviour. (After Figure 4 in Holzwarth et al. [76].)...

Figure 12. UV (protein) fluorescence decay of the red-light adapted mixture P, + Pfr (124kDa) at 275 K Aelc = 295 nm, = 330 nm. Inset calculated lifetimes t(t,P)i -4 and relative amplitudes Rftrp)1 -4 °f the decay components calculated by single-decay analysis. Top weighted residuals plot and autocorrelation function of the residuals. The fluorescence decay of pure Pr exhibited a comparable tetraexponential behaviour (Holzwarth et al. [108]).

In Figure 2.8 plots are given of the relative residuals of two correlation equations, which were discarded. We observe that the residuals start to deviate of the average systematically for higher acetylene and ethylene conversions. 

Our first objective was to determine whether microencapsulated methyl parathion Is unique In Its property to be carried back to the hive by bees. To that end a mixture of three commonly used insecticides along with MMP was applied to a plot of blooming rape. The agents were azlnphos-methyl (Guthlon), parathion, and carbaryl (Sevin). By using a mixture on a single plot the effects of variation In bee visitation were eliminated and the tendencies to be carried to the hive could be measured by the relative residue levels in the pollen samples. Five applications were made over a period of seventeen days. Pollen samples were collected from hives placed near the field after two, three, four, and five successive applications approximately two days after each application was made. The application rates were doubled for the last two applications. The data are shown In Table I. 

Because the e values are distributed relatively evenly around 0, there is no detected pattern of increase or decrease in the residual plot. Now view Figure 8.9a and Figure 8.9b. The residual errors get larger in Figure 8.9a and smaller in Figure 8.9b, as the x values increase. 

Fig. 4.29 First cycle relative residual stram on load-ing/unloading to e = 3, plotted versus first cycle relative hysteresis, showing correlation and trends with respect to choice of DI and MD. Symbols as in Fig. 4.24 [135]...

Fig. 13.3 Example of experimental data for solid electrolyte that are not Kramers-Kronig transformable, left, and residual plots (a) real to imaginary and imaginary to real, (b) relative errors of complex transformation, and (c) errors of CNLS fit to model in (a) circles real-to-imaginary squares imaginary-to-real transformations (From Ref. [575] Reproduced with permission of Electrochemical Society)...

The differences can also be easily visualized by plotting the relative residuals, that is, the differences between the experimental and model impedances. If the model is correct, then the residuals should be randomly distributed around the zero line. An example of such a plot is shown in Fig. 14.9. It is evident that the residuals display systematic differences, which suggests that the model is not correct. 

The changes in osmotic coefficients with temperature and concentration make it difficult to solve the above equations accurately, but accurate determinations of the composition and relative amounts of the concentrated liquid and ice can be made from phase diagrams which are plots of the freezing points of solutions versus their concentration. From these, it is possible to determine the exact NaCl concentration at any temperature. Examples are shown in Figure 9 for solutions of 0 to 2.0 M glycerol in 0.15 M NaCl. This figure nicely illustrates how the presence of glycerol reduces the concentration of NaCl in the residual unfrozen solution. 

The residuals relative to the smoothed trace (to ymean if o smoothing has been done) are plotted a vertical shift and an expansion factor can be chosen. 

On Delicious apples the initial residues were 0.9 and 0.4 p.p.m. in plots 7 and 10, respectively, both of which were sprayed with 1.25 ounces of parathion. The difference between the two plots was consistent throughout the individual trees sampled. The spray mixture used on plot 7 also contained DDT, while that used on plot 10 contained only parathion. These plots showed the same relative magnitude of residues 18 days after spraying, and at harvest, 74 days after the spraying. Plot 11, sprayed with 0.6 ounce of parathion. showed an initial residue of 0.3 p.p.m. 

A detailed quantitative analysis of the preferences of amino acids in folded proteins for different regions of the Ramachandran plot reveals that the 18 nonglycine, nonproline residues exhibit different preferences (Shortle, 2002). Figure 5 shows the range of relative propensities displayed by these 18 amino acids for a somewhat arbitrary subdivision... 

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