Least-squares plots

Fig. 2. Least-squares plot showing the determinants for the coefficient of determination. A, total deviation y — y) , B, unexplained deviation y — y) , and...

Kinetic measurements were made by monitoring the laser-induced fluorescence of CH following the excitation in the (0-0) band of the X — A transition as a function of the time delay after the ArF laser dissociation. In the absence of any added reactants, CH had a decay time of 100 to 300 /isec at a total pressure of 30 to 100 torr (CHBr3 pressures of 1 to 10 mtorr) which can be attributed mainly to the CH + CH reaction. The addition of the reactants listed in Table I shortened the CH radical decay times considerably, indicative of some removal process involving a bimolecular mechanism since the total pressure was always maintained constant. Least squares plots of the inverse lifetimes of CH radicals versus the partial pressure of the added reactant yielded... 

A least squares plot of F](x) vs. formate concentration gave a value of 16.3 for the intercept K and a slope of 197 which is in good agreement with the value of 192 for K.2 derived from F2 (x) The slope of 2 00 is zero and thus the major species present in solution are Eu(HCOO)+, Eu(HCOO)2+ and Eu3+. 

Least-squares plots of In [RHgX] vs. t by an IBM 1620 computer gave values for the pseudo-first-order rate constant k. Also, assuming a first-order rate dependence on ozone concentration, k was calculated via experimental saturation values for 03 in CHC13 at 0°C. The results of these calculations are shown in Table III. From Table III a few relative rate sequences can be formulated. These are listed below. 

Figure 8 shows a plot of thickness of PBS removed versus time in both the CF4/O2 and CF4/He/02 plasmas for samples priorly exposed to an oxygen plasma (lOOW, 0.5 Torr, 3 minutes 16X). The etching curves in the fluorocarbon plasma are characterized by two distinct regions. Initially, the etch rate of PBS is quite high being comparable to that of samples not subjected to pretreatment in O2 plasma (cf. Figure 1). The etch rate then quickly diminishes to a low constant value of 12 2A/min (for CF4/He/02 and 29 5A/min in CF4/O2. When the linear removal rate, obtained from a least-squares plot of the thickness removed versus plasma exposure time, is plotted as an Arrhenius expression at different temperatures (Figure 9), an activation energy of zero is obtained.

Second, the quantity x does not necessarily cause the regression of y, for another factor z may vary in a regular way with x and so be the actual cause. For example, the rate of an air-oxidation reaction could vary with pH and be the actual cause of a regression of titration volume with pH. A n, the slope of a least-squares plot of absorbance against concentration often is interpreted directly as a molar absorptivity, whereas the slope may in fact be affected by a third variable, such as the slit width of a spectrophotometer. Sometimes the calculation of simple correlation coefficients can elucidate such problems. 

Figure 2a is the weighted least squares plot of the logarithm... 

Arrhenius and Eyring activation parameters were obtained in the usual way from least-squares plots of log k vs. 1/T and log(k/T) vs. 1/T, respectively. Activation parameters and rate constants at a common temperature for Co(admh)3 and the related g-diketonate complexes, Co(acac)3 and Co(bzac)g (bzac = benzoylacetonate), are compared in Table VI. Co(admh)3 rearranges more slowly (by a factor of... 

A least square plot of log Ccsc as a function of number of carbon atoms in the alkyl chain is given in Fig. 4.13. obtained from the slope of this line is —0.95kT and is comparable to the free energy of micellization measured for similar surfactants in solution (Fig. 4.14). Heat and standard entropy changes associated with the adsorption process can be calculated by considering the adsorption of the long-chain molecules, X, as follows (Somasundaran and Fuerstenau, 1972). 

Fig. 4.13. Least square plot of Ccsc of alkyl ammonium acetates from zeta potential data as a function of the number of carbon atoms in the chain.

Fig. 8.1S. a Least-squares plot of zl(Cu-Nj,) versus. d(Cu-Oe,) for CUN4O2 chromophore b Lower part distortions of the CUN4O2 chromophore mapped by the coordinate in a upper part proposed adiabatic PES model for the pseudodegenerate ground and excited electronic states of the CUN4O2 chromophore... 

Estimate the uncertainty in the slope, intercept, and y for the least-squares plot in Example 3.21, and the uncertainty in the determined riboflavin concentration. 

Least-squares plots and coefficient of determination, pp. 102, 106 Using spreadsheets for plotting calibration curves, p. 107 Detection limits, p. 111 Statistics of sampling, p. 113... 

The deterioration progresses continuously from the surface, and the depth of the deteriorated layer increases in proportion to the square root of exposure time as shown in equations 7- and 8. This parabolic (/t" ) law was obtained as the natural derivation based upon unsteady state dynamics, assuming the simultaneous action of UV-li t and diffusive oxygen. Figure 12 is the least-square plot based on experimental data from Kubota et al. (2.) It can be seen that many polymers show the deterioration by the power law of exposure time (t n = 0.5 - l.O). The difference between theory and experiment is considered to be due to the complex mechanisms not explictly treated in this theory. 

Figure 12. Least-squares plot using the power law for the depth of the deteriorated layer of various polymers after various periods of outdoor exposure (at Chosi). Experimental data are from Kubota et al. Ref. 12.

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