Standard deviation of fit

The method of accounting for the overlapping of iridium Lm EXAFS in the analysis of data on the fine structure associated with the platinum Zm edge of platinum-iridium catalysts has been tested in EXAFS experiments on a physical mixture of platinum and iridium and on a bulk alloy of the two elements (48). Figure 4.29 shows the effect of the value assumed for Rw on the quality of fit to the experimental data for xf "(A0 that can be obtained by Eqs. 4.13, 4.16, and 4.17. The quality of fit is characterized by the normalized fitting error, which is defined in this case as the ratio of the standard deviation of fit for a given value of R to the minimum standard deviation obtained over the range of distances examined. 

Plots for 11 isoelectronic sequences having more than three data, or having three centered on IZ1-Z2I = zero, were prepared, one of which is shown in Fig. 8.3. Six of the plots have six data points, and three more have five points (one in the center and two duplicated on each side) the remainder have three non-redundant points. The average standard deviation of fitting for these is 2.595°. Figure 8.4 has the largest scatter around its trend line (a = 3.951°), so it is used as an example of what the ( — 1) standard deviations look like. There is no theoretical basis for using quadratic trend lines they are used for sake of simplicity. 

The parameters were determined by fitting osmotic coefficients from solvent vapor pressure measurements with a least-squares method. The maximum concentration was about 6 mdlal and the standard deviation of fit was. 005. They were surprised to find a minimum in the degree of dissociation at about 2 molal and an increase in dissociation as the concentration increased. This behavior was attributed to the strong negative value of the HjPO -HjPO interaction. Additional parameters were presented based on a study of the KC1-KH P0 -H20 system ... 

This gives some information about the errors (i.e., the variance and standard deviation of each data point), although the goodness of fit, P, cannot be calculated. 

In this case a-y is 419 m. The peak concentration can be found from the measurements, or from the Gaussian distribution fitted to the data and the peak concentration obtained from the fitted distribution. Provided that the emission rate Q, the height of release H, and the mean wind speed u are known, the standard deviation of the vertical distribution of the pollutant can be approximated from either the peak concentration (actual or fitted) or the cross wind integrated (CWI) concentration from one of the following equations ... 

Recorded kinetic curves were fitted to the five-parameter Equation (1). The parameters pj with their errors and the standard deviation of regressions are summarized in Tables 1-6. Comparison of the data confirm the previously reported (refs. 8,12) similarity in the behavior of the two isomers in the presence of strong bases in spite of the different shape of the kinetic curves. The relatively good agreement of exponents p2, P4 computed for the diastereomers at the same temperature and amine concentration demonstrates the validity of the model used. From comparison of Equations (4) and (7) it follows that both reaction must give the same exponent. 

As given above, the statements that adjust the exponents m and n have been commented out and the initial values for these exponents are zero. This means that the program will fit the data to. = k. This is the form for a zero-order reaction, but the real purpose of running this case is to calculate the standard deviation of the experimental rate data. The object of the fitting procedure is to add functionality to the rate expression to reduce the standard deviation in a manner that is consistent with physical insight. Results for the zero-order fit are shown as Case 1 in the following data ... 

The test for the significance of a slope b is formally the same as a t-test (Section 1.5.2) if the confidence interval CI( ) includes zero, b cannot significantly differ from zero, thus ( = 0. If a horizontal line can be fitted between the plotted CL, the same interpretation applies, cf. Figures 2.6a-c. Note that si, corresponds to fx ean). that is, the standard deviation of a mean. In the above example the confidence interval clearly does not include zero this remains so even if a higher confidence level with t(f = 3, p = 0.001) = 12.92 is used. 

CYANlDE.dat Section 4.13 Two calibration series over the same range, and one over a short range (three groups of columns Concentration/Signal), and a fourth group that combines all of the above data the data can he fitted to a parabola Y = -0.002125 + 0.005211 X - 0.0000009126 jc 2 with a residual standard deviation of 4.5 mAU. Use with LINREG, TESTFIT. 

The smaller the sample mass is, the higher is the standard deviation of repetitive measurements. The case of Pb in IAEA 393, at masses greater than 2 mg, also shows that the overall standard deviation levels off at an approximate value of the instrument s precision ( 3%). The constant factor in the fitting curve (4.68) represents the homogeneity factor He for Pb in this particrdar material, IAEA 393, single cell algae (Sonntag and Rossbach 1997). Thus the standard deviation, which is... 

If one pursues the calibration approach, one has to stick to a given combination of density functional and basis set, since the calibration will change for each such combination. Calibration curves have been reported for a number of widely used density functionals and basis sets. The results of a relatively comprehensive study are collected in Table 5.4. The standard deviation of the best fits is on the order of 0.08 mm s which appears to be the intrinsic reliability of DFT for predicting Mossbauer isomer shifts. 

Data at two temperatures were obtained from Zeck and Knapp (1986) for the nitrogen-ethane system. The implicit LS estimates of the binary interaction parameters are ka=0, kb=0, kc=0 and kd=0.0460. The standard deviation of kd was found to be equai to 0.0040. The vapor liquid phase equilibrium was computed and the fit was found to be excellent (Englezos et al. 1993). Subsequently, implicit ML calculations were performed and a parameter value of kd=0.0493 with a standard deviation equal to 0.0070 was computed. Figure 14.2 shows the experimental phase diagram as well as the calculated one using the implicit ML parameter estimate. 

To construct the Hill plot (Figure 5.10E), it was assumed that fimax was 0.654 fmol/mg dry wt., the Scatchard value. The slope of the plot is 1.138 with a standard deviation of 0.12, so it would not be unreasonable to suppose % was indeed 1 and so consistent with a simple bimolecular interaction. Figure 5.10B shows a nonlinear least-squares fit of Eq. (5.3) to the specific binding data (giving all points equal weight). The least-squares estimates are 0.676 fmol/mg dry wt. for fimax and... 

The 0.4 cm i.d. capillary tubes were used instead of the recommended 0.2 cm i.d. 1 28 1 in order to facilitate the addition of highly viscous oils. Figure 2 shows the effect of spinning rate on the interfacial tension of an n-butanol/deionized water system us i ng two tube s izes. The dashed Ii ne represents the best fit for 15 data points measured using a 0.2 cm i.d. tube, where the mean interfacial tension is 1.76 mN/m (standard deviation of 0.02) with a range of 1.73 to 1.80 mN/m for speeds ranging from... 

We also fit a Gaussian surface to the spots. The average spot width, expressed as the standard deviation of the Gaussian, was 1.6 transfers in the CSE dimension and 0.19s in the MECC dimension. Each peak migrating from the sieving capillary was sampled roughly three times as it was transferred to the second-dimension capillary. 

The identification of the crystalline thickness may be possible from the result of the fit. As a frequent result of a model fit, the relative standard deviations of the fundamental domain thickness distributions, G /d and differ considerably. 

The radial velocities were estimated by identifying a few lines (3 to 6, depending on the quality of the spectra) and fitting a Gaussian profile to each line to find the line core. We estimated the average radial velocity, and we present here only the stars with standard deviation of the mean less than 7 km s 1. 

Concentratons of Sr in people living in New York City between 1953 and 1959 who were exposed to nuclear weapons fallout were reported by Kulp and Schulert (1962). They suggested that the distribution of observed values was well fit by a log-normal distribution that had a geometric standard deviation of about 1.7. The Federal Radiation Council (FRC, 1961), after review of the accumulated data on Sr in human bone, concluded that a log-normal distribution was the appropriate description of the distribution of this age-controlled, exposuretime controlled population. The main exposure to Sr from fallout was by way of ingestion. 

If separate D-RESP charge sets are fitted for every single one of the 36 frames, the standard deviation of the electrostatic field generated varies between 3.5 and 5% with respect to the full quantum reference. This accuracy is the best (in the least-squares sense) that can be obtained if the system is modeled with time-dependent atomic point-charges and represents the accuracy limit for a fluctuating point charge model of the dipeptide. 

Preparation of a calibration curve has been described. From the fit of the least-squares line we can estimate the uncertainty of the results. Using similar equations we can determine the standard deviation of the calibration line (similar to the standard deviation of a group of replicate analyses) as... 

Thus, both the mean droplet size and the size distribution may be predicted using these correlations [Eqs. (26), (27), (28), or (29) and Eqs. (30), (31)] for given process parameters and material properties. For a given atomizer design, the standard deviation of droplet size distribution has been found to increase with the melt flow rate, but appears to be less sensitive to the gas flow rated5 Moreover, the variation of the standard deviation is very atomizer- and melt-specific. An empirical correlation which fits with a wide range of atomization data has the following form ... 

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