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standard errors
According to the calculations, the measurement of the levels of, e.g., oil, petroleum products, and underlying water is possible with relative standard errors of the order of 0.1-1%.
      
For most of the stars, the standard errors in the Mg abundances do not exceed 0.07 dex.
      
As the error of aerosol imaginary index is within 0.01, standard errors of aerosol optical depth and vegetation reflectance solutions for 14 spectral channels from 410 nm to 900 nm are respectively less than 0.063 and 0.063 and 0.023.
      
And as the radiance error is within 2%, the standard errors are less than 0.023 and 0.0056.
      
In case of the homogeneous atmosphere, standard errors of the 120060 upward fluxes from the present model are 1.08% and 1.04% for clean and turbid aerosol models, respectively; and those of the downward fluxes are 4.12% and 3.31%.
      
The standard errors of estimate comparing the predicted to measured values were low for both the physical model and the post-mortem heart data.
      
Therefore, the resulting fit paramters of the statistic software as well as their standard errors have to be transformed to obtain D50 and k as well as their standard errors.
      
Two problems related to non-linear regression, the evaluation of the best set of fitting parameters and the reliability of the methods used for the estimation of the standard errors of these parameters, are examined.
      
In this case only Monte Carlo methods of data simulation can give accurate information about the standard errors and the confidence intervals of these parameters.
      
In addition, the physical meaning and significance of the fitted coefficients is discussed together with the standard errors calculated previously.
      
It was found that the relative standard errors of prediction (RSEP) for the validation set of PLS of quercetin and luteolin was 1.31 and 2.23%, and the RSEP of PCR was found to be 3.56 and 4.32%, respectively.
      
Geometric means and standard errors are presented for each element, along with a summary of the effects of age, sex, and treatment on the concentration of each element.
      
An iterative procedure based on the Gauss-Newton algorithm is implemented to produce the generalized least squares estimates and the standard errors estimates.
      
An appendix provides extensions of Kendall and Stuart's (1977) standard errors of bivariate moments to the third and fourth order.
      
Of particular importance, the statistical properties inherent to this data structure permit calculation of standard errors, confidence intervals and statistical tests, without subjectively subdividing the data.
      
As a result, it was possible to achieve estimations of the quantal release distribution with sufficiently low standard errors.
      
Since, if the errors of measurement are large, standard errors inQ are unreliable, curves are given by means of which the compatibility of any given event with Λ0 and θ0-decay may be checked.
      
The solution of these systems by means of weighted least squares yields the parameter estimates and their standard errors.
      
All estimates of dominance variance, additive X additive variance, and interactions between genetic variances and years were smaller than twice their standard errors.
      
Approximate standard errors of genetic parameter estimates were obtained using a simulation technique and approximation formulae for a simple statistical model.
      
 

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