Once we have estimated the unknown parameter values in a linear regression model and the underlying assumptions appear to be reasonable, we can proceed and make statistical inferences about the parameter estimates and the response variables. [Pg.32]

Calibration curve quality. Calibration curve quality is usually evaluated by statistical parameters, such as the correlation coefficient and standard error of estimate, and by empirical indexes, such as the length of the linear range. Using confidence band statistics, curve quality can be better described in terms of confidence band widths at several key concentrations. Other semi-quantitative indexes become redundant. Alternatively, the effects of curve quality can be incorporated into statements of sample analysis data quality. [Pg.126]

Cornish-Bowden, A., Eisenthal, R. (1974) Statistical Considerations in the Estimation of Enzyme Kinetic Parameters by the Direct Linear Plot and other Methods, Biochem.J. 139, 721-730. [Pg.320]

Table 13.11 Results of linear regression for relative area (Y) vs concentration of the analyte (X) in the standard solution. Estimation of the model parameters and statistics for the fit |

A useful method to test the overall impact a subject has on the parameters is to first perform principal component analysis (PCA) on the estimated model parameters. PCA is a multivariate statistical method the object of which is to take a set of p-variables, (Xi,X2,. ..Xn = X and find linear functions of X to produce a new set of uncorrelated variables Z, Z2,. .. Zn such that Zi contains the largest amount of variability, Z2 contains the second largest, etc. [Pg.257]

The application of optimisation techniques for parameter estimation requires a useful statistical criterion (e.g., least-squares). A very important criterion in non-linear parameter estimation is the likelihood or probability density function. This can be combined with an error model which allows the errors to be a function of the measured value. A simple but flexible and useful error model is used in SIMUSOLV (Steiner et al., 1986 Burt, 1989). [Pg.114]

Parameter estimation to fit the data is carried out with VARY YM Y1 Y2, FIT M, and OPTIMIZE. The result is optimized values for Ym (0.7835), Y1 (0.6346), and Y2 (1.1770). The statistical summary shows that the residual sum of squares decreases from 0.494 to 0.294 with the parameter optimization compared to that with starting values (Ym=Yl=Y2=l. 0. ) The values of after optimization of Ym, Yl, and Y2 are shown in Figure 2, which illustrates the anchor-pivot method and forced linearization with optimization of the initiator parameters through Yl and Y2. [Pg.314]

Several related problems have been previously considered in the literature. In addition to the afore mentioned statistical approaches for structural change detection in data sets and their application for linear system identification [7], the joint problem of model structure determination and parameter estimation was addressed by [8-10]. A related approach was used by [11-13] in the context of data reconciliation. Additional aspects of model selection in chemical engineering are covered in [14]. Although the present problem shares common features with the all of the previous applications, it also presents unique characteristics that require a specific formulation. [Pg.344]

Linear mixed effects models are primarily used in pharmacodynamic analysis or in the statistical analysis of pharmacokinetic parameters. Linear mixed effects models could also be used to analyze concentrationtime data from a 1-compartment model with bolus administration after Ln-transformation. The advantages to using mixed effects in an analysis are that observations within a subject may be correlated and that in addition to estimation of the model parameters, between- and within-subject variability may be estimated. Also, the structural model is based on the population, not on data from any one particular subject, thus allowing for sparse sampling. Most statistical packages now include linear mixed effects models as part of their analysis options, as do some pharmacokinetic software (Win-Nonlin). While linear mixed effects models are not cov- [Pg.202]

In equation 3.4-18, the right side is linear with respect to both the parameters and the variables, j/the variables are interpreted as 1/T, In cA, In cB,.. . . However, the transformation of the function from a nonlinear to a linear form may result in a poorer fit. For example, in the Arrhenius equation, it is usually better to estimate A and EA by nonlinear regression applied to k = A exp( —EJRT), equation 3.1-8, than by linear regression applied to Ini = In A — EJRT, equation 3.1-7. This is because the linearization is statistically valid only if the experimental data are subject to constant relative errors (i.e., measurements are subject to fixed percentage errors) if, as is more often the case, constant absolute errors are observed, linearization misrepresents the error distribution, and leads to incorrect parameter estimates. [Pg.58]

Before collecting data, at least two lean/rich cycles of 15-min lean and 5-min rich were completed for the given reaction condition. These cycle times were chosen so as the effluent from all reactors reached steady state. After the initial lean/rich cycles were completed, IR spectra were collected continuously during the switch from fuel rich to fuel lean and then back again to fuel rich. The collection time in the fuel lean and fuel rich phases was maintained at 15 and 5 min, respectively. The catalyst was tested for SNS at all the different reaction conditions and the qualitative discussion of the results can be found in [75], Quantitative analysis of the data required the application of statistical methods to separate the effects of the six factors and their interactions from the inherent noise in the data. Table 11.5 presents the coefficient for all the normalized parameters which were statistically significant. It includes the estimated coefficients for the linear model, similar to Eqn (2), of how SNS is affected by the reaction conditions. [Pg.339]

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