The same caveats that apply to linear models when the predictor variables are measured with error apply to nonlinear models. When the predictor variables are measured with error, the parameter estimates may become biased, depending on the nonlinear model. Simulation may be used as a quick test to examine the dependency of parameter estimates within a particular model on measurement error (Fig. 3.14). The SIMEX algorithm, as introduced in the chapter on Linear Models and Regression, can easily be extended to nonlinear models, although the computation time will increase by orders of magnitude. [Pg.119]

By calculating relative partial regression coefficients, the role of solvent acidity and basicity in determining the thermodynamic quantity can be clearly seen [50]. In order to do this, one must estimate the variance for the independent and dependent variable involved in the multiparameter analysis. For the parameter Q, the variance is defined as [Pg.197]

In the case of multivariate modeling, several independent as well as several dependent variables may operate. Out of the many regression methods, we will learn about the conventional method of ordinary least squares (OLS) as well as methods that are based on biased parameter estimations reducing simultaneously the dimensionality of the regression problem, that is, principal component regression (PCR) and the partial least squares (PLS) method. [Pg.231]

The models in chemical kinetics usually contain a number of unknown parameters, whose values should be determined from experimental data. Regression analysis is a powerful and objective tool in the estimation of parameter values. The task in regression analysis can be stated as follows the value of the dependent variable (y) is predicted by the model a function (/), contains independent variables (x) and parameters (/ ). The independent variable is measured experimentally, at different conditions, i.e. at different values of the independent variables (x). The goal is to find such numerical values of the parameters (/ ) that the model gives the best possible agreement with the experimental data. Typical independent variables are reaction times, concentrations, pressures and temperatures, while molar amounts, concentrations, molar flows [Pg.431]

Within the procedure, the major part of the code is virtually identical to the code that would be used to obtain the usual least-squares regression parameters for y = mx + b, namely, obtaining the sum of x values, the sum of squares of x values, etc. The difference is that pairs of values are used the mean value of each pair of x values or of y values is used as the independent variable or dependent variable, respectively, and the estimate of the standard errors for the two sets of data is obtained from the differences between pairs. [Pg.302]

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