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Linear regression polynomials

Testing the adequacy of a model with respect to its complexity by visually checking for trends in the residuals, e.g., is a linear regression sufficient, or is a quadratic polynomial necessary ... [Pg.383]

Nonlinear calibration is carried out by nonlinear regression where two types have to be distinguished (1) real (intrinsic) nonlinear regression and (2) quasilinear (intrinsic linear) regression. The latter is characterized by the fact that only the data but not the regression parameters are nonlinear. Typical examples are polynomials... [Pg.177]

The calibration function calculation uses multiple linear regression to obtain hydrodynamic volume as a polynomial function of elution volume for a given column set. [Pg.133]

POLYMATH. AIChE Cache Corp, P O Box 7939, Austin TX 78713-7939. Polynomial and cubic spline curvefitting, multiple linear regression, simultaneous ODEs, simultaneous linear and nonlinear algebraic equations, matrix manipulations, integration and differentiation of tabular data by way of curve fit of the data. [Pg.12]

Examples Polynomial regression is applied in problem Pi.03.02. Several examples of POLYMATH multilinear regression are in sections P3.06, P3.08 and P3.10. A non-linear regression is worked out in PI.02.07. [Pg.14]

When linear regression does not yield a good correlation, application of a non-linear function may be feasible (see Chapter 10). The parameter estimates for higher-order or polynomial equations may prove to be more difficult to interpret than for a linear relationship. Nevertheless, this approach may be preferable to using lower-order levels of correlation (B or C) for evaluating the relationship between dissolution and absorption data. [Pg.344]

The third step of computation is to find M(Vr) by linear regression or polynomial fitting after the crosspoint coordinates of all of the samples have been evaluated. [Pg.128]

Regression generally means the fitting of mathematical equations to experimental data ( 3). Nonlinear regression, unlike linear regression, encompasses methods vdiich are not limited to fitting equations linear in the coefficients (e.g. simple polynomial forms). [Pg.203]

In order to make the comparison between Ep and Ep/2 measurements summarized in Table 9, the two quantities were measured in separate experiments. A recent study by Eliason and Parker has shown that this is not necessary [57]. Analysis of theoretical LSV waves by second-order linear regression showed that data in the region of Ep are very nearly parabolic. The data in Fig. 9 are for the LSV wave for Nernstian charge transfer. The circles are theoretical data and the solid line is that described by a second-order polynomial equation. It was concluded that no detectable error will be invoked in the measurement of LSV Ep and Ip by the assumption that the data fit the equation for a parabola as long as the data is restricted to about 10 mV on either side of the maximum. This was verified by experimental measurements on both a Nernstian and a kinetic system. [Pg.167]

Figure 10. S180 versus elevation for various groupings of the data presented by Gondiantini et al. (2001) based on data in their Table 6. Black dashed curve is the polynomial regression curve derived from the unweighted mean isotopic composition as a function of elevation used by Garzione et al. (2006) as corrected by Garzione et al. (2007) and the bold line is the linear regression relationship preferred by Garzione et al. (2007). Figure 10. S180 versus elevation for various groupings of the data presented by Gondiantini et al. (2001) based on data in their Table 6. Black dashed curve is the polynomial regression curve derived from the unweighted mean isotopic composition as a function of elevation used by Garzione et al. (2006) as corrected by Garzione et al. (2007) and the bold line is the linear regression relationship preferred by Garzione et al. (2007).
The equations for compound quantitation are shown in Appendix 22. Most of these equations apply to linear calibration models that rely on average response (calibration) factor for compound quantitation. Calibrations that use linear regression and non-linear polynomial equations read compound concentrations in the analyzed sample aliquot directly from the calibration curve. Once this concentration has been obtained, the final sample concentration can be calculated using the same rationale as for the linear concentration model. [Pg.251]

Numerical integration is needed when the functional form of the integrand is such as to preclude analytical integration or when the data to be integrated are obtained in tabular form as the result of measurements. In the latter case, the data have varying amounts of scatter, and linear or polynomial regression should often be use before (analytical) integration. [Pg.387]

Fig. 5. Difference between calculated and given mole ratios for a linear and polynomial regression line, constructed from the data in Ref. Cll, describing an IDMS assay for y-aminobutyric acid (CABA) with [2,2-2H2]CABA as internal standard. Reprinted with permission from Anal. Chem. 55, 153-155 (1982). Copyright ACS. Fig. 5. Difference between calculated and given mole ratios for a linear and polynomial regression line, constructed from the data in Ref. Cll, describing an IDMS assay for y-aminobutyric acid (CABA) with [2,2-2H2]CABA as internal standard. Reprinted with permission from Anal. Chem. 55, 153-155 (1982). Copyright ACS.
Polynomial Regression Polynomial regression is a special case of multiple linear regression. The regression function is given by ... [Pg.142]

Meloun and co-workers published a two volume text in die early 1990s [12,13]. These are veiy thorough texts aimed primarily at die analytical chemist. The first volume contains detailed descriptions of a large number of graphical metiiods for handling analytical data, and a good discussion of error analysis, and the second volume is a veiy detailed discussion of linear and polynomial regression. [Pg.10]

A particnlarly easy type of least-sqnares analysis called multiple linear regression is possible for fitting data with a low-order polynomial, and this technique can be used for many of the experiments in this book. The nse of spreadsheet programs, as discussed in Chapter III, is strongly recommended in snch cases. In the case of more complicated nonlinear fitting procednres, other techniqnes are described in Chapter XXL... [Pg.33]

Generate a calibration curve by linear or polynomial regression of the scan areas and weights of the standards and interpolate the weights in the sample zones from the curve. [Pg.1079]

To obtain the isosteres, one must interpolate the pressure at a given quantity adsorbed at each temperature. To avoid large interpolation errors, particularly at low pressures, the data were fitted piecewise to well behaved polynomial functions by a least squares method. Typical isosteres are shown in Figure 5. The slope of an isostere was determined by linear regression on the interpolated points. The resulting isosteric heat curves are shown in Figure 6. [Pg.84]

A multivariate linear regression can successfully be employed for moderately wide range calibration. As an example parabolic regression (17) 31,72) should be mentioned. Higher order polynomials have disadvantages in terms of degree of freedom and error propagation, and the results are less precise. [Pg.84]


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See also in sourсe #XX -- [ Pg.114 , Pg.124 ]




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