Adjusted coefficient determination

In the above equations, a is a coefficient with the value of 1.0 for single phase flow and 2.0 for multi-phase flow [6], and pis an adjustable coefficient and has a value of 2.1 by fitting the experimental results for the two phase flow. The flow resistant coefficient is determined by the Blasius equation. 

Confining their study to monofunctional molecules, Roberts et al. [38] compared seven different models for predicting human stratum corneum permeability coefficients. The performance of the models was assessed by the adjusted coefficient of determination r2dj and the Akaike Information Criterion (AIC) [39], Both r2dj and AIC allow for comparing models with different numbers of variables (degrees of freedom). Exclusion of polyfunctional molecules led to a comparatively small set of only 24 molecules. The previously reported... 

The samples were analyzed for trace metals and sulfate as well as for three fractions of particulate organic matter (POM) using sequential extraction with cyclohexane (CYC), dichloromethane (DCM) and acetone (ACE). Factor analysis was used to identify the principal types of emission sources and select source tracers. Using the selected source tracers, models were developed of the form POM = a(V) + b(Pb) + - - -, where a and b are regression coefficients determined from ambient data adjusted to constant dispersion conditions. The models for CYC and ACE together, which constitute 90% of the POM, indicate that 40% (3.0 pg/m ) of the mass was associated with oil-burning, 19% (1.4 pg/m ) was from automotive and related sources and 15% (1.1 pg/m ) was associated with soil-like particles. 

Figure 4.9 shows the lit of experimental results obtained for the epoxidized novolac DDS system, using Eq. (4.12) with X = 0.15 (Oyanguren et al., 1993b). As Acpmax could not be determined with enough precision, X was used as an adjustable coefficient. 

Pattern writing experiments have been performed with an almost symmetric PDMS/PEMS (16.4/15.9) blend having a critical composition cc = 0.48 and a convenient critical temperature Tc = 290.15K. It has been shown in [100] in detail that the parameterization of the transport coefficient determined for the higher PEMS molar mass still yields a good description for this blend too after adjusting the critical concentration and taking (T - Tsp)/T as dimensionless temperature. 

One way to identify important predictor variables in a multiple regression setting is to do all possible regressions and choose the model based on some criteria, usually the coefficient of determination, adjusted coefficient of determination, or Mallows Cp. With this approach, a few candidate models are identified and then further explored for residual analysis, collinearity diagnostics, leverage analysis, etc. While useful, this method is rarely seen in the literature and cannot be advocated because the method is a dummy-ing down of the modeling process—the method relies too much on blind usage of the computer to solve a problem that should be left up to the modeler to solve. 

Note The coefficient of determination was 0.4574 with an adjusted coefficient of... 

Note also that the adjusted coefficient of determination, r, is about 99% (see Table 7.10). The fit is not perfect, but for preliminary work, it is all right These data are also in easily understandable terms for presenting to management, a key consideration in statistical applications. 

In this expression, is the shift factor of an isotherm determined at temperature T, in relation to the isotherm at the reference temperature T, and a and b are two adjustable coefficients dependent upon the material. By definition, when T=T there is no shift to apply. 

The goodness of fit of the burr size mathematical models was also tested through the coefficient of determination (R ) and adjusted coefficient of determination (R adj) (Montgomery, 2003). The is the proportion of variation in the response explained by the regression model. In contrast, R dj is the coefficient of determination adjusted for the number of variables in the regression model. Unlike R, the R adj decrease if the variables are entered in the model that does not add drastically to the model fit. The coefficient of determination is given by (Montgomery, 2003) ... 

Strategy Determine the formulas and physical states of all reactants and products, and use them to write a chemieal equation that makes the correct chemical statement. Finally, adjust coefficients in the resulting chemical equation to ensure that there are identical numbers of each type of atom on... 

In this equation, both log Kq (Pr>0.0001) and F (Pr>0.0074) are significant descriptors. The adjusted coefficient of determination, adjusted by the equation Adjusted r = [(n-ljr - (p-1)]/(n-p), for equation 1 is 0.909. This modification makes comparisons between models based on degrees of freedom (i.e., number of test chemicals and number of descriptors) more equal. The best three parameter model is... 

Table 1 summarizes the regressed parameters a. and jS both for hydrophihc and hydro-phobic surfaces. It should be pointed out that the adjusted coefficient of multiple determination (/f ) was at least 0.9. Moreover, the standard error associated with each parameter was, on average, about 10% of the magnitude of the parameter itself... 

The value of correlation coefficient of and adjusted value determine the quality of the results, in which R is equal to 0.8517 while adjusted R is equal to 0.7364. Table 2 shows the value of R. ... 

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