Adjusted coefficient

Equations are balanced by adjusting coefficients in front of formulas, never by changing subscripts within formulas. On paper, the equation discussed above could have been balanced by writing N6 on the right, but that would have been absurd. Elemental nitrogen exists as diatomic molecules, N2 there is no such thing as an N6 molecule. 

Whenever one property is measured as a function of another, the question arises of which model should be chosen to relate the two. By far the most common model function is the linear one that is, the dependent variable y is defined as a linear combination containing two adjustable coefficients and X, the independent variable, namely. 

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... 

In equation 5.24, Wy.j and are adjustable coefficients valid for a given distance j in a given site i", and Xi. are the atomic fractions of i ions in site s. 

The multiple linear regression (MLR) method was historically the first and, until now, the most popular method used for building QSPR models. In MLR, a property is represented as a weighted linear combination of descriptor values F=ATX, where F is a column vector of property to be predicted, X is a matrix of descriptor values, and A is a column vector of adjustable coefficients calculated as A = (XTX) XTY. The latter equation can be applied only if the matrix XTX can be inverted, which requires linear independence of the descriptors ( multicollinearity problem ). If this is not the case, special techniques (e.g., singular value decomposition (SVD)26) should be applied. 

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. 

Equation 8.1 is valid for ideal solutions only. In the case of non-ideal concentrated solutions, an activity coefficient y, is inserted as an adjusting coefficient to keep the expression of chemical potential pt in the same form as Eq. 8.1 ... 

A GMCSC configuration can be viewed as a linear combination, with adjustable coefficients, of f(Ne,S) structures with a common orbital string , each of them analogous to a classic-VB structure except for orbital optimization and for the use of YK spin functions. Note the latter is not actually a limitation inasmuch as all of them are included, since they span the full spin space for Ne electrons with given values of S and M. One should perhaps note that for Nc=l the wavefunction in Eq. (1) reduces to a single-configuration spin-coupled wavefiinction [3]-[6], and d then becomes simply a normalization constant. 

We may combine this with Et]. (20-6) and the adjusted coefficients to obtain... 

Make the change in oxidation numbers equal in magnitude by adjusting coefficients in the equation. 

For each equation, two statistics that describe the adequacy of the equations were calculated—the adjusted coefficient of de-termination(3)(adjusted R ) and the standard error of estimate (SEE). The adjusted R denotes the proportion of the variability observed in the property that was explained in the terms of the equation. The SEE is a measure of the unexplained variability that still existed after the significant effects were taken into account, Table III. 

These Saul-Wagner nonanalytic equations for water have been transformed into the FEOS-coefficients by one-to-one map without any adjustable coefficients. The distinction is that the transformation into the set a(T), b(T), c(T) by eqs. (2-4) is based on the actual A/7)-values from eq. (5) while the predicted by the generalized WMG-model A (Tj-values in Fig. 2 are classical. In other words, the consistent description of the order parameter is not a guaranty of the correct disorder parameter prediction. 

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... 

Column (G) contains nitrate concentrations analogous to column (D) used for oxygen. In this example, the same diffusion coefficients were used to calculate the fluxes. Here, different individually adjusted coefficients can certainly also be used. Again, cell Gil contains the flux rate directed from... 

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