Initial regression analysis

In a curve-fitting method the concentration of a reactant or product is monitored continuously as a function of time, and a regression analysis is used to fit an appropriate differential or integral rate equation to the data. Eor example, the initial concentration of analyte for a pseudo-first-order reaction, in which the concentration of a product is followed as a function of time, can be determined by fitting a rearranged form of equation 13.12... 

On the basis of regression analysis of the initial rate data obtained for both isolated reactions (Vila) and (Vllb) and for each of the three reactions proceeding in the coupled system [reactions (Vlla)-(VIIc)], of the set of twenty-five equations, the best equation was always found to be of the... 

The MO concentrations versus time profiles were fitted to second order polynomial equations and the parameters estimated by nonlinear regression analysis. The initial rates of reactions were obtained by taking the derivative at t=0. The reaction is first order with respect to hydrogen pressure changing to zero order dependence above about 3.45 MPa hydrogen pressure. This was attributed to saturation of the catalyst sites. Experiments were conducted in which HPLC grade MIBK was added to the initial reactant mixture, there was no evidence of product inhibition. 

This classification of bonds allowed the application of logistic regression analysis (LoRA), which proved of particular benefit for arriving at a function quantifying chemical reactivity. In this method, the binary classification (breakable or non-breakable, represented by 1/0, respectively) is taken as an initial probability P0, which is modelled by the following functional dependence (Eqs. 7 and 8) where f is a linear function, and x. are the parameters considered to be relevant to the problem. The coefficients c. are determined to maximize the fit of the calculated probability of breaking (P) as closely as possible to the initial classification (P0). 

The separation of synthetic red pigments has been optimized for HPTLC separation. The structures of the pigments are listed in Table 3.1. Separations were carried out on silica HPTLC plates in presaturated chambers. Three initial mobile-phase systems were applied for the optimization A = n-butanol-formic acid (100+1) B = ethyl acetate C = THF-water (9+1). The optimal ratios of mobile phases were 5.0 A, 5.0 B and 9.0 for the prisma model and 5.0 A, 7.2 B and 10.3 C for the simplex model. The parameters of equations describing the linear and nonlinear dependence of the retention on the composition of the mobile phase are compiled in Table 3.2. It was concluded from the results that both the prisma model and the simplex method are suitable for the optimization of the separation of these red pigments. Multivariate regression analysis indicated that the components of the mobile phase interact with each other [79],... 

In reference 88, response surfaces from optimization were used to obtain an initial idea about the method robustness and about the interval of the factors to be examined in a later robustness test. In the latter, regression analysis was applied and a full quadratic model was fitted to the data for each response. The method was considered robust concerning its quantitative aspect, since no statistically significant coefficients occurred. However, for qualitative responses, e.g., resolution, significant factors were found and the results were further used to calculate system suitability values. In reference 89, first a second-order polynomial model was fitted to the data and validated. Then response surfaces were drawn for... 

In our studies, the catalyst and initiator system was comprised of caprolactam-magnesium-bromide and isophthaloyl-bis-caprolactam, respectively. We determined the optimum values of the kinetic parameters in Malkin s autocatalytic model (Eq. 1.3), which consist of k, U, and b, by regression analysis. 

Plot net RFI versus protein concentration (%), and then find the slope (S0, a hydrophobic index) of the line by linear regression analysis (or the initial slope at the origin of quadratic fitting for a more precise measurement as seen in Figure B5.2.1, curve 1). 

Figure 3 Determination of S. pneumoniae MurD kinetic parameters. Initial velocities as a function of substrate concentration were measured using the ADP coupled enzyme assay with PK and LDH. Data were fit with a nonlinear regression analysis using GraphPad Prism. Top panel is for UMA and bottom panel is for d-G1u.

Because the British group applied extensively their statistical method to determine causation of large interindividual pharmacokinetic variations without describing its strengths and weaknesses, others have attempted to assess critically the application of multiple regression analysis for this particular purpose (31,32) While this statistical method has great potential, it requires considerable modification beyond its initial applications in this area (27-29), if that potential is to be realized (H,32). Thus far, its applications in pharmacokinetics (27-29) have been disappointing because those who have employed it neither formulated nor addressed, much less demonstrated fulfillment of, several fundamental assumptions inherent in its use ( 1, 32). 

If the number of experimental data points exceeds the minimum requirements to describe the retention line by a selected function, then the coefficients may be calculated using regression analysis. The method may then be referred to as a regressive method and the initial experiments form a regression design. 

Results of Regression Analysis. For simplification, it was assumed that all activation energies for initial formation of hydrocarbons from coal are the same, i.e. E 3 E = E. A rationale for this is that during decomposition, coal is in equilibrium with the same transition complex regardless of the final products. 

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