Non-linear least-squares regression

The rates and mechanisms of hydrolysis and transesterification of phenyl benzoate in aqueous ethanolic KOH solution were determined by non-linear least-squares regression.4 Kinetic studies of the transesterification of a series of 4-nitrophenyl 3- and 4-substituted benzoates by 4-chlorophenol in DMF in the presence of potassium carbonate at various temperatures were reported.5... 

The solid curves in Fig. 3 were calculated by simultaneous non-linear least-squares regression of reaction-rate data at all alkali-metal cation concentrations (20 kobs values using three different cations) to the complex rate constant in eq 15. The calculation was performed subject to the stipulation that aU three curves converge to a single k value. (Convergence to a single kobs value, k, at infinite dilution is implicit to derivation ofeq 15.) Simultaneous analysis of the three curves (one for each of the cations, Li, Na and K ) provides unique values for rate and equilibrium constants, kMi and Kmi, i.e., for kui, knai, kxi, Kbii, KnbI and Kki. 

Experimental chemical-shift values, 8, as a function of [Lisljtmai were fitted to eq 34 by non-linear least-square regression by varying the parameters 80, 81 and Ktii. The activity coefficient of Li" (yLi) was calculated using the parameters a and b obtained from non-linear least-squares fit of the kinetic data. The ratio yui/yi was assigned a value of 1. 

Figure 4 Adenosine receptor agonist inhibition of the specific binding of [125j]hpia to membrane bound (A) and solubilized (B) porcine atrial adenosine receptor preparations. Each point represents the mean of 3-9 experiments and the lines drawn are the best fits derived from non-linear least squares regression analysis using EBDA software.

All calculations of Dl can be carried out simultaneously by a GW-BASIC personal computer program, written for non-linear least-squares regression analysis and based on the experimental pair values H and t in centimeters and seconds, respectively. The experimental Dl values are of the same order of magnitude and, in some cases, very close to those obtained by other techniques or calculated theoretically from empirical equations. The precision ( 13%) and the accuracy (8 7%) of the RF-GC method, as determined from the Dl values of Refs. compared to those computed from the more accurate empirical equation of Wilke-Qiang," are relatively satisfactory, considering the difficulties in obtaining experimental Dl values, and the large dispersion of the predicted diffusion coefficients. ... 

DOSY NMR experiments are popular for analysing diffusional properties of mixtures. Quality of the results is affected by experimental factors such as baseline drift, peak shift and phase shift. Huo et al proposed a series of pre-processing operations to reduce the experimental distortions, including baseline correction and reference deconvolution to remove frequency and phase shifts. The corrected data can be successfully analysed with a combination of multivariate curve resolution with non-linear least square regression. 

Structural parameters such as interatomic distance, coordination number, and temperature factor for an atomic pair were estimated simultaneously from D(r)/r in real space. But for better understanding the melt structure, the structural parameters for each atomic pair are needed to be refined by the correlation method in the [Q, Q-i(Q)] space, using the non-linear least squares regression of Equation 6.6.5 ... 

A non-linear least-squares regression analysis was used to fit the observed ethene fluxes to Equation 5. From this analysis, K" = 0.7 0.1 atm and c = (1.4 0.1)xl0. Based on data reported by Trueblood and Lucas (6), this result is of the same order as in bulk silver nitrate aqueous solutions. A water content, f, of about 14 weight % was determined for the silver ion-exchanged fibers. Based on ICP analysis, the silver ion concentration, Ct, within the fibers was estimated to be about 5 M, which corresponds to an ion exchange of sodium with silver of about 80 %. The estimated effective diffusion coefficient for ethene in the facilitated mode, calculated from c in Equation 6, was on the order of 2x10 cm s. Table HI shows a summary of the constants obtained for the module with an effective membrane area of 25 cm. ... 

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