Least-squares procedures, weighted requirements

As part of a study of biscyclic dibenzacridines, the crystal structure of 1,2-8,9-dibenzacridine (72) has been investigated by Mason (1957, 1960). The space group was shown to be Pna2v thus, with four molecules in the unit cell, no molecular symmetry is required. The structure was determined from an examination of the weighted reciprocal lattice and trial and error methods, refinement being by two-dimensional least-squares procedures. At the conclusion of the analysis,... 

Another approach for the determination of the kinetic parameters is to use the SAS NLIN (NonLINear regression) procedure (SAS, 1985) which produces weighted least-squares estimates of the parameters of nonlinear models. The advantages of this technique are that (1) it does not require linearization of the Michaelis-Menten equation, (2) it can be used for complicated multiparameter models, and (3) the estimated parameter values are reliable because it produces weighted least-squares estimates. 

The procedure described for calibration of K and a is laborious because of the required fractionation process. The two constants are derived as described from the intercept and slope of a linear least squares fit to [t ]-A/ values for a series of fractionated polymers. Experimentally, K and a are found to be inversely correlated. If different laboratories determine these MHS constants for the same polymer-solvent combination, the data set which yields the higher K value will produce the lower a. Thus, My from Eq. (3-44) is often essentially the same for different K and a values provided the molecular weight ranges of the samples used in the two calibration processes overlap. 

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