Linear least-squares regression analysis

Rate constants were determined by linear least-squares regression analysis, and error limits are reported as standard deviations (S.D.). 

Data for the feed and copolymer compositions for each experiment with a given feed are substituted into Eq. 6-36 and r2 is plotted as a function of various assumed values of r. Each experiment yields a straight line and the intersection of the lines for different feeds gives the best values of r and r2. Any variations observed in the points of intersection of various lines are a measure of the experimental errors in the composition data and the limitations of the mathematical treatment (see below). The composition data can also be treated by linear least-squares regression analysis instead of the graphical analysis. 

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.

Linear Least-squares Regression Analysis of Species Within Fragment Clusters... 

A second method was used to determine if there was a significant difference between HPS, DPS, and the 50 50 mixture. Linear least-squares regression analysis was used to correlate the spectra of HPS and DPS with the 50 50 mixture. The point of maximmn correlation was calculated as 60 4% HPS and 40 7% DPS. The residuals showed no systematic series of peaks indicating that the deviations from 50 50 were due to random chance. Therefore, based on two data analysis methods, one can conclude that there is not a significant amount... 

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. ... 

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. ... 

The Iterative Method and Linear Least-Squares Regression Analysis of Kinetic Data... 

What is the equivalent four-parameter linear model expressing y, as a function of jci and xfl Use matrix least squares (regression analysis) to fit this linear model to the data. How are the classical factor effects and the regression factor effects related. Draw the sums of squares and degrees of freedom tree. How many degrees of freedom are there for SS, 55, and SS 7... 

The following protocol was proposed and consisted of 4 measuring days. Each day, four (or six at day 1) standards and four samples are analyzed. The calibration curves are constructed by least squares regression analysis and statistically tested for nonlinearity by means of an F-test on the residuals. The amount of cortisol in the serum samples is obtained by linear interpolation on the daily calibration curve. Preliminary experiments were also set up to determine the influence of the use of peak height or peak area ratios. For the cortisol measurement, some separation takes place between syn and anti isomers, therefore the use of peak heights is less favorable. 

Near-infrared (NIR) spectroscopy is becoming an important technique for pharmaceutical analysis. This spectroscopy is simple and easy because no sample preparation is required and samples are not destroyed. In the pharmaceutical industry, NIR spectroscopy has been used to determine several pharmaceutical properties, and a growing literature exists in this area. A variety of chemoinfometric and statistical techniques have been used to extract pharmaceutical information from raw spectroscopic data. Calibration models generated by multiple linear regression (MLR) analysis, principal component analysis, and partial least squares regression analysis have been used to evaluate various parameters. 

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. 

Performing a least squares regression analysis on the experimental calibration data to evaluate instrument linearity over a range of concentrations of interest and to establish the best relationship between response and concentration. 

Butte, W. and Blum, J.K. 1984. Calculation of bioconcentration factors from kinetic data by non-linear iterative least-squares regression analysis using a programmable minicalculator. Chemosphere 13 151-160. 

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