Least-square linear regression

The data are also represented in Fig. 39.5a and have been replotted semi-logarithmically in Fig. 39.5b. Least squares linear regression of log Cp with respect to time t has been performed on the first nine data points. The last three points have been discarded as the corresponding concentration values are assumed to be close to the quantitation limit of the detection system and, hence, are endowed with a large relative error. We obtained the values of 1.701 and 0.005117 for the intercept log B and slope Sp, respectively. From these we derive the following pharmacokinetic quantities ... 

A least squares linear regression has been applied to the data pertaining to the p-phase, yielding the values of 1.745 and 0.005166 for the intercept log B and slope Sp, respectively. Using these results, we can compute the extrapolated plasma concentrations between 0 and 20 minutes. From the latter, we subtract the observed concentrations C which yields the concentrations of the a-phase C ... 

The residual a-phase concentrations C are shown in the semilogarithmic plot of Fig. 39.13b. Least-squares linear regression of log C upon time produced 1.524 and -0.02408 for the intercept log and the slope respectively. 

Concentrations of terbacil and its Metabolites A, B and C are calculated from a calibration curve for each analyte run concurrently with each sample set. The equation of the line based on the peak height of the standard versus nanograms injected is generated by least-squares linear regression analysis performed using Microsoft Excel. 

Least-squares linear regression analysis was performed on the data. 

Where AG is free energy, R is gas constant (1.987 cal/deg K mole-1), T is degrees Kelvin, and AS is entropy. Kd is the distribution constant of the herbicide between the solution phase and the adsorbed phase (equation 4). Thus, least squares linear regression analysis of ln(Kd) vs. 1/T yielded values for heats of adsorption (AH) for the herbicides in Keeton soil. 

As shown in Figure 6.21, excellent linearity was obtained, as represented by the high coefficient of correlation obtained for the least square linear regression. Similar results were obtained for the evaluation of autosampler accuracy when other analytes (propyl paraben and rhodamine 110 chloride) were employed in the determinations. Liu et al.9 conducted similar evaluations for the samples employed in the evaluation of the drug release rate profile of OROS with similar results to those discussed above. 

Fig. 5.6. Calibration curve for permanganate standards. Line is a least-squares linear regression for the data. Graphical interpolation is illustrated for an unknown with an absorbance of 0.443.

If a calibration function is used with coefficients obtained by fitting the response of an instrument to the model in known concentrations of calibration standards, then the uncertainty of this procedure must be taken into account. A classical least squares linear regression, the default regression... 

The data fitting of the linear interval is made with a least squares linear regression. The obtained calibration lines were... 

Comparison of V/Al atomic ratios for A120, and V/(Si+Al) atomic ratios for V-loaded gels are presented rrrFig. 8. Overall, and somewhat independent of whether or not the samples have been subjected to H, reduction, these ratios for the gel are approximately 30 s smaller than the values observed for V on Al-O,. The least squares linear regression fits to the V/A120, data extrapolates near the origin whereas the corresponding aaxa for V/gel does not, Fig. 8. Hence, V dispersion on the gel surface, as monitored by XPS, is lower than on Al-O,. The hydrothermal instability of V loaded gel (Table 1) is prooably responsible for the lower V dispersion and for the lower V/Al+Si ratios seen in Fig. 8. 

Least squares linear regression analyses of the data over the range of 20%-50% ACN gave the following equations ... 

An alternative method was also studied. This involved ratioing the intensity of the 698 cm 1 styrene band to the intensity of the 2921 cm-1 C-H stretching vibration. Since oils and other additives would interfere with this approach they were extracted with acetone. Vacuum oven drying was then necessary to remove all traces of acetone prior to PA analysis. Otherwise the PA spectrum would be that of acetone rather than that of the rubber since the gas phase spectrum of the acetone would overwhelm that of the solid phase rubber. This technique allowed both solution and emulsion SBR to be analysed by a common method. The results can be expressed by a least squares linear regression equation over the range of 5%-40% styrene in SBR. 

These methods have been reviewed by Silas, Yates and Thornton [55]. In a PA-FTIR method Parker and Waddell also used the intensity of the 910 cm"1 butadiene band and ratioed it to the intensity of the 1450 cm 1 C-H bending band as a function of the % vinyl-butadiene [51]. The results can be expressed by a least squares linear regression equation over a range of 10%-60% vinyl-butadiene. 

The 1378 cm"1 band is from the CH3 symmetric bending and the 1156 cm 1 band is a complex skeletal vibration involving the CH3 branch of propylene. The 722 cm"1 band represents the CH2 rock and the 1462 cm"1 band is a combination of the CH2 scissor and the asymmetric CH3 bend. In the photoacoustic spectra the 1378 and 1462 bands are strong while the 1154 and 722 cm"1 bands are weak. Least squares linear regression... 

Linearity A calibration curve was obtained using the eight calibration standards that were described above. A 1/x2 weighted least squares linear regression using the area ratios of analyte/intemal standard against the nominal concentration was performed. A regression line was obtained from these data, which was used for back calculation of the concentration for unknowns and quality controls. 

The sensitivity estimates for the effect of changes in cost factor values on leve lized H2 production and PV electricity prices are estimated by the least squares, linear regression method. The regression results provide an estimate of the effect of unit changes in cost factor values on H2 production and PV electricity prices. The sensitivity results are presented in Table 5, Fig. 4, and Fig. 5. 

Fig. 23. Dependence on log water activity of log ratio of powder to solution amide hydrogen exchange rate for lysozyme. Log rate ratio data for pH 2 (bottom) to pH 10 (top) are given as a function of log(/ /Po). The slopes of the lines give the order of the protein exchange reaction with respect to water. The slopes from least-squares linear regression are the following pH 2, 2.57 pH 3, 2.90 pH 5, 3.14 pH 7, 3.14 and pH 10, 2.53. Displacement along the log rate ratio axis is arbitrary. Numbers indicate some of the H m values for which rate ratios were determined. From Schinkel et at. (1985).

Fig. 6.3 Negative correlation between under-wrapping or packing deficiency (v) and miRNA target coincidence (r) for human families in Ks classes I (A), II (B), and III (C). The linear fits were obtained by least-squares linear regression...

The enthalpy of sorption for each of the coals plotted versus carbon content is presented in Figure 6. The data were derived from a least squares linear regression of the IGC data taken above the temperature of the major transition. As with the temperature of the major transition, a trend is definitely indicated. However, several of the enthalpies are unrealistically high. This is probably due to loss of volatile matter from the coal in this temperature region. Since the actual mass of coal in the column at each... 

Table 11 gives the permeability data for seepage of water through phosphogypsum. The data were fitted by least squares linear regression to Eq 1... 

Within each of the assays A, B, C, and D, least squares linear regression of observed mass will be regressed on expected mass. The linear regression statistics of intercept, slope, correlation coefficient (r), coefficient of determination (r ), sum of squares error, and root mean square error will be reported. Lack-of-fit analysis will be performed and reported. For each assay, scatter plots of the data and the least squares regression line will be presented. 

Figure 2. (A) Correlation by least squares linear regression of...

Figure 3. Correlation by least squares linear regression of inhibitory potencies in [ 5S]TBPS binding assays (4) with inhibitory potencies in chloride flux assays (1 5, 17) for seven cyclodienes. The data point for lindane is also shown but not included in the calculated regression. Redrawn from Ref. 17 ...

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