Least squares linear regression analysi

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. 

Least Squares Linear Regression Analysis of VT H NMR Data for Ring Protons in Uranocene, Octamethyluranocene and the Unsubstituted Ring in Monosubstituted Uranocenes. 

For quantification of the analytes, the external standard method was used, based on the peak obtained in the bold SRM transition (see Tabl.2). Six or eight points calibration curves were constructed from the online analysis of Milli Q water spiked with the standard mixture of the analytes at concentrations ranging between 0.5 and 30 ng/1 in Milli Q water using a least- squares linear regression analysis. 

CH O )] - ion records of the compound of interest versus this of its H labeled analog. Ratios for the standard mixtures were plotted against the concentrations in ng mT, and an unweighted least squares linear regression analysis was performed. Using the regression parameters of the calibration curve,the... 

In addition to the conventional spectral analysis methods and chemometrics, two-dimensional (2D) correlation spectroscopy has recently been introduced to NIR spectroscopy (4,12-16). In this method spectral peaks are spread over a second dimension to simplify the visualization of complex spectra consisting of many overlapped bands and to explore correlation between the bands. There are two kinds of 2D correlation spectroscopy used in NIR spectroscopy. One is statistical 2D correlation proposed originally by Barton et al (16). This method employs cross-correlation based on the least-squares linear regression analysis to assess spectral changes in two regions, such as the NIR and mid-IR regions, that arise from variations in sample composition (16). In another 2D correlation spectroscopy proposed by Noda (12, 13), 2D spectra are constructed from a set of spectral data collected from a system under an external physical perturbation, which induces selective alterations in spectral features. 

The method which satisfies these conditions is partial least squares (PLS) regression analysis, a relatively recent statistical technique (18, 19). The basis of tiie PLS method is that given k objects, characterised by i descriptor variables, which form the X-matrix, and j response variables which form the Y-matrix, it is possible to relate the two blocks (or data matrices) by means of the respective latent variables u and 1 in such a way that the two data sets are linearly dependent ... 

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. 

Finally, the possibility to study with linear regression models using principal component analysis (PGA) and partial least squares (PLS) regression analysis pharmacophores as descriptors for the corresponding molecules represents an interesting and novel approach in QSAR. 

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. 

Fig. 6. 15 A suite of five whole-rock samples of the Wyatt Formation collected by V.H. Minshew from outcrops between Mt. Wyatt and Mt. Gardiner in the Scott Glacier area define two straight lines labeled A and B derived by least-squares linear regression. Line A which includes all five samples plus one duplicate analysis yields a date of 524 13 Ma and a high initial Sr/ Sr ratio of 0.711919 0.000547 (la). Line B is defined by three selected samples and corresponds to a precise date of 802 2 Ma but it has an impossibly low initial Sr/ Sr ratio of 0.69775. We conclude that the igneous rocks of the Wyatt Formation are older than 524 13 Ma but younger that 802 2 Ma. These previously unpublished data by G. Faure are presented in Appendix 6.133. In addition. Appendices 6.7.3.1 and 6.7.3.2 contain modal analyses and chemical compositions of rocks of the Wyatt Formation from Minshew (1967)...

Quantitative analysis, A series of 5 aqueous standards, covering the concentration range of interest (10-100 ng ml was used to construct a calibration curve. A typical curve is shown in fig.4 in order to demonstrate the linearity and the precision. The curves were obtained by unweighted least squares linear regression based on previous research, which indicated that this type of statistical analysis can be employed with stable isotope labeled internal standards and for a 10-fold range of x-values because the errors associated with the y-values are approximately constant (16). Using the regression line(fig.4) in reverse, a standard error of 1. 2 ng ml could be... 

The estimation of RRs is usually performed by ordinary least-square linear regression. This should be done by preferably testing at least six different concentration levels within the linear range plus the blank (if this last exists or it is measurable). To minimize eventual experimental drifts, test samples should be examined in random order (not in order of increasing concentration values). Possibly, standard or test samples should be analyzed in duplicate (or more), especially when it is not possible to analyze at least six standards. If repeating the analysis of some... 

To gain insight into chemometric methods such as correlation analysis, Multiple Linear Regression Analysis, Principal Component Analysis, Principal Component Regression, and Partial Least Squares regression/Projection to Latent Structures... 

Most of the 2D QSAR methods are based on graph theoretic indices, which have been extensively studied by Randic [29] and Kier and Hall [30,31]. Although these structural indices represent different aspects of molecular structures, their physicochemical meaning is unclear. Successful applications of these topological indices combined with multiple linear regression (MLR) analysis are summarized in Ref. 31. On the other hand, parameters derived from various experiments through chemometric methods have also been used in the study of peptide QSAR, where partial least square (PLS) [32] analysis has been employed [33]. 

A statistical algorithm, also known as linear regression analysis, for systems where Y (the random variable) is linearly dependent on another quantity X (the ordinary or controlled variable). The procedure allows one to fit a straight line through points xi, y0, X2,yi), x, ys),..., ( n,yn) where the values jCi are defined before the experiment and y values are obtained experimentally and are subject to random error. The best fit line through such a series of points is called a least squares fit , and the protocol provides measures of the reliability of the data and quality of the fit. 

---