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Linear regression analysis, calibration

A linear regression analysis should not be accepted without evaluating the validity of the model on which the calculations were based. Perhaps the simplest way to evaluate a regression analysis is to calculate and plot the residual error for each value of x. The residual error for a single calibration standard, r , is given as... [Pg.124]

Standardizations using a single standard are common, but also are subject to greater uncertainty. Whenever possible, a multiple-point standardization is preferred. The results of a multiple-point standardization are graphed as a calibration curve. A linear regression analysis can provide an equation for the standardization. [Pg.130]

Construct an appropriate standard additions calibration curve, and use a linear regression analysis to determine the concentration of analyte in the original sample and its 95% confidence interval. [Pg.133]

One-dimensional data are plotted versus an experimental variable a prime example is the Lambert-Beer plot of absorbance vs. concentration, as in a calibration run. The graph is expected to be a straight line over an appreciable range of the experimental variable. This is the classical domain of linear regression analysis. [Pg.91]

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. [Pg.582]

Famoxadone, IN-JS940, and IN-KZ007 residues are measured in soil (p-g kg ), sediment (p-gkg ), and water (pgL ). Quantification is based on analyte response in calibration standards and sample extract analyses determined as pg mL Calibration standard runs are analyzed before and after every 1 samples in each analytical set. Analyte quantification is based on (1) linear regression analysis of (y-axis) analyte concentration (lagmL Q and (x-axis) analyte peak area response or (2) the average response factor determined from the appropriate calibration standards. The SLOPE and INTERCEPT functions of Microsoft Excel are used to determine slope and intercept. The AVERAGE and STDEV functions of Microsoft Excel are used to determine average response factors and standard deviations. [Pg.1188]

However, as regards the conventional method, a linearity exists only in the case when the fan was off, and the track densities T in the turbulent atmosphere were higher than those in the still atmosphere. The calibration coefficients K and K were calculated with a multi-step method of linear regression analysis (Skinner and Nyberg,... [Pg.185]

Plot the average response against the quantity (or concentration) of the component and use linear regression analysis to calculate the calibration line. If an internal standard is used, the linearity of its curve has to be determined similarly. [Pg.454]

Some basic aspects of EDA will be explored in Section 8.1, and in Section 8.2 the most frequently used CDA technique, linear regression analysis for calibration, will be covered. It is not intended to provide a statistical recipe approach to be slavishly followed. The examples used and references quoted are intended to guide rather than to prescribe. [Pg.42]

Create a calibration curve by performing a linear regression analysis of the area under the 966 cm"1 band versus the amount of TE (as percent of total fat) in the calibration standards. [Pg.507]

Generate five calibration curves (i.e., each sugar standard) by plotting a first-order curve of integrated peak area versus concentration (mg/ml) and performing linear regression analysis. [Pg.664]

Method validation is important to ensure that the analytical method is in statistical control. A method may be validated by the so-called method evaluation function (MEF) (Christensen et al., 1993), which is obtained by linear regression analysis of the measured concentrations versus the true concentrations. A true concentration in a solution can be obtained by use of a high purity standard obtained from another manufacturer or batch than the one used for calibration. Both the high purity standard and the solvent are weighed using a traceable calibrated balance. If certified reference material is available this is preferred. The method evaluation includes the most important characteristics of the method as the following elements (see Figure 2.7) ... [Pg.37]

In many chemical studies, the measured properties of the system can be regarded as the linear sum of the fundamental effects or factors in that system. The most common example is multivariate calibration. In environmental studies, this approach, frequently called receptor modeling, was first applied in air quality studies. The aim of PCA with multiple linear regression analysis (PCA-MLRA), as of all bilinear models, is to solve the factor analysis problem stated below ... [Pg.383]

If the IS contributes to the signal of the analyte, but the reverse is not true, a linear calibration curve with a positive intercept is obtained. Provided that the variance on the isotope ratios measured is uniform throughout the whole calibration range, linear regression analysis may be applied. Otherwise, weighting factors should be introduced, e.g., the reciprocals of the variances at different concentration levels (Claeys et al., 1977 Schoeller, 1976). [Pg.129]

Calibration is performed by measuring Rm for a number of standard mixtures with a known concentration of analyte x. Depending on the type of ion interference, linear regression analysis is applied if both C1 and C2 (type 1 ion interference, Section 3.1) or only C2 (type 2) are negligible. In all other cases (types 3 and 4), a NONLIN computer program is used to calculate the nonlinear calibration curve after experimental determination of Clt C2, and C3 on the pure components. Apart from the fact that the exact form of the NONLIN data regression was not specified, the experimental determination of ion interferences and the assumption that qj = pt are limiting factors to accuracy (Jonckheere, 1982). [Pg.132]

It is also worth mentioning that, depending upon the nature of the internal standard, weighted or non-weighted linear regression analysis to construct the calibration curve should be considered [22],... [Pg.268]

On the other hand, a transformation of the independent variable does not change the variance. Therefore, transformations of m into log m, as described by Pataki69) for fluorescence or by Connors 70), Huber 12) and Koleva71) for reflectance are possible bases for linear regression analysis. Instead of calibration with (15) the inverse transformation (16) should be preferred towards a correct regression. [Pg.84]

Not all calibration curves generate a perfect straight line due to indeterminate or random errors. Most scattered points can be corrected using linear regression analysis to... [Pg.83]

NIR laboratory data of whole fresh leaves were evaluated with respect to leaf chemical composition [140]. NIR spectra were measured for 211 foliage samples, which included both broad- and needle-leafed species. Multiple linear regression analysis was used to determine if reflectance data from fresh leaf samples contained information on nitrogen, lignin, and cellulose concentrations. Calibration... [Pg.127]

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. [Pg.386]

The definition of calibration function does not specify that the measurement be made in the presence of potential interferants. This serves as an introduction to a discussion of the appropriate approach to calibration in an analytical method for veterinary drug residues, such as antibiotics. Construction of a calibration curve requires a sufficient number of standard solutions to define the response in relation to concentration, where the number of standard solutions used is a function of the concentration range. In most cases, a minimum of five concentrations (plus a blank, or zero ) is considered appropriate for characterization of the calibration curve during method validation. It is also typically recommended that the curve be statistically tested and expressed, usually through linear regression analysis. However, for LC/ESI-MS analysis of residues, the function tends to be quadratic. The analytical range for the analysis is usually defined by the minimum and maximum concentrations used in establishing the calibration curve. [Pg.276]

Fig. 2. Fibrin zymography of PA standards. (A) Fibrin zymogram demonstrating electrophoretic migration of uPA (45-kDa), tPA (70-kDa), and higher molecular weight tPA/PAI-1 complex (110-kDa). Fibrin indicator gels were stained with amido black (see Section 3.5). Samples 1-5 correspond to PAs and PAIs of various compositions as described (R4, R5). (B) Calibration curve obtained with PA standards. Linear regression analysis was performed and correlation coefficient (r) is shown (r = 1.000, perfect correlation). Fig. 2. Fibrin zymography of PA standards. (A) Fibrin zymogram demonstrating electrophoretic migration of uPA (45-kDa), tPA (70-kDa), and higher molecular weight tPA/PAI-1 complex (110-kDa). Fibrin indicator gels were stained with amido black (see Section 3.5). Samples 1-5 correspond to PAs and PAIs of various compositions as described (R4, R5). (B) Calibration curve obtained with PA standards. Linear regression analysis was performed and correlation coefficient (r) is shown (r = 1.000, perfect correlation).
The membrane-coated fiber technique has overcome these experimental difficulties. A membrane material coated onto a fiber is used as the absorption membrane to determine the membrane/solvent partition coefficients of chemicals. Multiple membrane/solvent systems can be calibrated with the probe compounds with known solute descriptors as follows. The partition coeffidrait of each probe compound in a given membrane/solvent system log is detmmined experimentally by the membrane-coated fiber technique. The log value of each probe compound is scaled to the solute descriptors of the compound with the LEER equation (Equation 5.1, where log SP = log K ). A LEER equation matrix is generated from all of the probe compounds (Equation 5.2). The system coefficients of each membrane/solvent system can be obtained by multiple linear regression analysis of the LEER equation matrix. [Pg.76]

The first step in developing a relative analytical method is calibration. It is based on the use of standard solutions or of a solid standard. The calibration function (Eq. (4.1)) is constructed by means of linear regression analysis as discussed in Section 6.1. [Pg.346]

Injection of a derivatized blank should not produce contaminant peaks m the chromatogram. Inject denvatized standard solutions of increasing concentrations and calculate the calibration curve y = ax + b using linear regression analysis, where y is the peak area of the standard solutions and x the concentration. Linearity is verified by visual inspection of the calibration graph and calculation of the correlation coefficient that must exceed 0 9970. The detection limit of an ammo... [Pg.203]

The resulting concentration correlation plots are provided for the best glutamine model in Figure 4 where Figures 4a and 4b corre ond to the calibration and prediction data sets, respectively. Linear regression analysis of these data yields slopes of 0.998 0.003 and 1.001 + 0.004 as well as y-intercepts of 0.009 + 0.116 and -0.009 0.104 mM for the calibration and prediction data sets, respectively. This calibration model is capable of predicting glutamine concentrations with a 0.10 mM SEP and a 2.19% mean percent error. [Pg.122]


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