Calibration regression analysis

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... 

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. 

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. 

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. 

Perform a regression analysis on the calibration curve and calculate the values of slope (m), intercept i) and for a number of standards n. 

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. 

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. 

As a side aspect, the HPLC-Raman correlation results allow us to calibrate the RRS instruments in terms of carotenoid concentration. According to the regression analysis, the cumulative skin carotenoid content c, measured in pg per g of skin tissue, is linked to the height of the C=C RRS skin carotenoid intensity, I, via c [pg/g]=4.3 x 10 5=/ [photon counts]. Integrating the RRS spectra with the instrument s data acquiring software therefore allows us to display skin carotenoid content directly in concentration units, i.e., in pg carotenoid content per g of tissue. 

In a well-behaved calibration model, residuals will have a Normal (i.e., Gaussian) distribution. In fact, as we have previously discussed, least-squares regression analysis is also a Maximum Likelihood method, but only when the errors are Normally distributed. If the data does not follow the straight line model, then there will be an excessive number of residuals with too-large values, and the residuals will then not follow the Normal distribution. It follows, then, that a test for Normality of residuals will also detect nonlinearity. 

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,... 

With that we get (by regression analysis) the calibration function... 

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. 

In some instances, calibration test data may need to be subjected to some kind of mathematical transformation, prior to the regression analysis, in order to obtain linear calibration plots. In some cases, however, such as in immunochemical assays, linearity cannot be demonstrated even after any transformation. The use of nonlinear calibration curves for analysis has been discussed (27). 

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. 

Create a calibration curve by either plotting or performing regression analysis of the fluorescence intensity versus concentration of the standards. Using the fluorescence intensity of the sample protein, determine the concentration from the calibration curve. 

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. 

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. 

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) ... 

Briefly, the method involves determining the capacity factors (retention time corrected for an unretained substance) for a suitable set of reference substances (having known K(k values) using RP-HPLC. The relationship between the capacity factors and Kol for the reference or calibration compounds is determined from regression analysis of a log-log plot of the two properties. The capacity factors of compounds having unknown Koc values then are determined using the identical experimental conditions, and Koc values then are calculated from the regression expression. 

Potyrailo and May used the acoustic-wave sensor to quantify cresol and benzo-quinone [21]. They tested sensors for the quantification of cresol and benzoqui-none in mixtures with multivariate regression analysis tools. Only 2 mL of solution was used for analysis, which included cresol and/or benzoquinone on the order of pg. After the sensor had been calibrated with a standard library of pure cresol or benzoquinone solution, 19 model libraries, including mixtures of cresol and benzoquinone, were analyzed (Fig. 8.9). A linear correlation occurs between actual... 

Ordinary least squares technique, used for treatment of the calibration data, is correct only when uncertainties in the certified value of the measurement standards or CRMs are negligible. If these uncertainties increase (for example, close to the end of the calibration interval or the shelf-life), they are able to influence significantly the calibration and measurement results. In such cases, regression analysis of the calibration data should take into account that not only the response values are subjects to errors, but also the certified values. 

Calibration curves were constructed with the NIST albumin (5 concentrations in triplicate) and with the FLUKA albumin (5 concentrations in duplicate) in the concentration range of 50 250 mg/1. The measured values of individual concentrations fluctuated around the fitted lines, with a standard error of 0.007 of the measured absorbance. The difference between FLUKA and NIST albumin calibration lines was statistically insignificant, as evaluated by the t-test P=0.14 > 0.05. The calibration lines differed only in the range of a random error. The FLUKA albumin was, thus, equivalent to that of NIST. Statistical evaluation was carried out using the regression analysis module of the statistical package SPSS, version 4.0. 

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 ... 

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). 

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