Analytical Regression line

Three replicate determinations are made of the signal for a sample containing an unknown concentration of analyte, yielding values of 29.32, 29.16, and 29.51. Using the regression line from Examples 5.10 and 5.11, determine the analyte s concentration, Ca, and its 95% confidence interval. 

Linearity is often assessed by examining the correlation coefficient (r) [or the coefficient of determination (r )] of the least-squares regression line of the detector response versus analyte concentration. A value of r = 0.995 (r = 0.99) is generally considered evidence of acceptable fit of the data to the regression line. Although the use of r or is a practical way of evaluating linearity, these parameters, by... 

The MSWD and probability of fit All EWLS algorithms calculate a statistical parameter from which the observed scatter of the data points about the regression line can be quantitatively compared with the average amount of scatter to be expected from the assigned analytical errors. Arguably the most convenient and intuitively accessible of these is the so-called ATS ITD parameter (Mean Square of Weighted Deviates McIntyre et al. 1966 Wendt and Carl 1991), defined as ... 

Less strict descriptions of linearity are also provided. One recommendation is visual examination of a plot (unspecified, but presumably also of the method response versus the analyte concentration). Another recommendation is to use statistical methods , calculation of a regression line is advised. If regression is performed, the correlation... 

The authors determined specificity using the known hydrolytic degradation products. The precision of spiked samples of these degradation products were determined and found to be acceptable (99.9 0.4%). Accuracy of the method was determined using spiked recoveries of piroxicam benzoate, and the recoveries were acceptable (99.1-100.5%). Assay precision n = 6, RSD = 0.4%) was in accord with recommended criteria [7]. Within-day precision was performed on two instruments on two separate days, and the overall intermediate precision was 1.0%. The method was linear over the expected analyte concentration range giving a regression line of 1 = 0.999. The detection (DL) and quantification levels (QL) were assessed, and the latter was determined as 0.185 pg/ml (ca. 0.04%). 

The standard addition method is a calibration in the sample. Known amounts of analyte are added to the samples and the signal-concentration regression line is extrapolated to a signal of zero. 

The procedure starts with dividing the sample into n sub-samples. We spike n-1 sub-samples with the analyte in equidistant steps and measure all n sub-samples. We use least-square regression to calculate the regression line and extrapolate to the intersection, , "... 

The slope S may be estimated from the calibration curve of the analyte. The value of may be estimated by (1) calculating the standard deviation of the responses obtained from the measurement of the analytical background response of an appropriate number of blank samples or (2) calculating the residual standard deviation of the regression line from the calibration curve using samples containing the analyte in the range of the QL. 

Another approach is to prepare a stock solution of high concentration. Linearity is then demonstrated directly by dilution of the standard stock solution. This is more popular and the recommended approach. Linearity is best evaluated by visual inspection of a plot of the signals as a function of analyte concentration. Subsequently, the variable data are generally used to calculate a regression line by the least-squares method. At least five concentration levels should be used. Under normal circumstances, linearity is acceptable with a coefficient of determination (r2) of >0.997. The slope, residual sum of squares, and intercept should also be reported as required by ICH. 

The concentration of the CSF analyte is calculated by interpolation of the observed analyte IS peak-area ratio into the linear regression line for the calibration curve, which is obtained by plotting the peak-area ratios against analyte concentration. 

As a calibration procedure in ICP-MS via calibration curves, external calibration is usually applied whereby the blank solution is measured followed by a set of standard solutions with different analyte concentrations (at least three, and it is better to analyze more standard solutions in the same concentration range compared to the sample). After the mass spectrometric measurements of standard solutions, the calibration curve is created as a plot of ion intensities of analyte measured as a function of its concentration, and the linear regression line and the regression coefficient are calculated. As an example of an external calibration, the calibration curve of 239 Pu+ measured by ICP-SFMS with a shielded torch in the pgC1 range is illustrated in Figure 6.15. A regression... 

It is usual to test the slope of the regression line to ensure that it is significant using the F ratio, but for most analytical purposes this is an academic exercise. Of more importance is whether the intercept is statistically indistinguishable from zero. In this instance, the 95% confidence interval for the intercept is from — 0.0263 to +0.0266 which indicates that this is the case. 

The online statistical calculations can be performed at http //members.aol.com/ johnp71/javastat.html. To carry out linear regression analysis as an example, select Regression, correlation, least squares curve-fitting, nonparametric correlation, and then select any one of the methods (e.g., Least squares regression line, Least squares straight line). Enter number of data points to be analyzed, then data, x and y . Click the Calculate Now button. The analytical results, a (intercept), b (slope), f (degrees of freedom), and r (correlation coefficient) are returned. 

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. 

Definition of Linearity The linearity of an analytical method is its ability (within a given range) to elicit test results that are directly, or by a well-defined mathematical transformation, proportional to the concentration of analyte in samples within a given range. Linearity is usually expressed in terms of the variance around the slope of the regression line (correlation coefficient), calculated according to an established mathematical relationship from test results obtained by the analysis of samples with varying concentrations of analyte. 

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