Calibration zero intercept

Referring to equation [40], we can see that we require the absorbance at each wavelength to equal zero whenever the concentrations of all the components in a sample are equal to zero. We can add some flexibility to the CLS calibration by eliminating this constraint. This will add one additional degree of freedom to the equations. To allow these non-zero intercepts, we simply rewrite equation [40] with a constant term for each wavelength ... 

We perform CLS on A6 to produce 2 calibrations. K6 and K6, are the matrices holding the pure component spectra and calibration coefficients, respectively, for CLS with zero intercepts. K6a and K6aMl are the corresponding matrices for CLS with nonzero intercepts. 

We can see that the ILS calibrations are noticeably better than the CLS calibrations done with zero intercept. And they are as good or somewhat better that the CLS calibrations with nonzero intercept. This is remarkable when we consider how badly we have degraded the spectra when we condensed them The main reason for the advantage of ILS over CLS can be seen in equation [47],... 

CLS calibration with non-zero intercept from Al/Cl predicts concentrations for AI... 

Provided that rA and d are known, the concentration of absorbing species can be found. A calibration graph of A versus c should be linear with slope d and zero intercept. Microwave, infra-red, Raman, visible and UV spectra are all used. 

Prerequisites for the Calibration Types. It depends on the design of the analytical procedure as to which regression parameters are meaningful and which results are acceptable. In other words, the model to be used for quantitation must be justified. For a singlepoint calibration (external standardization), a linear function, zero intercept, and the homogeneity of variances are required. The prerequisites for a linear multiple-point calibration are a linear function and in case of an unweighted calibration also the homogeneity of variances. A non-linear calibration requires only a continuous function. With respect to the 100%... 

If two or more standards of different concentrations within the linear range are measured, the RF value can be taken as the average value of the response factors for all these standards to minimize the uncertainty in determining the RF. In the example shown in Fig. 1, the RF is the slope of the calibration plot and equals 2 X 10 for all three standards because the plot is linear with a zero intercept. The concentration (X) of the analyte in the unknown sample (U) can be calculated as... 

The constant is equal to the zero-intercept of the line. In the present case, it is almost zero. Based on these results, the calibration equation of this MCA is E = 4.15C. 

The criteria for acceptable linearity of least squares fit and zero intercept when plotting ratios of analyte to internal standard areas vs. concentration are similar to the case for external standard calibrations described earlier. More than one IS can be used, both for calculating RRTs to compensate for retention time variations as well as the RRFs for improving quantitation. The variations that a quantitation IS can compensate for depend upon the point at which it is introduced in the analysis. If it is put into the final extract prior to injection on the chromatograph, it can correct for concentration variations due to evaporative volume changes, variations in injection volume, and variations in detector response. This is called an injection internal standard. If the internal standard is put into the initial sample, and into calibration standards prepared in an equivalent matrix, it can additionally correct for variations in recovery during the sample preparation process. This is called a method internal standard. Combined use of separate compounds for each purpose can aid in determining the causes of peak area variability. 

Linear Model With Intercept. There are two distinct linear first-order regression models that are generally encountered in analytical calibration. The non-zero intercept model is the most familiar, and it is given by Equation 1. 

The estimates of Intercept (b ) and slope (b ) are calculated so as to minimize the sum of squares (SS) of the deviations of the observed signals (y ) from the predicted value (y) at any concentration (x) without constraints. For some determinations, however, theory predicts that the response of the instrument should be linear with concentration and should also be zero when there is no analyte present. Thus, if the Instrument has been calibrated correctly, the calculated line should pass through the origin by definition. The proper regression model would then be the zero Intercept model shown as Equation 2. 

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