Regression analysis, calibration graphs

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. 

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. 

Figure 12. Graphs of observed versus diatom-inferred total phosphorus concentrations (TP) and observed minus diatom-inferred TP (i.e., a residual analysis) are based on weighted averaging regression and calibration models and classical deshrinking. The large circles indicate two coincident values. This analysis is discussed in detail in reference 46.

Figure 6.6 presents a UV spectrum of the amino acid tryptophan. For quantitative analysis, measurements at a single wavelength, e.g. Ah, would be adequate if no interfering species are present. In the presence of other absorbing species, however, more measurements are needed. Table 6.10 presents the concentrations and measured absorbance values at Ah of seven standard solutions containing known amounts of tryptophan along with three samples which we will assume contain unknown amounts of tryptophan. All solutions have unknown concentrations of a second absorbing species present, in this case the amino acid tyrosine. The effect of this interferent is to add noise and distort the univariate calibration graph, as shown in Figure 6.7. The best-fit linear regression line is also shown, as derived from...

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... 

Table 4 summarises the p>arameters obtained from the calibration graphs for all of the reductive sulfur analytes, along with the method detection and quantification limits for each compoimd. Linear regression analysis revealed that very good linearities (R > 0.992) were obtained in the calibration graphs for all of the reductive sulfur compounds. The method provided very good detection limits, which were well below the sensory thresholds (See Table 1) of the analysed sulfur compounds. 

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