Standard deviation of intercept

The DL and QL for chromatographic analytical methods can be defined in terms of the signal-to-noise ratio, with values of 2 1-3 1 defining the DL and a value of 10 1 defining the QL. Alternatively, in terms of the ratio of the standard deviation of the blank response, the residual standard deviation of the calibration line, or the standard deviation of intercept (s) and slope (5) can be used [40, 42], where ... 

Standard deviation of slope Sj, Standard deviation of intercept ... 

Standard deviation of slope Sb Standard deviation of intercept sa... 

Standard deviation of slope 90.8772 Standard deviation of intercept 0.2927... 

A more useful representation of uncertainty is to consider the effect of indeterminate errors on the predicted slope and intercept. The standard deviation of the slope and intercept are given as... 

Data from several laboratories within the Interregional Research Project No. 4 (IR-4) in the USA have been evaluated for determining the values of MDL and MQL. These data have been presented in Table 1. The two-step procedure described in the EPA guideline was used to calculate the values of MDL and MQL. For the first step, the slope, intercept and RMSE values for the first three calibration curves of each study were separately calculated, then the IDL and IQL values calculated and the value of LQQ estimated for the method. These values were compared with the actual values of LLMV. The standard deviation of the spike recoveries at the LLMV (xllmv) was used to calculate the MDL and MQL. The values of LLMV were separately determined by the laboratory not using any of the methods described in this article. 

Phosphoric Acid. The 2nd-order rate method for analyzing the TGA data was statistically best (Table IV) for the cellulose/H PO samples. This suggests that the conclusions from a prior study which assumed a lst-order reaction (29) may need to be reexamined. While Wilkinson s approximation method gave high r values, the rate constant is determined by the intercept rather than the slope in this method. Thus, the standard deviation of the rates determined by Wilkinson s approximation method is still relatively high when compared to the other methods. In addition, the reaction order as determined by the Wilkinson approximation method was unrealistically high, ranging from 2.6 to 5.8. 

From this the standard deviations of the slope, sm, and intercept, Sb, are... 

Also determine the slope and intercept of the least-squares line for this set of data. Determine the concentration and standard deviation of an analyte that has an absorbance of 0.335. 

In practice, the interpretation of test results strongly depends on the accuracy of the estimated intercepts of the theoretical isobole with the axis, which represents the doses of the single compounds that induce the desired effect. In fact, large standard deviations of these intercepts prevent a rehable conclusion as to the deviation from additivity. 

Another approach estimates the DL from the standard deviation of the response and the slope of the calibration curve. The standard deviation can be determined either from the standard deviation of multiple blank samples or from the standard deviation of the intercepts of the regression lines done in the range of the DL. This estimate will need to be subsequently validated by the independent analysis of a suitable number of samples near or at the DL ... 

If the measurement of LOD is not critical, an estimate can be made from the calibration parameters taking the intercept as the blank measurement and the standard error of the regression as the standard deviation of the blank. Equation (8.1) becomes... 

Values of the right-hand side of Equation 6 (that is, those denoting the term E0/) are expected to be linear in terms of m, when a suitable value for the ion-size parameter is chosen. Several different values for a0 (e.g., 0.2, 0.4, 0.6, and 0.8 nm) were tested, and the computer calculations showed that the deviations of E0/ vs. m from linearity were at a minimum when a0 is equal to 0.6 nm. These results are shown in Table VIII. By means of Equation 6, the intercepts of the extrpolation lines (E°) can be found and the slopes (—2k(3) computed. The values of the standard emf are summarized in Tables IV, V, and VI for x = 10,30, and 50 mass percent monoglyme, together with the standard deviations of the intercepts (E°). For a0 = 0.6 nm, the values of are entered in Table IX. 

Fig. 2. Compensation plot for cracking and related (see text) reactions on nickel (Table I, A). The error in the individual points is indicated by the size of each cross the line was calculated by the least squares method (Appendix II),and standard deviations of slope (erj and intercept (nB) are indicated,...

Figure 5. Variation of Mott-Schottky intercept with pCl for (100) orientation n-GaAs, 40°C. Circles denote intercept values from automated admittance measurements. Bars signify standard deviation of least-squares straight line.

The limit of detection, calculated as the concentration corresponding to a signal which is three times the standard deviation of the intercept, results to be 5pM. This means an improvement of various orders of... 

Figure 16. The data shown in Figure IS are hourly averages and the bars surrounding each point represent the variation ( 1 s.d.) of the measured values during the hour the standard deviation of individual measurements are far smaller. The correlation, as shown in Figure 16, is good (correlation coefficient 0.88 System 1 SO2 = 1.162 x System 2 SO + 59 pptv) with a relatively small intercept. The more than unity slope is likely due to the H2O2 interference experienced by System 1.

Fig. 4.16 shows a typical chromatogram for a standard 42pg L 1 phosphate solution and hypoxanthine peaks resulting from various phosphate samples after reaction with the enzyme. The calibration curve had a slope of 0.043 0.002 and an intercept of 0.124 0.033 with a correlation coefficient of 0.998. Linearity up to 30mg L 1 was observed. Relative standard deviation of triplicate runs was 10% or less. The detection limit, twice the signal of the blank, was determined to be 1.5mg L 1. 

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