Calibration best-fit curve

The final best fit calibration curve can be seen at Figure 2.9. Note the limitations on the use of the lower, extrapolated, portion of the curve. The line obtained will always pass through the centroid of all the points, i.e. the point on the graph corresponding to x y. A further aspect is the uncertainty associated with the values of a and b. These may be estimated in terms of the variability ofx and y. 

Use the least squares method to plot the best fit calibration curve. Comment upon its suitability for use. 

Summarized Procedure to Determine Best-Fit Calibration Curve... 

Equations (2.12) and (2.13) enable the best-fit calibration line to be drawn through the experimental x,y points. Once the slope m and the y intercept b for the least squares regression line are obtained, the calibration line can be drawn by any one of several graphical techniques. A commonly used technique is to use Excel to graphically present the calibration curve. These equations can also be incorporated into computer programs that allow rapid computation. 

If one pursues the calibration approach, one has to stick to a given combination of density functional and basis set, since the calibration will change for each such combination. Calibration curves have been reported for a number of widely used density functionals and basis sets. The results of a relatively comprehensive study are collected in Table 5.4. The standard deviation of the best fits is on the order of 0.08 mm s which appears to be the intrinsic reliability of DFT for predicting Mossbauer isomer shifts. 

The amount of tebuconazole residue is calculated by using a least-squares fitting algorithm to generate the best line which can be used to calculate the corresponding concentration for a given peak area or peak height. Calculate the slope and the intercept of the standard calibration curve. 

An ideal calibration curve (Figure 2.7) is a straight line with a slope of about 45 degrees. It is prepared by making a sequence of measurements on reference materials which have been prepared with known analyte contents. The curve is fundamental to the accuracy of the method. It is thus vitally important that it represents the best fit for the calibration data. Many computer software packages, supplied routinely with various analytical instruments, provide this facility. It is, however, useful to review briefly the principles on which they are based. 

This is perhaps the "best solution for the given data set, and it is certainly the most interesting. It is not offered as a rigorous solution, however, for the lack of fit (x /df -[9.64]2) implies additional sources of error, which may be due to additional scatter about the calibration curve (oy -"between" component), residual error in the analytic model for the calibration function, or errors in the "standard" x-values. (We believe the last source of error to be the most likely for this data set.) For these reasons, and because we wish to avoid complications introduced by non-linear least squares fitting, we take the model y=B+Axl 12 and the relation Oy = 0.028 + 0.49x to be exact and then apply linear WLS for the estimation of B and A and their standard errors. 

P-outine chemical analysis. This implies analysis of many samples, and use of calibration curves is an economic necessity. In general, the two-standard method, with standards bracketing each sample analyzed, is economical for the analysis of up to about 10 samples. Conventional least squares curve of best fit procedures are economical for analysis of 10 to 500 samples. The procedures described here are cost effective for the analysis of 500 samples or more. 

For example. Figure 8 shows both RSD and RCB data for determination of chloride and lead in water. In Figure 8a, the least-squares curve of best fit closely fits the lead standard data, and the calibration process has little adverse effect on precision. RSD s and RGB s are almost equal. On the other hand, chloride standard data in Figure 8b does not closely fit the mathematical model, and the RSD data overstates the precision of the analysis by a factor of about two. 

A calibration curve is a model used to predict the value of an independent variable, the analyte concentration, when only the dependent variable, the analytical response, is known. The normal procedure used to establish a calibration curve is based on a linear least-squares fit of the best straight line for a linear regression, as indicated in... 

Figure 10.3 Comparison of experimental calibration curves of Rp =/(AT) (dotted lines) with best fit using a simplified Kelvin equation Rp = A/AT + t (solid line). The data are adapted from reference [29] for water (a) and from reference [28] for acetone (b).

The experiments were repeated with the new adapter. Three sets of samples were welded and analyzed with three different fiber sections. Each section was calibrated prior to the analyses. The slopes for each response curve were calculated and compared to the theoretical data. A best fit was obtained with an apparent diffusion coefficient of Deff = 7.5 x 105 cm2/sec. The results are presented in Figures 11-13. 

Because pressure transducers from different manufacturers can vary significantly, it is important to understand their performances such as accuracy. An ideal device would have a direct linear relationship between pressure and output voltage. In reality, there will always be some deviations this is referred to as nonlinearly. The best straight line is fitted to the nonlinear curve. The deviation is quoted in their specifications and expressed as a percent of full scale. The nonlinear calibration curve is determined in ascending direction from zero to full rating. This pressure will be slightly different from the pressure measured in descending mode. This difference is termed hysteresis it can be reduced via electrical circuits. 

To determine the calibration curve, aspirate the Cadmium Calibration Standards and the Calibration Blank Solution. If possible, use the calibration function incorporated in the ICP-AES instrument s soft- or firmware. If necessary, plot instrument response versus concentration of cadmium Fit this line with a linear equation of the form y = mx + b, in which y is instrument response, m is the slope of the best-fit line, x is concentration, and b is the y intercept of the best-fit line. The correlation coefficient for the best-fit line should be >0.99. Concentrations of cadmium in the calibration blanks, calibra-... 

Figure 11-2. Least-squares best fit line through data points of a calibration curve.

A calibration curve for 1 -naphthyl glucuronide is shown in Figure 4. For this data, the best fit straight line has a correlation coefficient of 0.989. When fitted to a quadratic equation the correlation coefficient was 1.00. Quadratic calibration curves were also seen for the other compounds in this study, and this is consistent with another report in this symposium (Brown, M. A., et al. this volume). 

In anal3rtical chemistry, developii a calibration curve or modelling a phenomenon often requires the use of a mathematical fitting procedure. Probably the most familiar of these procedures is linear least-squares fitting [1]. Criteria other than least-squares for defining the best fit have been developed for linear parameters when the data possibly contain outliers [2,3]. Sometimes, the model equation to be fit is nonlinear in the parameters. This requires appeal to other fitting methods [4]. 

A linear relationship between a measurable parameter (like absorbance) and concentration is observable in many analytical methods, and the least-squares method is used to fit the best calibration curve. 

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