Standard error of calibration

Precision. The uncertainty of calibration and prediction of unknown concentrations are expressed by the standard error of calibration (SEC), defined as... 

SEP without any index is mostly used for prediction errors obtained from a test set (for clarity better named SEPtest). SEPCv is calculated from prediction errors obtained in CV, for instance during optimization of the number of components in PLS or PCR. SEPcv is usually smaller (more optimistic) than SEPtest. If Equation 4.6 is applied to predictions of the calibration set, the result is called standard error of calibration (SEC) SEC is usually a too optimistic estimation of the prediction errors for new cases. 

Paracetamol Tablet Drug determination of grinded tablets in reflectance mode. Standard error of calibration (0.48%m/m) and prediction (0.71 %m/m) 32... 

SEC standard error of calibration TAE total analytical error... 

Multiple regression programs also calculate auxiliary statistics, designed to help decide how well the calibration fits the data, and how well it can be expected to predict future samples. For example, two of these statistics are the standard error of calibration (SEC) and the multiple correlation coefficient (R). The SEC (also called standard error of estimate, or residual standard deviation) and the multiple correlation coefficient indicate how well the calibration equation fits the data. Their formulas are given in Table 3. 

Significant changes in absorption were observed at 1,720 nm (-CH2-) and 2,140 nm (-CH= CH-) as iodine number changed. These are absorption bands of oil. In the case of calibration for rapeseed, correlation coefficient (R) and standard error of calibration (SEC) were 0.9993 and 0.476, respectively. However, the selected wavelengths did not appear in the report. 

This work was supported by a grant from the National Science Foundation, t Abbreviations used are as follows. FTIR Fourier transform infrared spectroscopy, ATR attenuated total reflectance, IRE internal reflection element, SATR solution ATR FTIR, FSD Fourier self-deconvolution, PLS partial least-squares analysis, PRESS prediction residual sum of squares from PLS. SECV standard error of calibration values from PLS, PLSl PLS analysis in which each component is predicted independently, PLS2 PLS analysis in which all components are predicted simultaneously. 

For PLS solution basis sets, bulk spectra were generated as described above. Standard error of calibration values (SECV) were determined from prediction residual sum of squares (PRESS) analyses of various permutations of the amide I, II, and III bands (always including amide I) from both Ge and ZnSe spectra. After determination of the effects of different types of normalization on the results, these bands were individually normalized to an area of 100 absorbance units before PLS 1 training. 

This may be defined as the degree of agreement between the value found and the true value. Inaccuracy, systematic error, or bias arises from nonspecificity, interference, and faulty calibration or standardization. Errors of calibration are entirely instrumental (see Section 2.3), but the other causes of inaccuracy depend also on the nature of the specimen. 

SE Standard error, R coefficient of determination, SEC standard error of calibration, SEV(C) standard error of cross-validation, PLS terms number of terms used for modified partial least squares regression. 

Standard errors of calibration and prediction (RMSEC and RMSEP) ... 

Visual inspection should be possible from plots of predicted versus measured concentrations, from principal component plots of loadings and scores in the case of soft modeling techniques, and by plotting the standard error of calibration (SEC) or the standard error of prediction (SEP(-y, Eq. (6.68)) from cross-validation in dependence on the number of eigenvalues or of principal components. 

Evalnate standard errors of calibration and cross-validation for each model and plot as a function of the number of variables in the model... 

We use the example of glucose to illustrate the procedure that is used to gauge the appropriate number of PLS factors to include in the final model. Recalling that the pool of spectra is divided into a calibration set of 200 samples and a validation set of 100 samples, the aim was to arrive at a final model that optimally extracted the analytical information latent in the calibration spectra. To guard against the possibility of overfitting, the IR-predicted analytical levels were typically compared to reference values for models with 1-15 factors. The trends illustrated in Figure 13 are typical the standard error of calibration (SEC) in the calibration set specimens decreases rapidly as the initial factors are added, and then tends to plateau as aU of the analytically relevant factors were extracted. Additional factors provide rapidly... 

One approach to establishing a calibration sample set is to scan a large number of samples that represent the potential population to be predicted and to submit the spectra to an analysis that establishes which combination of samples shows the largest spectral variability overall. This smaller subset of samples can then be analyzed by the laboratory method. In practice, it will seldom be possible to establish calibrations that will optimally predict all future samples. It is therefore helpful to include new samples in the calibration that are spectrally different from the original calibration set. The standard error of calibration (SEC) is used as an indication of the efficacy of a calibration. 

An attempt was made to find robust calibration equations for sugar content and acidity by MLR, PCR, and PLS, where the optical parameters were employed as explanatory variables. Normally, chemometrics by NIR spectra employs the absorbance as the explanatory variable, where only wavelength-dependent characteristics of the materials can be considered. In this case, it is very difficult to precisely evaluate the small amount of a constituent such as acid content in a fruit. On the other hand, chemometrics by TOF-NIRS would be related to both wavelength- and time-dependent characteristics as the explanatory variables, where the light absorption and light scattering phenomena in a sample are included. It may therefore be possible to detect the acid content in a fruit on the basis of this new optical concept. The statistical results are summarized in Tables 4.2.1 and 4.2.2. Figure 4.2.9 shows the PLS analysis in a optimum model for acidity in apple. In the case of normal analysis by second-derivative NIR spectra, standard error of calibration (SEC) and correlation coefficient between measured and predicted acidity r were limited to 0.048% and... 

Table 7.3.2 gives an overview of the chemical reference analysis. Reflectance NIR measurements gave better prediction results compared to transmittance NIR measurements. Transmittance measurements will not be discussed further. The lowest prediction error for reflectance measurements for pork was 0.60% for moisture, 0.66% for protein, and 0.16% for fat (Table 7.3.3). The latter is probably somewhat overoptimistic, because the standard error of calibration was significantly higher, that is, SEC = 0.27%. The corresponding prediction errors for beef were comparable, namely, 0.52%, 0.61%, and 0.31% for moisture, protein, and fat, respectively. By...

In a glycolipid fermentation, mannosyl erythritol lipid (MEL) is produced from soybean oil added to a medium as a source of carbon. NIR can be used to measure the concentrations of MEL and soybean oil extracted from the fermentation process with ethyl acetate. NIR bands at 1436, 1920, and 2052 nm were assigned to MEL, and a MLR calibration equation was developed using the second derivative spectral data at 2040 and 1312 nm. Thin-layer chromatography with a flame-ionization detector (TLC/FID) was used as the reference method. The regression coefficient (R) and the standard error of calibration (SEC) were 0.994 and 0.48 g-l respectively. Absorption bands due to soybean oil were observed at 1208,1716,1766,2182, and 2302 nm and the second derivative bands at 2178 and 2090 nm were used for the calibration, yielding values of R and SEC of 0.974 and 0.77 g-l respectively. The NIR method was applied to the measurement of the concentrations of MEL and soybean oil in an actual fermentation process with good results (38). 

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