Calibration methods regression and correlation

SEC calibration methods which employ a series of narrow MWD standards are based upon a peak position method and traditionally have been the most widely practiced calibration procedures. The peak position method simply correlates the peak elution volume of each standard to its nominal molecular weight or size value. A curve fitting procedure (usually a least squares regression) is used to obtain a working calibration curve. The serious limitation of polymer chemical types for which a series of narrow MWD standards covering a wide molecular weight range can be obtained led to the development of experimental approaches which could be applied to polymer chemical types other than that of the narrow MWD standards employed in calibration. 

Tablet hardness is a property that, when measured, destroys the sample. The destructive nature of the test, coupled with the variability of the test itself does not contribute to an incentive to test a large number of samples. Morisseau and Rhodes99 correlated the diffuse reflectance NIR spectra of tablets pressed at different pressures and subsequently tested the tablet hardness with an Erweka Hardness Tester. The tablet hardness, as predicted by the NIR method, was at least as precise as the laboratory test method. Kirsch and Drennen100 evaluated NIR as a method to determine potency and tablet hardness of Cimetidine tablets over a range of 1-20% potency and 107-kPa compaction pressure. Hardness at different potency levels was used to build calibration models using PCA/ principal component regression and a new spectral best-fit algorithm. Both methods provided acceptable predictions of tablet hardness.

CONTENTS 1. Chemometrics and the Analytical Process. 2. Precision and Accuracy. 3. Evaluation of Precision and Accuracy. Comparison of Two Procedures. 4. Evaluation of Sources of Variation in Data. Analysis of Variance. 5. Calibration. 6. Reliability and Drift. 7. Sensitivity and Limit of Detection. 8. Selectivity and Specificity. 9. Information. 10. Costs. 11. The Time Constant. 12. Signals and Data. 13. Regression Methods. 14. Correlation Methods. 15. Signal Processing. 16. Response Surfaces and Models. 17. Exploration of Response Surfaces. 18. Optimization of Analytical Chemical Methods. 19. Optimization of Chromatographic Methods. 20. The Multivariate Approach. 21. Principal Components and Factor Analysis. 22. Clustering Techniques. 23. Supervised Pattern Recognition. 24. Decisions in the Analytical Laboratory. 

In the arsenal of calibration methods there are methods more suited for modelling any number of correlated variables. The most popular among them are Principal Component Regression (PCR) and Partial Least Squares (PLS) [3], Their models are based on a few orthogonal latent variables, each of them being a linear combination of all original variables. As all the information contained in the spectra can be used for the modelling, these methods are often called the full-spectrum methods. ... 

Calibration curve data should be assessed to determine the appropriate mathematical regression that describes the instrument s response over the range of thecalibration curve (Section8.5). The report should include the back-calculated concentration values, accuracies, slopes, y-intercepts and correlation coefficients (R) and the coefficients of determination (R ) (Equation[8.18] in Section 8.3.1) for aU curves used in the validation. The value should be > 0.98 for each calibration curve. The R value (if used) must be > 0.99 for each calibration curve. An example table used to summarize the calibration curve statistics for each run used for method validation is shown as Table 10.2. 

This is the model equation for the calibration of isotope amount ratios based on the log-linear temporal isotope amount ratio regression. Note that a and b are perfectly correlated (p = +1) if Rtp < 1 (inRup < 0) and perfectly anti-correlated (p = —1) if Rk/i > 1 (InRfe/ > 0). It is important to stress that this calibration method is fundamentally different from the conventional mass bias correction la vs. Since the regression model does not invoke the principle of time-mass separation, it does not need either the discrimination exponent or the equality of the discrimination functions [17]. 

We will see that CLS and ILS calibration modelling have limited applicability, especially when dealing with complex situations, such as highly correlated predictors (spectra), presence of chemical or physical interferents (uncontrolled and undesired covariates that affect the measurements), less samples than variables, etc. More recently, methods such as principal components regression (PCR, Section 17.8) and partial least squares regression (PLS, Section 35.7) have been... 

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