Quality of Analytical Measurements: Univariate Regression

Ortiz, M.C.; Sánchez, M.S.; Peinador, Luis Antonio Sarabia

doi:10.1016/b978-0-12-409547-2.14869-3

Cited by 6 publications

(17 citation statements)

References 56 publications

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“…As there is a negative strong correlation between the LS estimates of the intercept and the slope, a Joint Confidence Region for β 0 and β 1 at level 100(1-α) is used. 5,16 If point (0, 1) belongs to this region, the calibration method is considered true (unbiased). So Joint Confidence Regions, JCR, for the regressions "estimated concentration vs. true concentration" have been computed for the proposed calibration method wPCR.…”

Section: Methodsmentioning

confidence: 99%

“…Concerning univariate calibration, linear regression by LS has been used with the response weighted by the variance of the experimental signal. 5 Recently, [6][7][8] different weights have been suggested (1/y 2 , 1/y,1/y 0.5 ,1/x 2 ,1/x,1/x 0.5 , x being the concentration and y the signal) aiming at selecting the one that best fit the data. Nevertheless, this does not result in the univariate version of LSRE, since relative errors are not those of the concentration but those of the experimental signal.…”

Section: Introductionmentioning

confidence: 99%

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Principal component regression that minimizes the sum of the squares of the relative errors: Application in multivariate calibration models

Valencia

Ortiz

Sarabia

2021

Journal of Chemometrics

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Relative errors are typically used in chemometrics to evaluate the performance of a multivariate predictive model. However, these models are not obtained through the criterion of minimizing relative errors, as would be expected in a model whose response is the concentration of an analyte. There are no studies in chemometrics on the use of a principal component regression that minimizes the sum of the squares of the relative errors. This work proposes a model, which serves this purpose. The suggested model, wPCR, has been applied to 7 datasets with 12 predicted responses, 10 of which are multivariate calibrations of analytes in complex mixtures based on instrumental signals coming from various analytical techniques. As PCR and wPCR are methods seeking to optimize different criteria, each one achieves a better performance with respect to its own criterion. Therefore, the new model wPCR leads to better results insofar as the relative errors are considered, especially for the smallest responses. In this sense, the wPCR model also outperforms PCR with logarithmic transformation of the response (logPCR). In addition, as for the performance of the method using Joint Confidence Regions for the intercept and the slope of the accuracy line, it is shown that the application of wPCR does not introduce bias, neither constant nor proportional for the models built, nor a systematic alteration of the achievable accuracy.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Principal component regression that minimizes the sum of the squares of the relative errors: Application in multivariate calibration models

Valencia

Ortiz

Sarabia

2021

Journal of Chemometrics

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“…The type of data distribution for a linear equation ( [21], Ex.1) is shown in Figure 1. This shows the relationship between the ascorbic concentration and the peak area of HPLC.…”

Section: Linear Equationsmentioning

confidence: 99%

“…Ortiz et al used univariate regression for calibration curves and proposed a quadratic polynomial equation for nonlinear calibration curves. The regression results were verified using an ANOVA, a lack of fit test, and residual plots [21].…”

Section: Introductionmentioning

confidence: 99%

Evaluation of Calibration Equations by Using Regression Analysis: An Example of Chemical Analysis

Chen

2022

Sensors

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A calibration curve is used to express the relationship between the response of the measuring technique and the standard concentration of the target analyst. The calibration equation verifies the response of a chemical instrument to the known properties of materials and is established using regression analysis. An adequate calibration equation ensures the performance of these instruments. Most studies use linear and polynomial equations. This study uses data sets from previous studies. Four types of calibration equations are proposed: linear, higher-order polynomial, exponential rise to maximum and power equations. A constant variance test was performed to assess the suitability of calibration equations for this dataset. Suspected outliers in the data sets are verified. The standard error of the estimate errors, s, was used as criteria to determine the fitting performance. The Prediction Sum of Squares (PRESS) statistic is used to compare the prediction ability. Residual plots are used as quantitative criteria. Suspected outliers in the data sets are checked. The results of this study show that linear and higher order polynomial equations do not allow accurate calibration equations for many data sets. Nonlinear equations are suited to most of the data sets. Different forms of calibration equations are proposed. The logarithmic transformation of the response is used to stabilize non-constant variance in the response data. When outliers are removed, this calibration equation’s fit and prediction ability is significantly increased. The adequate calibration equations with the data sets obtained with the same equipment and laboratory indicated that the adequate calibration equations differed. No universe calibration equation could be found for these data sets. The method for this study can be used for other chemical instruments to establish an adequate calibration equation and ensure the best performance.

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“…When a statistical model has been set up for a certain application, it is essential to examine its adequacy with respect to the data before drawing any inferential conclusions. Whole chapters of linear model books are devoted to the subject of model validation, which is beyond the scope of this text ( [30], [31] , [2], [32]). The section below enumerates the most common tools applied when analyzing the results of designs of experiments.…”

Section: Model Validationmentioning

confidence: 99%

The Essentials on Linear Regression, ANOVA, General Linear and Linear Mixed Models for the Chemist

Govaerts¹,

Francq²,

Marion³

et al. 2020

Comprehensive Chemometrics

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This text provides a brief and accessible guide for implementing general, ANOVA and linear mixed models for the analysis of real world data from chemistry, industrial, bio or life-sciences experiments. The reader is introduced to the main concepts and vocabulary of the subject and to the main statistical methods available for formalizing, estimating and performing statistical inference on these models. Mathematical notations are not avoided but kept accessible, methods are illustrated on several detailed applications and the use of appropriate computer software is discussed.

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Quality of Analytical Measurements: Univariate Regression

Cited by 6 publications

References 56 publications

Principal component regression that minimizes the sum of the squares of the relative errors: Application in multivariate calibration models

Principal component regression that minimizes the sum of the squares of the relative errors: Application in multivariate calibration models

Evaluation of Calibration Equations by Using Regression Analysis: An Example of Chemical Analysis

The Essentials on Linear Regression, ANOVA, General Linear and Linear Mixed Models for the Chemist

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