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Fitting Straight Lines with Replicated Observations by Linear Regression. III. Weighting Data.

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Title: Fitting Straight Lines with Replicated Observations by Linear Regression. III. Weighting Data.
Authors: Asuero, AgustinG.1 (AUTHOR) asuero@us.es, González, Gustavo1 (AUTHOR)
Source: Critical Reviews in Analytical Chemistry. 2007, Vol. 37 Issue 3, p143-172. 30p. 10 Charts, 4 Graphs.
Subjects: Regression analysis data processing, Information processing, Data analysis, Factor analysis, Analysis of variance, Chemometrics, Analytical chemistry, Statistical weighting, Statistical sampling
Abstract: The purpose of this article is to stress the importance of weighting in fitting straight lines with replicated observations. Nevertheless, single response data are also taken into account. Although the concept of weighting is treated on chemometric texts, a detailed procedure is not given. For this reason the present review covers the information concerning this topic. Ignoring non-constant variance (heterocedasticity) often leads to improper estimation and inference in a statistical model which quantifies a given relationship. There are two main solutions to remedy this problem: transform the data or perform a weighted least-squares regression analysis. Weighting with replication in homocedastic and heterodedastic condition, including transformation depending weights, and normalization of the weights are considered. Weighting of observations, however, presents a more difficult problem that has commonly been recognized. The review covers briefly topics as random errors and noise, modelling the variance as a function of the independent variable and variation of precision with concentration. By transforming variable it is possible to introduce non-linear terms to the mathematical framework of linear regression, in order to improve fit as to satisfy the necessary assumptions such as homocedasticity. However, transformation data, the analysis of variance and summary data analysis will be the subject of a future report. A number of applications concerning the uses of weighting in analytical chemistry and weighted linear regression are given in tabular form. The analytical, pharmaceutical, biochemical and clinical literature has been thoroughly revised. [ABSTRACT FROM AUTHOR]
Copyright of Critical Reviews in Analytical Chemistry is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Fitting Straight Lines with Replicated Observations by Linear Regression. III. Weighting Data.
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  Data: The purpose of this article is to stress the importance of weighting in fitting straight lines with replicated observations. Nevertheless, single response data are also taken into account. Although the concept of weighting is treated on chemometric texts, a detailed procedure is not given. For this reason the present review covers the information concerning this topic. Ignoring non-constant variance (heterocedasticity) often leads to improper estimation and inference in a statistical model which quantifies a given relationship. There are two main solutions to remedy this problem: transform the data or perform a weighted least-squares regression analysis. Weighting with replication in homocedastic and heterodedastic condition, including transformation depending weights, and normalization of the weights are considered. Weighting of observations, however, presents a more difficult problem that has commonly been recognized. The review covers briefly topics as random errors and noise, modelling the variance as a function of the independent variable and variation of precision with concentration. By transforming variable it is possible to introduce non-linear terms to the mathematical framework of linear regression, in order to improve fit as to satisfy the necessary assumptions such as homocedasticity. However, transformation data, the analysis of variance and summary data analysis will be the subject of a future report. A number of applications concerning the uses of weighting in analytical chemistry and weighted linear regression are given in tabular form. The analytical, pharmaceutical, biochemical and clinical literature has been thoroughly revised. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of Critical Reviews in Analytical Chemistry is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1080/10408340701244615
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        Text: English
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      – SubjectFull: Data analysis
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      – SubjectFull: Factor analysis
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      – SubjectFull: Analysis of variance
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      – SubjectFull: Chemometrics
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      – SubjectFull: Statistical weighting
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      – SubjectFull: Statistical sampling
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      – TitleFull: Fitting Straight Lines with Replicated Observations by Linear Regression. III. Weighting Data.
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              Text: 2007
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