Least squares regression with errors in both variables: case studies
Analytical curves are normally obtained from discrete data by least squares regression. The least squares regression of data involving significant error in both x and y values should not be implemented by ordinary least squares (OLS). In this work, the use of orthogonal distance regression (ODR) is...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Sociedade Brasileira de Química
2013-01-01
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| Series: | Química Nova |
| Subjects: | |
| Online Access: | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0100-40422013000600025&lng=en&tlng=en |
| _version_ | 1818253911975264256 |
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| author | Elcio Cruz de Oliveira Paula Fernandes de Aguiar |
| author_facet | Elcio Cruz de Oliveira Paula Fernandes de Aguiar |
| author_sort | Elcio Cruz de Oliveira |
| collection | DOAJ |
| description | Analytical curves are normally obtained from discrete data by least squares regression. The least squares regression of data involving significant error in both x and y values should not be implemented by ordinary least squares (OLS). In this work, the use of orthogonal distance regression (ODR) is discussed as an alternative approach in order to take into account the error in the x variable. Four examples are presented to illustrate deviation between the results from both regression methods. The examples studied show that, in some situations, ODR coefficients must substitute for those of OLS, and, in other situations, the difference is not significant. |
| first_indexed | 2024-12-12T16:47:36Z |
| format | Article |
| id | doaj.art-6933fa4e4f584e35aacdf1e40b5fe556 |
| institution | Directory Open Access Journal |
| issn | 1678-7064 |
| language | English |
| last_indexed | 2024-12-12T16:47:36Z |
| publishDate | 2013-01-01 |
| publisher | Sociedade Brasileira de Química |
| record_format | Article |
| series | Química Nova |
| spelling | doaj.art-6933fa4e4f584e35aacdf1e40b5fe5562022-12-22T00:18:26ZengSociedade Brasileira de QuímicaQuímica Nova1678-70642013-01-0136688588910.1590/S0100-40422013000600025S0100-40422013000600025Least squares regression with errors in both variables: case studiesElcio Cruz de Oliveira0Paula Fernandes de Aguiar1PetrobrasUniversidade Federal do Rio de JaneiroAnalytical curves are normally obtained from discrete data by least squares regression. The least squares regression of data involving significant error in both x and y values should not be implemented by ordinary least squares (OLS). In this work, the use of orthogonal distance regression (ODR) is discussed as an alternative approach in order to take into account the error in the x variable. Four examples are presented to illustrate deviation between the results from both regression methods. The examples studied show that, in some situations, ODR coefficients must substitute for those of OLS, and, in other situations, the difference is not significant.http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0100-40422013000600025&lng=en&tlng=enorthogonal distance regressionleast squares regressionerror in x and y variables |
| spellingShingle | Elcio Cruz de Oliveira Paula Fernandes de Aguiar Least squares regression with errors in both variables: case studies Química Nova orthogonal distance regression least squares regression error in x and y variables |
| title | Least squares regression with errors in both variables: case studies |
| title_full | Least squares regression with errors in both variables: case studies |
| title_fullStr | Least squares regression with errors in both variables: case studies |
| title_full_unstemmed | Least squares regression with errors in both variables: case studies |
| title_short | Least squares regression with errors in both variables: case studies |
| title_sort | least squares regression with errors in both variables case studies |
| topic | orthogonal distance regression least squares regression error in x and y variables |
| url | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0100-40422013000600025&lng=en&tlng=en |
| work_keys_str_mv | AT elciocruzdeoliveira leastsquaresregressionwitherrorsinbothvariablescasestudies AT paulafernandesdeaguiar leastsquaresregressionwitherrorsinbothvariablescasestudies |