# Direct solution of polynomial regression of order up to 3

 dc.citation.epage 42 dc.citation.issue 3 dc.citation.journalTitle Вимірювальна техніка та метрологія dc.citation.spage 35 dc.citation.volume 83 dc.contributor.affiliation Lviv Polytechnic National University dc.contributor.author Dorozhovets, Mykhaylo dc.coverage.placename Львів dc.coverage.placename Lviv dc.date.accessioned 2023-05-09T10:30:46Z dc.date.available 2023-05-09T10:30:46Z dc.date.created 2022-02-28 dc.date.issued 2022-02-28 dc.description.abstract This article presents results related to the direct solution of the polynomial regression parameters based on the analytical solving of regression equations. The analytical solution is based on the normalization of the values of independent quantity with equidistance steps. The proposed solution does not need to directly solve a system of polynomial regression equations. The direct expressions to calculate estimators of regression coefficients, their standard deviations, and also standard and expanded deviation of polynomial functions are given. For a given number of measurement points, the parameters of these expressions have the same values independently of the range of input quantity. The proposed solution is illustrated by a numerical example used from a literature source. dc.format.extent 35-42 dc.format.pages 8 dc.identifier.citation Dorozhovets M. Direct solution of polynomial regression of order up to 3 / Mykhaylo Dorozhovets // Measuring equipment and metrology. — Lviv : Lviv Politechnic Publishing House, 2022. — Vol 83. — No 3. — P. 35–42. dc.identifier.citationen Dorozhovets M. Direct solution of polynomial regression of order up to 3 / Mykhaylo Dorozhovets // Measuring equipment and metrology. — Lviv : Lviv Politechnic Publishing House, 2022. — Vol 83. — No 3. — P. 35–42. dc.identifier.doi doi.org/10.23939/istcmtm2022.03.035 dc.identifier.uri https://ena.lpnu.ua/handle/ntb/59071 dc.language.iso en dc.publisher Видавництво Львівської політехніки dc.publisher Lviv Politechnic Publishing House dc.relation.ispartof Вимірювальна техніка та метрологія, 3 (83), 2022 dc.relation.ispartof Measuring equipment and metrology, 3 (83), 2022 dc.relation.references [1] M. G. Kendall and A. Stuart (1966) The advanced theory of statistics. Vol. 2. Inference and relationship. Second Edition. Chares Griffin and Company Limited, London. https://archive.org/details/in.ernet.dli.2015.212877. dc.relation.references [2] Draper, N. and Smith, H. (1981) Applied Regression Analysis. 2nd ed., Wiley, New York. https://onlinelibrary.wiley.com/doi/book/10.1002/9781118625590. dc.relation.references [3] J. O. Rawlings, S. G. Pantula, D. A. Dickey (1998) Applied Regression Analysis: A Research Tool, Second Edition, Springer-Verlag. New York, Berlin, Heidelberg. https://doi.org/10.1007/b98890. dc.relation.references [4] Handbook of Applicable Mathematics. Vol. VI: Statistics, Part A, (1984). Edited by Emlyn Lloyd, John Wiley and Sons. https://www.amazon.com/Handbook-Applicable-Mathematics-Statistics-6/dp/0471900249. dc.relation.references [5] J. H. Pollard. (1977) Handbook of Numerical and Statistical Techniques. Cambridge University Press. https://cc.bingj.com/cache.aspx?q=J.H.+Pollard.+(1977)+Handbook+of+Numerical+and+Statistical+Techniques.d=4579616625657925&mkt=en-WW&setlang=en-US&w=lYKqOOVXlYsikZD-qV7p9HJrRgt2oDA3. dc.relation.references [6] Applied Linear Regression, 3rd ed. Willey, Hoboken (2005). https://openlibrary.org/books/OL3306403M/Applied_linear_regression. dc.relation.references [7] J. R. Taylor (1982). An introduction to error analysis. University Science Books Mill Valley, California 1982. https://openlibrary.org/books/OL3786923M/An_introduction_to_error_analysis. dc.relation.references [8] B. Forbes (2009), Parameter estimation based on leastsquares methods. In F. Pavese and A. B. Forbes, editors, Data modeling for metrology and testing in measurement science, New York. Birkauser-Boston. https://link.springer.com/chapter/10.1007/978-0-8176-4804-6_5. dc.relation.references [9] G. Mejer (2008), Smart Sensor Systems. John Wiley, 2008. https://onlinelibrary.wiley.com/doi/book/10.1002/9780470866931. dc.relation.references [10] Evaluation of measurement data – Guide to the expression of uncertainty in measurement Joint Committee for Guides in Metrology, JCGM 100: 2008. https://www.iso.org/sites/JCGM/GUM/JCGM100/. dc.relation.references [11] JCGM 101:2008. Evaluation of measurement data – Supplement 1 to the ‘Guide to the Expression of Uncertainty in Measurement – propagation of distributions using a Monte Carlo method’. BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP and OIML. https://www.bipm.org/documents/20126/2071204/JCGM. dc.relation.references [12] Dorozhovets M. Study of the effect of correlation of observation results on the uncertainty of linear regression. Pomiary, Automatyka, Kontrola. N12, 2008, s. 31–34 (in Polish). https://bibliotekanauki.pl/issues/8204. dc.relation.references [13] Dorozhovets M. Include measurement uncertainty of both quantities in linear regression. Pomiary, Automatyka, Kontrola. N9, 2008, pp. 612–615 (in Polish). https://bibliotekanauki.pl/issues/8089. dc.relation.referencesen [1] M. G. Kendall and A. Stuart (1966) The advanced theory of statistics. Vol. 2. Inference and relationship. Second Edition. Chares Griffin and Company Limited, London. https://archive.org/details/in.ernet.dli.2015.212877. dc.relation.referencesen [2] Draper, N. and Smith, H. (1981) Applied Regression Analysis. 2nd ed., Wiley, New York. https://onlinelibrary.wiley.com/doi/book/10.1002/9781118625590. dc.relation.referencesen [3] J. O. Rawlings, S. G. Pantula, D. A. Dickey (1998) Applied Regression Analysis: A Research Tool, Second Edition, Springer-Verlag. New York, Berlin, Heidelberg. https://doi.org/10.1007/b98890. dc.relation.referencesen [4] Handbook of Applicable Mathematics. Vol. VI: Statistics, Part A, (1984). Edited by Emlyn Lloyd, John Wiley and Sons. https://www.amazon.com/Handbook-Applicable-Mathematics-Statistics-6/dp/0471900249. dc.relation.referencesen [5] J. H. Pollard. (1977) Handbook of Numerical and Statistical Techniques. Cambridge University Press. https://cc.bingj.com/cache.aspx?q=J.H.+Pollard.+(1977)+Handbook+of+Numerical+and+Statistical+Techniques.d=4579616625657925&mkt=en-WW&setlang=en-US&w=lYKqOOVXlYsikZD-qV7p9HJrRgt2oDA3. dc.relation.referencesen [6] Applied Linear Regression, 3rd ed. Willey, Hoboken (2005). https://openlibrary.org/books/OL3306403M/Applied_linear_regression. dc.relation.referencesen [7] J. R. Taylor (1982). An introduction to error analysis. University Science Books Mill Valley, California 1982. https://openlibrary.org/books/OL3786923M/An_introduction_to_error_analysis. dc.relation.referencesen [8] B. Forbes (2009), Parameter estimation based on leastsquares methods. In F. Pavese and A. B. Forbes, editors, Data modeling for metrology and testing in measurement science, New York. Birkauser-Boston. https://link.springer.com/chapter/10.1007/978-0-8176-4804-6_5. dc.relation.referencesen [9] G. Mejer (2008), Smart Sensor Systems. John Wiley, 2008. https://onlinelibrary.wiley.com/doi/book/10.1002/9780470866931. dc.relation.referencesen [10] Evaluation of measurement data – Guide to the expression of uncertainty in measurement Joint Committee for Guides in Metrology, JCGM 100: 2008. https://www.iso.org/sites/JCGM/GUM/JCGM100/. dc.relation.referencesen [11] JCGM 101:2008. Evaluation of measurement data – Supplement 1 to the ‘Guide to the Expression of Uncertainty in Measurement – propagation of distributions using a Monte Carlo method’. BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP and OIML. https://www.bipm.org/documents/20126/2071204/JCGM. dc.relation.referencesen [12] Dorozhovets M. Study of the effect of correlation of observation results on the uncertainty of linear regression. Pomiary, Automatyka, Kontrola. N12, 2008, s. 31–34 (in Polish). https://bibliotekanauki.pl/issues/8204. dc.relation.referencesen [13] Dorozhovets M. Include measurement uncertainty of both quantities in linear regression. Pomiary, Automatyka, Kontrola. N9, 2008, pp. 612–615 (in Polish). https://bibliotekanauki.pl/issues/8089. dc.relation.uri https://archive.org/details/in.ernet.dli.2015.212877 dc.relation.uri https://onlinelibrary.wiley.com/doi/book/10.1002/9781118625590 dc.relation.uri https://doi.org/10.1007/b98890 dc.relation.uri https://www.amazon.com/Handbook-Applicable-Mathematics-Statistics-6/dp/0471900249 dc.relation.uri https://cc.bingj.com/cache.aspx?q=J.H.+Pollard.+(1977)+Handbook+of+Numerical+and+Statistical+Techniques.d=4579616625657925&mkt=en-WW&setlang=en-US&w=lYKqOOVXlYsikZD-qV7p9HJrRgt2oDA3 dc.relation.uri https://openlibrary.org/books/OL3306403M/Applied_linear_regression dc.relation.uri https://openlibrary.org/books/OL3786923M/An_introduction_to_error_analysis dc.relation.uri https://link.springer.com/chapter/10.1007/978-0-8176-4804-6_5 dc.relation.uri https://onlinelibrary.wiley.com/doi/book/10.1002/9780470866931 dc.relation.uri https://www.iso.org/sites/JCGM/GUM/JCGM100/ dc.relation.uri https://www.bipm.org/documents/20126/2071204/JCGM dc.relation.uri https://bibliotekanauki.pl/issues/8204 dc.relation.uri https://bibliotekanauki.pl/issues/8089 dc.rights.holder © Національний університет “Львівська політехніка”, 2022 dc.subject Regression dc.subject Function dc.subject Polynomial dc.subject Estimation dc.subject Solution dc.subject Standard Deviation dc.subject Uncertainty dc.title Direct solution of polynomial regression of order up to 3 dc.type Article

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