{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T11:44:27Z","timestamp":1787312667268,"version":"build-2736575974"},"reference-count":7,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[1951,1,1]],"date-time":"1951-01-01T00:00:00Z","timestamp":-599616000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1951,1,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>If a set of normal equations, derived from the least squares fitting of a linear representation to a set of observations, is solved by the Choleski method of solving a system of linear simultaneous algebraic equations involving a symmetric matrix, a certain vector is obtained as an intermediate step in the solution. The squares of the elements of this vector are the components in the resolution of the total sum of squares of the observations into squares corresponding to individual degrees of freedom. Each such square represents the contribution corresponding to one of a certain set of orthonormal vectors.<\/jats:p>\n                  <jats:p>The theory is applied to the fitting of a polynomial to a set of observations, not necessarily equidistant. The appropriate orthonormal polynomials can be derived explicitly and the total sum of squares can be resolved into individual squares corresponding to each of these. A practical computation scheme for this case is given and illustrated by a numerical example.<\/jats:p>","DOI":"10.1111\/j.2517-6161.1951.tb00073.x","type":"journal-article","created":{"date-parts":[[2018,12,7]],"date-time":"2018-12-07T01:34:34Z","timestamp":1544146474000},"page":"92-99","source":"Crossref","is-referenced-by-count":10,"title":["On Least Squares Fitting by Orthonormal Polynomials Using the Choleski Method"],"prefix":"10.1093","volume":"13","author":[{"given":"S.","family":"Rushton","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2018,12,5]]},"reference":[{"key":"2024090920085269900_cit1","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1017\/S0370164600014346","volume":"55","author":"Aitken","year":"1934","journal-title":"Proc. Roy. Soc. Edin."},{"key":"2024090920085269900_cit2","first-page":"69","volume":"2","author":"David","year":"1938","journal-title":"Stat. Res. Mem."},{"key":"2024090920085269900_cit3","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1111\/j.2517-6161.1950.tb00049.x","volume":"12","author":"Fox","year":"1950","journal-title":"J.R. Statist. Soc., B"},{"key":"2024090920085269900_cit4","first-page":"13","volume-title":"ibid., B","author":"Fox","year":"1951"},{"key":"2024090920085269900_cit5","volume":"1","author":"Fox","year":"1948","journal-title":"Qu. J. Mech. and App. Math."},{"key":"2024090920085269900_cit6","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1080\/14786445008521774","volume":"41","author":"Guest","year":"1950","journal-title":"Phil. Mag."},{"key":"2024090920085269900_cit7","doi-asserted-by":"crossref","first-page":"13","DOI":"10.2307\/2002655","volume":"3","author":"Ladermann","year":"1948","journal-title":"Mathematical Tables and Aids to Computation"}],"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2Fj.2517-6161.1951.tb00073.x","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/13\/1\/92\/49093714\/jrsssb_13_1_92.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/13\/1\/92\/49093714\/jrsssb_13_1_92.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,9]],"date-time":"2024-09-09T16:15:08Z","timestamp":1725898508000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/13\/1\/92\/7026594"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1951,1,1]]},"references-count":7,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2018,12,5]]},"published-print":{"date-parts":[[1951,1,1]]}},"URL":"https:\/\/doi.org\/10.1111\/j.2517-6161.1951.tb00073.x","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[1951,1]]},"published":{"date-parts":[[1951,1,1]]}}}