• 责任者：Fan Wenbo (School of Earth Sciences and Resources ; China University of Geosciences ; Beijing 100083 ; China) ; Wang Wenlong
• 刊名：Geological Review
• 出版年：2013
• 卷期：59(5)
• 关键词：同位素地质年代学 ; isotopic geochronology ; 最小二乘法 ; least-squares methods
• 页码：p.801-815
• 图表：2 illus., 1 table, 62 refs.
• 分类号：1300
• issnNo：ISSN0371-5736
• isbnNo：CN11-1952/P

     The methods for least squares fitting of a straight line are applied widely in natural sciences and social sciences, and geology is no exception, especially in geochronology. It is the normal/ordinary least squares that is well known by much of the population, where errors in only one coordinate are considered. In fact, The least square linear regressions is much more complex, especially when errors in both coordinates even the error correlations are considered. Based on the previous research, an overview of the methods for least squares fitting and its application in geochronology are provided here. These methods includes normal/ordinary least squares, normal/ ordinary weighting least squares, standard weighting model, standard independent weighting model, independent weighting model, and error correlated independent weighting model. What＇ s more, we give a brief study of the parameter of MSWD, which is commonly used but makes many people confused in geochronological study. It is very important for us to know all of these algorithm and their underlying assumption exactly, which will of course benefit us a lot in choosing the best approach to calculate the parameters we need and assessing the results in geochronology. Our study will also help improve the basic methods for least squares fitting in mathematics and could be used in other areas.