{"title":"曲线族的分析","authors":"J. Mandel, F. McCrackin","doi":"10.6028/jres.067A.027","DOIUrl":null,"url":null,"abstract":"A systematic approach is presented for fitting empirical expressions to data depending on two variables. The problem can also be described as the simultaneous fitting of a family of curves depending on a parameter. The proposed method reduces a surface fitting problem to that of fitting a few functions of one variable each. First, the surface is expressed in terms of these one-variable functions, and using an extension of two-way analysis of variance, the accuracy of this fit is assessed without having to determine, at this point, the nature of the one-variable functions. Then, the one-variable functions are fitted by customary curve-fitting procedures. For illustration, the method is applied to two sets of experimental data.","PeriodicalId":94340,"journal":{"name":"Journal of research of the National Bureau of Standards. Section A, Physics and chemistry","volume":"31 1","pages":"259 - 267"},"PeriodicalIF":0.0000,"publicationDate":"1963-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"10","resultStr":"{\"title\":\"Analysis of Families of Curves\",\"authors\":\"J. Mandel, F. McCrackin\",\"doi\":\"10.6028/jres.067A.027\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A systematic approach is presented for fitting empirical expressions to data depending on two variables. The problem can also be described as the simultaneous fitting of a family of curves depending on a parameter. The proposed method reduces a surface fitting problem to that of fitting a few functions of one variable each. First, the surface is expressed in terms of these one-variable functions, and using an extension of two-way analysis of variance, the accuracy of this fit is assessed without having to determine, at this point, the nature of the one-variable functions. Then, the one-variable functions are fitted by customary curve-fitting procedures. For illustration, the method is applied to two sets of experimental data.\",\"PeriodicalId\":94340,\"journal\":{\"name\":\"Journal of research of the National Bureau of Standards. Section A, Physics and chemistry\",\"volume\":\"31 1\",\"pages\":\"259 - 267\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1963-05-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"10\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of research of the National Bureau of Standards. Section A, Physics and chemistry\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.6028/jres.067A.027\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of research of the National Bureau of Standards. Section A, Physics and chemistry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.6028/jres.067A.027","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A systematic approach is presented for fitting empirical expressions to data depending on two variables. The problem can also be described as the simultaneous fitting of a family of curves depending on a parameter. The proposed method reduces a surface fitting problem to that of fitting a few functions of one variable each. First, the surface is expressed in terms of these one-variable functions, and using an extension of two-way analysis of variance, the accuracy of this fit is assessed without having to determine, at this point, the nature of the one-variable functions. Then, the one-variable functions are fitted by customary curve-fitting procedures. For illustration, the method is applied to two sets of experimental data.