Technical Note: Review of methods for linear least-squares fitting of data and application to atmospheric chemistry problems

被引:225
作者
Cantrell, C. A. [1 ]
机构
[1] Natl Ctr Atmospher Res, Div Atmospher Chem, Boulder, CO 80305 USA
关键词
D O I
10.5194/acp-8-5477-2008
中图分类号
X [环境科学、安全科学];
学科分类号
08 ; 0830 ;
摘要
The representation of data, whether geophysical observations. numerical model output or laboratory results. by a best fit straight line is a routine practice in the and other fields. While the literature is full of detailed analyses of procedures for fitting straight lines to values with uncertainties, a surprising number of scientists blindly use the standard least-squares method, such as found on calculators and in spreadsheet programs, that assumes no uncertainties in the x values. Here, the available procedures for estimating the best fit straight line to data, including those applicable to situations for uncertainties present in both the x and y variables, are reviewed. Representative methods that are presented in the literature for bivariate weighted fits are compared using several sample data sets, and guidance is presented as to when the somewhat more involved iterative methods are required, or when the standard least-squares procedure would be expected to be satisfactory. A spreadsheet-based template is made available that employs one method for bivariate fitting.
引用
收藏
页码:5477 / 5487
页数:11
相关论文
共 54 条
[1]   SIMPLE METHOD FOR FITTING DATA WHEN BOTH VARIABLES HAVE UNCERTAINTIES [J].
BARKER, DR ;
DIANA, LM .
AMERICAN JOURNAL OF PHYSICS, 1974, 42 (03) :224-227
[2]  
Bevington R., 1969, DATA REDUCTION ERROR
[3]  
Borcherds P. H., 1995, European Journal of Physics, V16, P204, DOI 10.1088/0143-0807/16/5/002
[4]  
Brauers T, 1997, INT J CHEM KINET, V29, P665, DOI 10.1002/(SICI)1097-4601(1997)29:9<665::AID-KIN3>3.0.CO
[5]  
2-S
[6]   When errors in both coordinates make a difference in the fitting of straight lines by least squares [J].
Bruzzone, H ;
Moreno, C .
MEASUREMENT SCIENCE AND TECHNOLOGY, 1998, 9 (12) :2007-2011
[7]   Peroxy radical behavior during the Transport and Chemical Evolution over the Pacific (TRACE-P) campaign as measured aboard the NASA P-3B aircraft [J].
Cantrell, CA ;
Edwards, GD ;
Stephens, S ;
Mauldin, RL ;
Zondlo, MA ;
Kosciuch, E ;
Eisele, FL ;
Shetter, RE ;
Lefer, BL ;
Hall, S ;
Flocke, F ;
Weinheimer, A ;
Fried, A ;
Apel, E ;
Kondo, Y ;
Blake, DR ;
Blake, NJ ;
Simpson, IJ ;
Bandy, AR ;
Thornton, DC ;
Heikes, BG ;
Singh, HB ;
Brune, WH ;
Harder, H ;
Martinez, M ;
Jacob, DJ ;
Avery, MA ;
Barrick, JD ;
Sachse, GW ;
Olson, JR ;
Crawford, JH ;
Clarke, AD .
JOURNAL OF GEOPHYSICAL RESEARCH-ATMOSPHERES, 2003, 108 (D20)
[8]   ERROR ANALYSIS OF THE PARAMETERS OF A LEAST-SQUARES DETERMINED CURVE WHEN BOTH VARIABLES HAVE UNCERTAINTIES [J].
CECCHI, GC .
MEASUREMENT SCIENCE AND TECHNOLOGY, 1991, 2 (12) :1127-1128
[9]   LINEAR LEAST-SQUARES FITS WITH ERRORS IN BOTH COORDINATES - COMMENT [J].
CHONG, DP .
AMERICAN JOURNAL OF PHYSICS, 1991, 59 (05) :472-474
[10]   ON THE USE OF LEAST-SQUARES TO FIT DATA IN LINEAR FORM [J].
CHONG, DP .
JOURNAL OF CHEMICAL EDUCATION, 1994, 71 (06) :489-490