P H Borcherds and C V Sheth 1995 Eur. J. Phys. 16 204 doi:10.1088/0143-0807/16/5/002
P H Borcherds and C V Sheth
Show affiliationsLeast squares fitting of a straight line y=a+bx to a set of data points, when there are errors in the values of both coordinates is reviewed. It is shown that if the errors are equal or unknown, then it is possible to solve the problem by a direct approach, using a quadratic equation, and avoiding iteration. If the errors in both coordinates are unknown, the 'best' line is not invariant under a change of scale: a possible criterion for uniquely determining the best line is suggested. If there are errors in both coordinates, and if each point has its own weighting factors for x and y, a new algorithm is given which involves the iterative solution of a quadratic equation: some remits for this algorithm are presented. A comparative analysis of existing and our methods is presented, using standard data sets. A FORTRAN-77 implementation of our algorithm, suitable for PCs is available.
Issue 5 (September 1995)
P H Borcherds and C V Sheth 1995 Eur. J. Phys. 16 204
A N Aliev et al 2006 Class. Quantum Grav. 23 591
G S Pawley and O W Dietrich 1975 J. Phys. C: Solid State Phys. 8 2549
I Zaharieva et al 2009 J. Phys.: Conf. Ser. 190 012142
Preeti Parashar and Swapan Rana 2009 J. Phys. A: Math. Theor. 42 462003
J A Peacock and J W Stairmand 1983 J. Phys. E: Sci. Instrum. 16 571
S Simons 1997 J. Phys. A: Math. Gen. 30 755
Bor-Yuan Shew et al 2005 J. Phys. D: Appl. Phys. 38 1097
Zheng-Jian Bai et al 2004 Inverse Problems 20 1675
T Harko and M K Mak 2004 Class. Quantum Grav. 21 1489