TY - JOUR

T1 - Fitting straight lines and planes with an application to radiometric dating

AU - Kent, John T.

AU - Watson, Geoffrey S.

AU - Onstott, Tullis C.

N1 - Funding Information:
This research was partially supported by a NSF Grant DMS 8421301 to G.S.W., and by a NSF PYI grant EAR 84-51696 to T.C.O. We are also grateful to Apple Corporation for the donation of a MAC II on which many of the calculations were performed.

PY - 1990/2

Y1 - 1990/2

N2 - Conventional practice in geochronology is to fit a straight line or "isochron" to data consisting of two isotopic ratios by a method (e.g. that of York, 1966, 1969, or perhaps the more modern version of Titterington and Haliday, 1979) that takes into account that fact that both ratios are measured with error. In this paper we use matrix algebra to lay out a general method for fitting linear relations between any number of variables, all subject to errors with known variances and covariances and the well-known Newton-Raphson method to do the optimization. This leads to a good computational algorithm which may also be used e.g. to check whether coefficients in several linear relations are the same. In many fields of science one needs to fit linear relations so our method is of wide utility; its use is in no way restricted to radiometric dating.

AB - Conventional practice in geochronology is to fit a straight line or "isochron" to data consisting of two isotopic ratios by a method (e.g. that of York, 1966, 1969, or perhaps the more modern version of Titterington and Haliday, 1979) that takes into account that fact that both ratios are measured with error. In this paper we use matrix algebra to lay out a general method for fitting linear relations between any number of variables, all subject to errors with known variances and covariances and the well-known Newton-Raphson method to do the optimization. This leads to a good computational algorithm which may also be used e.g. to check whether coefficients in several linear relations are the same. In many fields of science one needs to fit linear relations so our method is of wide utility; its use is in no way restricted to radiometric dating.

UR - http://www.scopus.com/inward/record.url?scp=0025206880&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0025206880&partnerID=8YFLogxK

U2 - 10.1016/0012-821X(90)90094-E

DO - 10.1016/0012-821X(90)90094-E

M3 - Article

AN - SCOPUS:0025206880

SN - 0012-821X

VL - 97

SP - 1

EP - 17

JO - Earth and Planetary Science Letters

JF - Earth and Planetary Science Letters

IS - 1-2

ER -