IUPAC > Gold Book > alphabetical index > L > least-squares technique
icon


Indexes

least-squares technique
A procedure for replacing the discrete set of results obtained from an experiment by a continuous function. It is defined by the following. For the set of variables Math - ei there are Math - ei measured values such as Math - ei and it is decided to write a relation:
Math - e
where Math - ei are undetermined constants. If it is assumed that each measurement Math - ei of Math - ei has associated with it a number Math - ei characteristic of the uncertainty, then numerical estimates of the Math - ei are found by constructing a variable Math - ei, defined by
Math - e,
and solving the equations obtained by writing
Math - e
Math - ei except Math - ei. If the relations between the Math - ei and Math - ei are linear, this is the familiar least-squares technique of fitting an equation to a number of experimental points. If the relations between the Math - ei and Math - ei are non-linear, there is an increase in the difficulty of finding a solution, but the problem is essentially unchanged.
Source:
PAC, 1981, 53, 1805 (Assignment and presentation of uncertainties of the numerical results of thermodynamic measurements (Provisional)) on page 1822
Interactive Link Maps
First LevelSecond LevelThird Level
GraphGraphGraph
Cite as:
IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by A. D. McNaught and A.Wilkinson. Blackwell Scientific Publications, Oxford (1997). XML on-line corrected version: http://goldbook.iupac.org (2006-) created by M. Nic, J. Jirat, B. Kosata; updates compiled by A. Jenkins. ISBN 0-9678550-9-8. doi:10.1351/goldbook.
Last update: 2008-10-07; version: 2.0.2.
DOI of this term: doi:10.1351/goldbook.L03492.
Original PDF version (may be out of date): http://www.iupac.org/goldbook/L03492.pdf.
Version for print | History of this term
picture