- LS:
-
Least squares
- LLS:
-
Linear least squares
- MF:
-
Model function
Definition
Least squares historically grew out of astronomy problems during the turn of the seventeenth century (Nievergelt 2000), in particular, finding trajectories of planetary motions in order to solve ocean’s navigation problems. The idea of LS was developed by Gauss, Legendre, Laplace, and many other mathematicians and scientists (Farebrother 1999). However, the first publication on LS appeared in 1805 by Legendre; he proposed the idea of minimizing the sum of squares of the errors to obtain the adjusted values of observed quantities (Plackett 1972).
“Least squares” is a mathematical procedure to find the best approximate curve or surface to a given set of data points, out of different model functions that approximate the data.
Linear Least Squares
The most common application of the least squares procedure is the LS curve fitting, for which the MF forms
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Anderson DR, Sweeney DJ, Williams TA (1994) Introduction to statistics: concepts and applications. West Group
Farebrother RW (1999) Fitting linear relationships: a history of the calculus of observations 1750–1900. Springer, New York
Lancaster P, Šalkauskas K (1986) Curve and surface fitting: an introduction. Academic, London
Lawson C, Hanson R (1974) Solving least squares problems. Prentice-Hall, Englewood Cliffs
Nievergelt Y (2000) A tutorial history of least squares with applications to astronomy and geodesy. J Comput Appl Math 121:37–72
Plackett RL (1972) The discovery of the method of least squares. Biometrica 59(2):239–251
Ryan TP (1997) Modern regression methods. Wiley, New York
Stigler SM (1986) The history of statistics: the measurement of uncertainty before 1900. Harvard University Press, Cambridge
Todhunter I (1865) A history of the mathematical theory of probability, from the time of Pascal to that of Laplace. Macmillan, London. [New York, Chelsea, 1949]
Vos D (2008) Risk analysis: a quantitative guide, 3rd edn. Wiley
Wackerly DD, Mendenhall W III, Scheaffer RL (2008) Mathematical statistics with applications, 7th edn. Cengage Learning
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Section Editor information
Rights and permissions
Copyright information
© 2018 Springer Science+Business Media LLC
About this entry
Cite this entry
Sayfy, A. (2018). Least Squares. In: Alhajj, R., Rokne, J. (eds) Encyclopedia of Social Network Analysis and Mining. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-7131-2_149
Download citation
DOI: https://doi.org/10.1007/978-1-4939-7131-2_149
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4939-7130-5
Online ISBN: 978-1-4939-7131-2
eBook Packages: Computer ScienceReference Module Computer Science and Engineering