Encyclopedia of Social Network Analysis and Mining

2018 Edition
| Editors: Reda Alhajj, Jon Rokne

Least Squares

Reference work entry
DOI: https://doi.org/10.1007/978-1-4939-7131-2_149

Glossary

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
$$ y=f(x)={a}_1{f}_1(x)+{a}_2{f}_2(x)+\cdots...
This is a preview of subscription content, log in to check access.

References

  1. Anderson DR, Sweeney DJ, Williams TA (1994) Introduction to statistics: concepts and applications. West GroupGoogle Scholar
  2. Farebrother RW (1999) Fitting linear relationships: a history of the calculus of observations 1750–1900. Springer, New YorkMATHCrossRefGoogle Scholar
  3. Lancaster P, Šalkauskas K (1986) Curve and surface fitting: an introduction. Academic, LondonMATHGoogle Scholar
  4. Lawson C, Hanson R (1974) Solving least squares problems. Prentice-Hall, Englewood CliffsMATHGoogle Scholar
  5. Nievergelt Y (2000) A tutorial history of least squares with applications to astronomy and geodesy. J Comput Appl Math 121:37–72MathSciNetMATHCrossRefGoogle Scholar
  6. Plackett RL (1972) The discovery of the method of least squares. Biometrica 59(2):239–251MathSciNetMATHGoogle Scholar
  7. Ryan TP (1997) Modern regression methods. Wiley, New YorkMATHGoogle Scholar
  8. Stigler SM (1986) The history of statistics: the measurement of uncertainty before 1900. Harvard University Press, CambridgeMATHGoogle Scholar
  9. 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]CrossRefGoogle Scholar
  10. Vos D (2008) Risk analysis: a quantitative guide, 3rd edn. WileyGoogle Scholar
  11. Wackerly DD, Mendenhall W III, Scheaffer RL (2008) Mathematical statistics with applications, 7th edn. Cengage LearningGoogle Scholar

Copyright information

© Springer Science+Business Media LLC 2018

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsAmerican University of SharjahSharjahUAE

Section editors and affiliations

  • Suheil Khoury
    • 1
  1. 1.American University of SharjahSharjahUnited Arab Emirates