# 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...
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## 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 York
3. Lancaster P, Šalkauskas K (1986) Curve and surface fitting: an introduction. Academic, London
4. Lawson C, Hanson R (1974) Solving least squares problems. Prentice-Hall, Englewood Cliffs
5. Nievergelt Y (2000) A tutorial history of least squares with applications to astronomy and geodesy. J Comput Appl Math 121:37–72
6. Plackett RL (1972) The discovery of the method of least squares. Biometrica 59(2):239–251
7. Ryan TP (1997) Modern regression methods. Wiley, New York
8. Stigler SM (1986) The history of statistics: the measurement of uncertainty before 1900. Harvard University Press, Cambridge
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]
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