The following sections of this BookRags Literature Study Guide is offprint from Gale's For Students Series: Presenting Analysis, Context, and Criticism on Commonly Studied Works: Introduction, Author Biography, Plot Summary, Characters, Themes, Style, Historical Context, Critical Overview, Criticism and Critical Essays, Media Adaptations, Topics for Further Study, Compare & Contrast, What Do I Read Next?, For Further Study, and Sources.
(c)1998-2002; (c)2002 by Gale. Gale is an imprint of The Gale Group, Inc., a division of Thomson Learning, Inc. Gale and Design and Thomson Learning are trademarks used herein under license.
The following sections, if they exist, are offprint from Beacham's Encyclopedia of Popular Fiction: "Social Concerns", "Thematic Overview", "Techniques", "Literary Precedents", "Key Questions", "Related Titles", "Adaptations", "Related Web Sites". (c)1994-2005, by Walton Beacham.
The following sections, if they exist, are offprint from Beacham's Guide to Literature for Young Adults: "About the Author", "Overview", "Setting", "Literary Qualities", "Social Sensitivity", "Topics for Discussion", "Ideas for Reports and Papers". (c)1994-2005, by Walton Beacham.
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The method of least squares is an important statistical tool used to obtain the best values, those containing the "least" errors, of unknown quantities. Commonly used by engineers, business managers, government officials, market analysts and others in the field of statistical analysis, the method of least squares permits an accurate, yet uncomplicated system for the estimation of exact values from a set of observations containing errors. The process is called "least squares" because the procedure minimizes the sum of the squares of the differences between the observed and estimated values. The method is also used in interpolation theory to find simplier functions that are the best approximations to a given function in an interval of specified points. In matrix theory, the method of least squares can be used to find a "solution" x for an inconsistent system of linear equations Ax = b that makes the distance between Ax and b as small as possible.
It is primarily through the efforts of the renowned mathematician Carl Friedrich Gauss that the method of least squares was discovered. Gauss was born 1777 in Brunswick, Germany, to a poor, uneducated family. His father was a gardener and it is reported that Gauss taught himself to read and count very early in life. According to history, he is said to have spotted a mistake in his father's arithmetic at the age of three. He entered high school at the age of eleven, and, at fifteen, began to study at the Collegium Carolinum, with financial assistance from the Duke of Brunswick. Gauss became interested in astronomy, studying the relationship of probability and errors as they related to astronomy. His interest resulted in the development of the theory of least squares. Although Gauss discovered the method of least squares in 1795 at the age of eighteen, he never published his findings. In 1806, French mathematician Adrien-Marie Legendre, while doing research on the orbit of comets, developed and published the method of least squares in his book Nouvelles méthodes pour la détermination des orbites des cometes. Unbeknownst to Legendre, it was the same technique Gauss had developed eleven years earlier. When Gauss claimed prior discovery, Legendre became infuriated, particularly as he had once before been upstaged by another prior discovery of Gauss'. Although history credits Gauss with the first discovery of the method of least squares, Legendre receives credit for the first published account.