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Fitting Linear Relationships

A History of the Calculus of Observations 1750–1900

  • Book
  • © 1999

Overview

Authors:
  1. Richard William Farebrother

    1. Department of Economic Studies, Victoria University of Manchester, Manchester, UK

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  • Gives a clear understanding of the historical development of commonly used statistical estimation procedures, an approach which is not found in other books Considers a wide variety of distinct approaches which lead to the same statistical techniques; this gives readers valuable insights into the essential nature of these procedures Of interest to both statisticians concerned with the fitting of linear models, as well as to engineers and scientists working with the empirical determination of linear relationships
  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer Series in Statistics (SSS)

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-xii
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  2. Introduction

    • Richard William Farebrother
    Pages 1-8

  3. The Methods of Boscovich and Mayer

    • Richard William Farebrother
    Pages 9-22

  4. Laplace’s Work on the Methods of Boscovich and Mayer

    • Richard William Farebrother
    Pages 23-31

  5. Laplace’s Minimax Procedure

    • Richard William Farebrother
    Pages 33-47

  6. The Method of Least Squares

    • Richard William Farebrother
    Pages 49-67

  7. Statistical Foundations of the Method of Least Squares

    • Richard William Farebrother
    Pages 69-81

  8. Adrain’s Work on the Normal Law

    • Richard William Farebrother
    Pages 83-90

  9. Gauss’s Most Probable Values

    • Richard William Farebrother
    Pages 91-104

  10. Laplace’s Most Advantageous Method

    • Richard William Farebrother
    Pages 105-130

  11. Gauss’s Most Plausible Values

    • Richard William Farebrother
    Pages 131-149

  12. Gauss’s Method of Adjustment by Correlates

    • Richard William Farebrother
    Pages 151-162

  13. Mechanical Analogies for the Method of Least Squares

    • Richard William Farebrother
    Pages 163-189

  14. Orthogonalisation Procedures

    • Richard William Farebrother
    Pages 191-205

  15. Thiele’s Derivation of the Method of Least Squares

    • Richard William Farebrother
    Pages 207-216

  16. Later Work on the Method of Situation

    • Richard William Farebrother
    Pages 217-231

  17. Concluding Remarks

    • Richard William Farebrother
    Pages 233-241

  18. Back Matter

    Pages 243-273
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Keywords

About this book

This book is intended for students of mathematical statistics who are interested in the early history of their subject. It gives detailed algebraic descriptions of the fitting of linear relationships by the method of least squares (L ) and the related least absolute 2 deviations (L ) and minimax absolute deviations (Loo) procedures. These traditional line J fitting procedures are, of course, also addressed in conventional statistical textbooks, but the discussion of their historical background is usually extremely slight, if not entirely absent. The present book complements the analysis of these procedures given in S.M. Stigler'S excellent work The History of Statistics: The Quantification of Uncertainty before 1900. However, the present book gives a more detailed account of the algebraic structure underlying these traditional fitting procedures. It is anticipated that readers of the present book will obtain a clear understanding of the historical background to these and other commonly used statistical procedures. Further, a careful consideration of the wide variety of distinct approaches to a particular topic, such as the method of least squares, will give the reader valuable insights into the essential nature of the selected topic.

Reviews

From the reviews:

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION

"Farebrother gives the details of the algebraic development of various procedures, striving to make them more understandable by modernizing and standardizing the notation as much as possible without departing too far from that used by the original developers. ...Readers interested in the history...will be gratified by the helpful historical and bigraphical notes...I thoroughly enjoyed reading this book, and recommend it without hesitation to readers interested in the subject."

 

Authors and Affiliations

  • Department of Economic Studies, Victoria University of Manchester, Manchester, UK

    Richard William Farebrother

Bibliographic Information

  • Book Title: Fitting Linear Relationships

  • Book Subtitle: A History of the Calculus of Observations 1750–1900

  • Authors: Richard William Farebrother

  • Series Title: Springer Series in Statistics

  • DOI: https://doi.org/10.1007/978-1-4612-0545-6

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1999

  • Hardcover ISBN: 978-0-387-98598-5Published: 14 December 1998

  • Softcover ISBN: 978-1-4612-6812-3Published: 04 October 2012

  • eBook ISBN: 978-1-4612-0545-6Published: 06 December 2012

  • Series ISSN: 0172-7397

  • Series E-ISSN: 2197-568X

  • Edition Number: 1

  • Number of Pages: XII, 271

  • Topics: Applications of Mathematics

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