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© 1999

Fitting Linear Relationships

A History of the Calculus of Observations 1750–1900

Benefits

  • 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

Book

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

Table of contents

  1. Front Matter
    Pages i-xii
  2. Richard William Farebrother
    Pages 1-8
  3. Richard William Farebrother
    Pages 9-22
  4. Richard William Farebrother
    Pages 23-31
  5. Richard William Farebrother
    Pages 33-47
  6. Richard William Farebrother
    Pages 49-67
  7. Richard William Farebrother
    Pages 69-81
  8. Richard William Farebrother
    Pages 83-90
  9. Richard William Farebrother
    Pages 91-104
  10. Richard William Farebrother
    Pages 105-130
  11. Richard William Farebrother
    Pages 131-149
  12. Richard William Farebrother
    Pages 151-162
  13. Richard William Farebrother
    Pages 163-189
  14. Richard William Farebrother
    Pages 191-205
  15. Richard William Farebrother
    Pages 207-216
  16. Richard William Farebrother
    Pages 217-231
  17. Richard William Farebrother
    Pages 233-241
  18. Back Matter
    Pages 243-273

About this book

Introduction

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.

Keywords

Curve fitting Fitting linear optimization mathematical statistics statistics

Authors and affiliations

  1. 1.Department of Economic StudiesVictoria University of ManchesterManchesterUK

Bibliographic information

  • Book Title Fitting Linear Relationships
  • Book Subtitle A History of the Calculus of Observations 1750–1900
  • Authors R.W. Farebrother
  • Series Title Springer Series in Statistics
  • DOI https://doi.org/10.1007/978-1-4612-0545-6
  • Copyright Information Springer-Verlag New York, Inc 1999
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-387-98598-5
  • Softcover ISBN 978-1-4612-6812-3
  • eBook ISBN 978-1-4612-0545-6
  • Series ISSN 0172-7397
  • Edition Number 1
  • Number of Pages XII, 271
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Applications of Mathematics
  • Buy this book on publisher's site

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."