Some Notes on Least Squares

Excerpts from the Preface: A bit of history will be helpful to anyone who may be wondering just how this brochure happens to be in existence. Beginning in 1932 the author has given annually a course in statistics at the Department of Agriculture Graduate School. The course consists of a survey of classical probability and an introduction to modern theoretical statistics, with some philosophy mixed in with it in an attempt to separate the mathematical developments from observations on the physical behavior of nature. The last six weeks of the course are devoted to the study of least squares. It is the lecture notes for this part of the course for 1937 that now appear. The assumption is that the reader knows when he needs to use least squares and when he should not, that is, when the question can be answered at all. In the course of study in which these notes have grown up, such things are discussed before least squares is commenced; the material presented here may therefore be regarded purely as an exposition on the principle and method. Naturally I have been partial to my own experience, which has embraced consultation on a wide variety of problems, mostly in the Department of Agriculture and the National Bureau of Standards. I have tried to stress points that have seemed inadequately covered or incorrectly pictured by previous writers. It is presumed that teachers using this as a text will heed the references for supplementary reading and will also illustrate the theoretical exercises with numerical examples.