Gauss was so prolific that he considered his invention of statistical regression , a central tool in modern statistics and data science, too trivial to even report when he discovered it. Specifically, Gauss invented least squares regression , a method used to calculate a straight line that best fits a set of data, and the earliest form of regression analysis. It is primarily used for understanding the relationship between variables, or to predict future outcomes.
For example, you could use regression to understand the strength of the relationship between parental height and the height of children, or even parental height and the income of children when they become adults. Although the French mathematician Adrien-Marie Legendre was the first to publish a paper using regression in , Gauss claimed to have invented the method in He asserted his discovery in an paper in which he used regression to predict the location of an asteroid. Legendre disputed that Gauss deserved credit for the invention, and it would lead to lifelong hostility between the two.
He also provided an algorithm to compute it. Gauss and Legendre never actually used the term regression for their method. Today, regression is one of the foundations of modern social science, and among the most important tools of computer scientists.
This sparked off one of the most famous priority disputes in mathematics second only to the Newton vs Leibniz controversy over the invention of calculus.
Plackett and Stigler attempted to verify some of these priority claims. The moral of the story seems to be to always publish your work first! The least squares approach to fitting lines and curves remains a mainstay in modern statistics. At first glance, the problem appears to be solvable by marking the observations as data points on graph paper and drawing in a line of best fit. I suspect that this was very likely the way that Gauss was thinking about the data when he invented the idea of least squares and proved the famous Gauss-Markov theorem in statistics.
While techniques continue to evolve, I suspect that Gauss would be very proud if he knew that his method of least squares is still a cornerstone of modern statistics and exciting new research is being done to build on and improve this fundamental technique within statistical machine learning theory. Figure 10 shows a series of diagrams to illustrate the evolution of our modern interpretation of the method of least squares. Gauss revealed his philosophy of learning and pursuit of knowledge, which many readers may relate to.
When I have clarified and exhausted a subject, then I turn away from it, in order to go into darkness again. The never-satisfied man is so strange; if he has completed a structure, then it is not in order to dwell in it peacefully, but in order to begin another. I imagine the world conqueror must feel thus, who, after one kingdom is scarcely conquered, stretches out his arms for others.
This passion for discovery and learning is evidenced by his work beyond pure mathematics. In his 70s, Gauss also dabbled in actuarial work. They approached Gauss, who applied his mathematical wizardry to build an actuarial model of the pension fund for both income e. As recounted in Read , his work reformed the Widow Fund onto a sound actuarial basis, which allowed the University to surprisingly increase the pension payments to widows by forecasting the expected increase in the number of professors and restricting their conditions for beneficiaries.
Using his financial acumen, Gauss later made shrewd investments in under-valued corporate bonds issued by private companies. Gauss ushered in an age where scientists used sophisticated mathematics to find things that were invisible to the naked eye. For example, both Neptune and Pluto were discovered in and respectively, by mathematical predictions i. Hopefully this little history lesson might help us to appreciate the simple yet powerful tool of linear regression in the context of data science, the art and science of extracting useful insights from data.
Adrain, R. Gauss, C. Hastie, T. Heideman, M. Kuppers, M. Plackett, R. Read, C. Stahl, S. Stigler, S. Teets D. This statement presumably represents an extension of current practice to the method of least squares. The problem of deciding when an error is large enough to warrant deletion was not discussed.
Legendre gave very little justification for choosing the sum of the squared errors as his optimality criterion other than its computational simplicity.
However he did note that it yields the arithmetic mean when there are a set of direct observations on a single unknown quantity. Of these criteria, the simplest is indeed the sum of the squared errors, which Gauss says he had used in practical calculations since , much to the annoyance of Legendre who published a venomous response in The method of least squares would seem to have been hanging in the air at this time as there are several claimants for the privilege of having first invented it including Gauss, Cotes, Simpson, and Huber.
Most of these claims can be rejected as having been made with the benefit of hindsight and in ignorance of the difficulty that eighteenth century mathematicians would have experienced in conceiving of minimising a sum of squared errors rather than a sum of absolute errors. However, the claim for priority made by Gauss at the time would seem to have been substantiated in the opinion of Laplace, Plackett , Stigler , , , and other authorities, but Legendre retains the priority of publication, for what that is worth.
Further, Gauss's practical fitting procedure was designed for use with nonlinear problems and its precise nature is still open to question, again see Stigler for details.
As noted above, Legendre's derivation of the method of least squares was entirely algebraic; statistical justifications for this fitting procedure were subsequently provided by Gauss, Laplace, Cauchy q.
Log in. Namespaces Page Discussion. Views View View source History. Jump to: navigation , search. Legendre died in Paris in Legendre's system of orthogonal polynomials have also found applications in statistics. References [1] Duren, P. Pages of the appendix reprinted in Stigler , p. English translation of these pages by H.
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