I was just wondering why regression problems are called "regression" problems. What is the story behind the name?
One definition for regression: "Relapse to a less perfect or developed state."
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The term "regression" was used by Francis Galton in his 1886 paper "Regression towards mediocrity in hereditary stature". To my knowledge he only used the term in the context of regression toward the mean. The term was then adopted by others to get more or less the meaning it has today as a general statistical method.
@Mark White mentioned the link already but for those of you who do not have much time to check the link, here's the exact properly referenced answer:
The term "regression" was coined by Francis Galton in the 19th century to describe a biological phenomenon. The phenomenon was that the heights of descendants of tall ancestors tend to regress down towards a normal average (a phenomenon also known as regression toward the mean)(Galton, reprinted 1989). For Galton, regression had only this biological meaning (Galton, 1887), but his work was later extended by Udny Yule and Karl Pearson to a more general statistical context (Pearson, 1903).
Galton, F. (1877). Typical laws of heredity. III. Nature, 15(389), 512-514.
Galton, F. (reprinted 1989). Kinship and Correlation. Statistical Science, 4(2), 80–86.
Pearson, K. (1903). The law of ancestral heredity. Biometrika, 2(2), 211-228.
I arrived here via a search for how a regression got its name. Here are the interesting parts of what I found (mostly from wikipedia.)
The term "regression" was coined by Francis Galton in the nineteenth century to describe a biological phenomenon. The phenomenon was that the heights of descendants of tall ancestors tend to regress down towards a normal average (a phenomenon also known as regression toward the mean).7,8 For Galton, regression had only this biological meaning,9,10 but his work was later extended by Udny Yule and Karl Pearson to a more general statistical context.11,12 In the work of Yule and Pearson, the joint distribution of the response and explanatory variables is assumed to be Gaussian. This assumption was weakened by R.A. Fisher in his works of 1922 and 1925.13,14,15 Fisher assumed that the conditional distribution of the response variable is Gaussian, but the joint distribution need not be. In this respect, Fisher's assumption is closer to Gauss's formulation of 1821.
Also very interesting:
In the 1950s and 1960s, economists used electromechanical desk "calculators" to calculate regressions. Before 1970, it sometimes took up to 24 hours to receive the result from one regression.16
Mogull, Robert G. (2004). Second-Semester Applied Statistics. Kendall/Hunt Publishing Company. p. 59. ISBN 978-0-7575-1181-3.
Galton, Francis (1989). "Kinship and Correlation (reprinted 1989)". Statistical Science. 4 (2): 80–86. doi:10.1214/ss/1177012581. JSTOR 2245330.
Francis Galton. "Typical laws of heredity", Nature 15 (1877), 492–495, 512–514, 532–533. (Galton uses the term "reversion" in this paper, which discusses the size of peas.)
Francis Galton. Presidential address, Section H, Anthropology. (1885) (Galton uses the term "regression" in this paper, which discusses the height of humans.)
Yule, G. Udny (1897). "On the Theory of Correlation". Journal of the Royal Statistical Society. 60 (4): 812–54. doi:10.2307/2979746. JSTOR 2979746.
Pearson, Karl; Yule, G.U.; Blanchard, Norman; Lee,Alice (1903). "The Law of Ancestral Heredity". Biometrika. 2 (2): 211–236. doi:10.1093/biomet/2.2.211. JSTOR 2331683.
Fisher, R.A. (1922). "The goodness of fit of regression formulae, and the distribution of regression coefficients". Journal of the Royal Statistical Society. 85 (4): 597–612. doi:10.2307/2341124. JSTOR 2341124. PMC 1084801.
Ronald A. Fisher (1954). Statistical Methods for Research Workers (Twelfth ed.). Edinburgh: Oliver and Boyd. ISBN 978-0-05-002170-5.
Aldrich, John (2005). "Fisher and Regression". Statistical Science. 20 (4): 401–417. doi:10.1214/088342305000000331. JSTOR 20061201.
Rodney Ramcharan. Regressions: Why Are Economists Obessessed with Them? March 2006. Accessed 2011-12-03.
"Regression" comes from "regress" which in turn comes from latin "regressus" - to go back (to something).
In that sense, regression is the technique that allows "to go back" from messy, hard to interpret data, to a clearer and more meaningful model. As a physicist, I like the idea, as physicists see natural phenomena as the multiple possible outcomes of a relatively simple natural law.
In other words, the word regression seems to suggest that data is just the visible, tangible effect of a "statistical model". In other words, the model comes first, and your desire is use the data "to go back" to what originated them.