# Why are regression problems called “regression” problems?

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."

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.

• Galton derived a linear approximation to estimate a son's height from the father's height in that paper. His equation was fitted so an average height father would have an average height son, but a taller than average father would have a son that is taller than average by 2/3 the amount his father is. Same with shorter than average. This could be argued to be a simple linear regression (today's meaning). And of course today regression has an even broader meaning: it's any model that makes continuous predictions. It is interesting how much his original usage of that word has changed. – rm999 May 21 '11 at 19:07
• Answer by NRH is correct. The following link gives lot more details on Francis Galton's paper "Regression towards mediocrity in hereditary stature" blog.minitab.com/blog/statistics-and-quality-data-analysis/… – Gaurav Singhal May 9 '16 at 8:23
• is it time for the statistics community to replace the word 'regression' with a more straightforward and clear term, maybe 'formulaic predictor' ? – Aviad Rozenhek Oct 27 '19 at 9:36

As opposed to progressing, we are falling back to the mean, i.e. regressing. Hence the term regression ! I think its something that got picked up and stuck.

@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:

# Origin of 'regression'

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).

# References

https://en.wikipedia.org/wiki/Regression_analysis#History

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.

• Galton's regression as in 'regression to the mean' makes sense. however I don't understand use of the word 'regression' to mean 'learn a formula from independant variables to an outcome variable' – Aviad Rozenhek Oct 27 '19 at 8:49
• It more generally means that, but machine learning uses regression but regression is not a machine learning technique, despite popular, incorrect opinion. Statistical learning is separate from machine learning but in general, ML proponents take statistical methods and incorrectly label them as ML so the apparent incongruities pop up. Galton's regression is regression; it has to do with modeling/predicting a tendency. – LSC Oct 27 '19 at 9:45

"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.

As I know the word of regression in statistical meaning is the measurement of the relation between the mean value of one variable and the corresponding values of other variables.