# What does the name “Logistic Regression” mean?

I am checking an implementation of Logistic Regression from here.

After I reading that article, it seems the important part is the find the best coefficients to determine the sigmoid function. So I just wonder why this method is called "Logistic Regression". Is it related to the logarithmic function? Maybe I need some historical background info to understand it better.

• It comes from the logistic function (en.wikipedia.org/wiki/Logistic_function) – rapaio Aug 7 '14 at 12:50
• @rapaio Thanks. I checked that link. I am not a native English speaker. Why are these functions called logistic? I checked the dictionary, it gives me the impression that "logistic" somehow means "logical, reasonable, rational" or something alike. I don't see its connection to this scenario. – smwikipedia Aug 7 '14 at 12:52
• I do not read the Verhulst papers, since are written in French. What I know is that logistic is the term given by Verhulst, it is used as a tribute to Verhulst, and Verhulst used the term logistic curve as an analogy with logarithmic curve. – rapaio Aug 7 '14 at 13:02

As it has been already pointed out, ''logistic'' comes from logistic curve/function/distribution (which is underlying logistic regression). So the question is: where is logistic coming in their names?

The reference to Verhulst (i.e. Wikipedia's statement) seems a bit false. While it is clearly true that it is most widely attributed to Verhulst, the first actual use seems to come from Edward Wright. See Thompson: On Growth and Form (1945), page 145. (Found via the well-known Earliest Known Uses of Some of the Words of Mathematics page.)

Thompson hints that Verhulst used it in connection with its S-shape, but gives no clue about Wright.

However, given that one of the most important parts of Wright's work was pertaining to logarithms, it seems logical that he used it as a reference to logarithm. Indeed (and more precisely), the 1911 edition of Encyclopaedia Britannica refers to the old mathematical term logistic number:

The old name for what are now called ratios or fractions are logistic numbers, so that a table of log (a/x) where x is the argument and a a constant is called a table of logistic or proportional logarithms; and since log (a/x) =log a-log x it is clear that the tabular results differ from those given in an ordinary table of logarithms only by the subtraction of a constant and a change of sign.

Also note that logarithm itself comes from proportion (logos) + number (arithmos); originally coined by John Napier.

So, I believe, this is the most likely explanation: ''logistic'' is used in Wright's time in connection with what we now call ''logarithm'', which was used by Wright when he constructed that curve.

• So it effectively means logarithmic regression? – Behrang Saeedzadeh Sep 3 '17 at 11:44
• @Behrang No, I definitely wouldn't say that. It's a regression that has a component that has something to do with logarithms. – Tamas Ferenci Sep 7 '17 at 10:08

Its related to the LOGISTIC distribution, which has an S-shaped curve.

• Logistic distribution, or logistic function? In either case, this answer begs the question, because we still do not know why the logistic function/regression takes on the moniker "logistic." – Sycorax Aug 7 '14 at 14:30
• This characterization is not specific enough. All unimodal symmetric continuous distributions (such as Normal, Student $t$) and many unimodal continuous distributions (such as $F$, $\chi^2$) have "S-shaped curves" (referring, of course, to the graphs of their CDFs). – whuber Jul 17 '17 at 14:17