# Why is the coefficient of determination ($R^2$) so called?

I have a very hard time remembering terms if I don't at least have some idea of their etymology or what other concepts in the field they relate to.

"Determination" doesn't seem to have any meaning outside of "coefficient of determination", contrary to say the "coefficient of correlation", where correlation is something well-defined in of itself. Why was this specific word chosen for $R^2$?

• See stats.stackexchange.com/questions/159593/…. Sewall Wright, whom Nick Cox cites in the answer there, was interested in causation, or "the degree of determination for which factor $A$ [in a path analysis] is directly responsible in the given system of factors. This definition implies that the sums of such coefficients must equal unity if all causes are accounted for" [at p. 562]. – whuber Jun 17 '17 at 18:53

This Google search turns up an interesting result.

What follows is my speculation.

A deterministic model is a "Mathematical model in which outcomes are precisely determined through known relationships among states and events, without any room for random variation." From: What is a deterministic model?

I think the coefficient of determination can be thought of in terms of what is determined/known (without variation) about a model. If $R^2 = 1.00$, then 100% of the relation between the predictors and the outcome is determined. If you put in values for your predictors, you always get a prediction with no error term. You know the outcome with no room for error, or variation of any type. Your model becomes akin to $2 + 3 = 5$.

Typically, you do not have 100% $R^2$, so even though we obtain the same predicted value for two cases with the same values on our predictors, there is some error. So the correct predictions for both cases remain unknown and the correct predictions are probably different. But these correct predictions are determined (or we know them) to some extent - the extent of the $R^2$.

• Although plausible, this is really just speculation and doesn't seem to be historically correct. See the 1921 paper by Sewall Wright (found by Nick Cox in a related thread) where the term was first defined and described. – whuber Jun 17 '17 at 18:57
• I know it is only my speculation, and it is why I write, "I think the coefficient of determination can be thought of ..." I'm assuming OP wants a way to make sense of the word "determination". I think this helps. I can modify my answer note it is all my speculation. – Heteroskedastic Jim Jun 17 '17 at 19:06
• This question is not asking about what $R^2$ means: it is asking about why it is called what it is. That requires some historical research, akin to that performed by Nick Cox in the related thread. – whuber Jun 17 '17 at 19:10
• If you follow on from the Dictionary of Mathematics link I posted and the quote in your above comment on the question, how does this differ from my response? OP writes: '"Determination" doesn't seem to have any meaning outside of "coefficient of determination"' I think my response helps show determination has a meaning. Beyond this, I have no defence for my response. – Heteroskedastic Jim Jun 17 '17 at 19:23
• @whuber Sir, you are correct. It is a sself-styled and naive answer. The mathematical modelling does not imply that the modelling results in a perfect or true relationship. r is just an estimate. In a squared form, it tells that a certain part of relationship is constant or fixed. – Subhash C. Davar Jun 25 '17 at 23:38