# Regression

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• #39527

New
Participant

What is the meaning of R sq ( adj ) in regression ?

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#120410

franz
Participant

Dear new,
I would say that R-sq describes the proportion of variation in the response Y that is explained by the predictor X. R-sq adj provides the same information but taking in account the R-sq tendency to overestimate the variation in the response Y. This is why R-sq Adj is sometimes a little bit lower than R-sq.
Hope this helps
Franz

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#120411

New
Participant

R-sq adj provides the same information but taking in account the R-sq tendency to overestimate the variation in the response Y.
What do you mean by that I didnt get that in simple terms

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#120412

NS
Participant

R2 (adj) corrects for the number of terms in the equation and the number of data points.  It is calculated using:
R2 (adj) = 1 – (n-1)/(n-p) * (1-R^2)
where n – number of observations (data points) and p = total number of terms (including the constant)
Practically, it tells you how good the model is.  For example, is a quadratic model better than a linear model (look at the R-sq-adj term).  If you have terms in the model that are not statistically significant, you reduce the usefulness of the model.

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#120414

Robert Butler
Participant

R2 is a summary of the amount of variation observed in your Y which is accounted for by the terms in you model – nothing more.  It is easily manipulated and tricked and, by itself, it provides little information about the goodness of the model.  The first post cited below can give you some idea of the real value of R2 and its very severe limitations.  The second will give you some idea of what needs to be done before you can make statements concerning model adequacy.
https://www.isixsigma.com/forum/showmessage.asp?messageID=43683
https://www.isixsigma.com/forum/showmessage.asp?messageID=71243

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#120416

BTDT
Participant

Robert:I remember a definition of r-sq from years back that defined it as the arcos of the angle beteen the model and the data points in hyperspace. I made enough sense to me that I remember it as a physical interpretation of r-sq.I couldn’t find a reference.Does this sound familiar?BTDT

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#120419

Robert Butler
Participant

It sounds like you are referring to the geometrical interpretation of the multiple correlation coefficient (square root of R2).  The reference I have is Kendall and Stuart volume II 4th edition pp. 356.  They state the multiple correlation coefficient R is the cosine of the minimized angle.  This angle would be the angle between the model and the data points in hyperspace.

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#120421

BTDT
Participant

Robert:It was nagging me for a while. I couldn’t even rememeber whether it was R of R-sq.Thanks, BTDT

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