Regression
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 This topic has 7 replies, 5 voices, and was last updated 15 years, 4 months ago by BTDT.

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May 30, 2005 at 9:23 am #39527
What is the meaning of R sq ( adj ) in regression ?
Thanks in advance
0May 30, 2005 at 10:06 am #120410Dear new,
I would say that Rsq describes the proportion of variation in the response Y that is explained by the predictor X. Rsq adj provides the same information but taking in account the Rsq tendency to overestimate the variation in the response Y. This is why Rsq Adj is sometimes a little bit lower than Rsq.
Hope this helps
Franz0May 30, 2005 at 10:28 am #120411Rsq adj provides the same information but taking in account the Rsq tendency to overestimate the variation in the response Y.
What do you mean by that I didnt get that in simple terms
0May 30, 2005 at 12:45 pm #120412R2 (adj) corrects for the number of terms in the equation and the number of data points. It is calculated using:
R2 (adj) = 1 – (n1)/(np) * (1R^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 Rsqadj term). If you have terms in the model that are not statistically significant, you reduce the usefulness of the model.0May 30, 2005 at 1:12 pm #120414
Robert ButlerParticipant@rbutler Include @rbutler in your post and this person will
be notified via email.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=712430May 30, 2005 at 3:30 pm #120416Robert:I remember a definition of rsq 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 rsq.I couldn’t find a reference.Does this sound familiar?BTDT
0May 30, 2005 at 4:08 pm #120419
Robert ButlerParticipant@rbutler Include @rbutler in your post and this person will
be notified via email.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.
0May 30, 2005 at 4:38 pm #120421Robert:It was nagging me for a while. I couldn’t even rememeber whether it was R of Rsq.Thanks, BTDT
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