What does it mean "centered/uncentered 𝑅2'

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גל ביטון‎

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Jun 20, 2019, 11:26:12 AM6/20/19
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Hello everyone,

While I was estimating 2sls regression, I have noticed there is "centered" R square as well as "uncentered"  R square. 
Yet I'm not sure I fully  understand what it means. 
Are they the same as R square and adjusted-R square? or is it something else?

Screen Shot 2019-06-20 at 17.42.14.png










Thank for your help, Gal.

Ramani Swarna

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Jun 20, 2019, 11:41:10 AM6/20/19
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Hi Gal,

Greetings for the day!

These differences are observed more in the studies using Econometrics. Centered R Square is same as R Square. However, Uncentered R Square has different meaning altogether in the model building. It is a model wherein the intercept term is missing or is absent. It is present in the OLS Models. 

As of now, I am collecting and trying my best to understand different kinds of models present under Regression.


Thanks and regards,
Ramani Swarna






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Ramani Swarna

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Jun 20, 2019, 11:47:24 AM6/20/19
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Gal,

For more information on it specially in terms of the concepts and formulae, you may checkout the following link:


and 


When I was attending a session on Asset Ratios, I was introduced to the concepts of outliers, errors and intercepts. I am still perplexed with the questions: can I really drop or ignore the intercept while studying the models? What are those scenarios? What happens when it is present and in its absence? 

I need to wait for another session exclusively focusing on the importance of the intercept itself.  

In case I come across more information, I will certainly share it with you also.

Thanks and regards,
Ramani Swarna





‪On Thu, Jun 20, 2019 at 8:56 PM ‫גל ביטון‬‎ <gal5b...@gmail.com> wrote:‬
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גל ביטון‎

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Jun 20, 2019, 9:51:15 PM6/20/19
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Hi Ramani,

Thank you very much for your reply. I find it very helpful.
I'll be happy to hear from you again if you would have more information. 

Have a wonderful day,
Gal.

Ramani Swarna

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Jun 21, 2019, 1:53:25 AM6/21/19
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Hi Gal,

Kindly see the following also, these will be really useful to you:


This page gives you a very good idea about "centering"

2. While attending a workshop, I was introduced to the qualitative approach towards the multivariate analysis wherein it was through the dummy variables one may proceed further. It was at this point, I got introduced to the centered and uncentered r squares and how to move from uncenter to the centered part and why it is important. I will be sharing the link for the paper with you.

There are discussions on the relationship between negative correlation and uncentered r square, unobserved and observed data and uncentered, multicollinearity and uncentered variables and mean and centering are related and meaningful in the analysis.Finally how VIF and TOL are useful in reducing the multi-collinearity amongst the variables. 

Neeraj Sir has uploaded videos on 


For Simple and Multiple Regression using OLS Method:

2. Multi-collinearity-

I will check this one and get back to you.

3. Using Hayes' Process in SPSS


4. Dummy Variables


Apart from these, you may check the following ones also:

a. Jeff Wooldridge-Introductory Econometrics: A Modern Approach(Edition 2016)


d. http://www-hsc.usc.edu/~eckel/biostat2/notes/notes9.pdf

e. https://www2.cirano.qc.ca/~dufourj/Web_Site/ResE/Dufour_1983_R2_W.pdf

f. http://eprints.whiterose.ac.uk/114588/1/Dawson%20%282014%29%20%28post-print%29.pdf


g. https://afni.nimh.nih.gov/pub/dist/doc/htmldoc/STATISTICS/center.html

h. "Mean-Centering Does Not Alleviate Collinearity Problems in Moderated Multiple Regression Models" by Raj Echambadi and James D.Hess, Marketing Science, Vol 26,May-June 2007

i. "Clarifying the role of mean centring in multicollinearity of interaction effects" by Gwowen Shieh, The britih Psychological Society, 2011.

There is one more paper which discussed about how one should convert uncertered to centered data.I will share it with you later.
I am happy that one must not restrict to just economics or finance to understand this method. One may use to other domains also. Once I learnt it from the Professor, I was extremely thrilled that one must incorporate it to other fields of knowledge also.

This may be done through R, SPSS, EViews, Stata and Excel also. 

 
Thanks and regards,
Ramani Swarna





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גל ביטון‎

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Jun 21, 2019, 9:02:24 PM6/21/19
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That is great!
Thanks for sharing.

Regards, 
Gal

‫בתאריך יום ו׳, 21 ביוני 2019 ב-8:58 מאת ‪Ramani Swarna‬‏ <‪ramani...@gmail.com‬‏>:‬
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