```Date: Wed, 19 Sep 2007 09:02:52 -0700 Reply-To: "Ornelas, Fermin" Sender: "SPSSX(r) Discussion" From: "Ornelas, Fermin" Subject: Re: Regression, centering and collinearity Comments: To: Mike Ford In-Reply-To: A<200709190902.l8J509qA032242@mailgw.cc.uga.edu> Content-Type: TEXT/plain; charset="us-ascii" When you fit a model without an intercept the collinearity diagnostics will give you a lower condition index. To me this is not a good idea since most often the final model will include an intercept in the regression function. I may reply to the second part later... but brushing up on linear algebra will help you understand how x'x and xy are being affected. -----Original Message----- From: SPSSX(r) Discussion [mailto:SPSSX-L@LISTSERV.UGA.EDU] On Behalf Of Mike Ford Sent: Wednesday, September 19, 2007 2:03 AM To: SPSSX-L@LISTSERV.UGA.EDU Subject: Re: Regression, centering and collinearity Thank you for the responses. I should have made clear that I was not talking about perfect collinearity. Having seen centering suggested as a method to reduce moderate collinearity in a number of sources, I have used it and thought it worked because of a change in the condition indices of models when I use centered variables. For example, with this makey-up toy data... y x1 x2 68 4.1 73.6 71 4.6 17.4 62 3.8 45.5 75 4.4 75.0 58 3.2 45.3 60 3.1 25.4 67 3.8 8.8 68 4.1 11.0 71 4.3 23.7 69 3.7 18.0 68 3.5 14.7 67 3.2 47.8 63 3.7 22.2 62 3.3 16.5 60 3.4 22.7 63 4 36.2 65 4.1 59.2 67 3.8 43.6 63 3.4 27.2 61 3.6 45.5 The condition index of the model = 21.7, which I would worry about if I got with real data. However if I center the DV and IVs and do the regression (with no constant) the condition index for the model of the centered data = 1.2. Obviously the beta, SE beta values etc. are the same for IVs in both cases. So, to my understanding the condition indices are saying that the model with the centered data is better than the model with the original data. Given the responses I have got to my posting, this change in the condition indices confuses me even more now. It must relate to a change in the cross products and sums of squares but I don't really understand. Thank you! NOTICE: This e-mail (and any attachments) may contain PRIVILEGED OR CONFIDENTIAL information and is intended only for the use of the specific individual(s) to whom it is addressed. It may contain information that is privileged and confidential under state and federal law. This information may be used or disclosed only in accordance with law, and you may be subject to penalties under law for improper use or further disclosure of the information in this e-mail and its attachments. If you have received this e-mail in error, please immediately notify the person named above by reply e-mail, and then delete the original e-mail. Thank you. ```

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