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From |
"Nick Cox" <n.j.cox@durham.ac.uk> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
st: RE: eivreg, deming, and R^2 |

Date |
Sun, 5 Oct 2008 18:07:43 +0100 |

Here, as indeed elsewhere, the answer depends on what you mean by R^2 -- in terms of algebraic definition and in terms of statistical interpretation. Suppose you have variables y and x. Let corr(,) mean Pearson correlation. Then one definition of R^2 is the square of corr(y, x) and this does not depend on any assumptions about whether x or y or both is measured with error or how that error behaves. Another definition would be the square of corr(x, predicted x) and another the square of corr(y, predicted y) where the predictions come from taking one variable as response and predicting it from the other by plain flavour linear regression. These definitions have distinct meanings but in practice give the same numerical result. Yet other definitions can of course be found. And, more importantly, once you move away from that plain regression territory the different definitions typically disagree in terms of numerical result. In the case of -deming- and -eivreg-, my take is as follows. (Note incidentally that -deming- is a user-written command: use -findit deming- to locate it. As a matter of fact, the user concerned is a Stata developer, but -deming- is not an official command.) -eivreg- can take multiple predictors, so R^2 in the first sense is not defined uniquely. I guess that you are in practice concerned with a single predictor as well as a single response. In that situation, you can use any of the definitions above, but it will be important to say which sense you are using and to realise that R^2 will depend on assumptions insofar as predictions do. R^2 doesn't I think play any formal part in either analysis; it's just a descriptive statistic that may seem convenient or attractive. Nick n.j.cox@durham.ac.uk David Airey Is R^2 as interpretable in regression models that account for errors in both y and x, like -deming- or -eivreg-? Can I interpret R^2 from - eivreg- just like in -regress-? * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: RE: eivreg, deming, and R^2***From:*David Airey <david.airey@vanderbilt.edu>

**References**:**st: eivreg, deming, and R^2***From:*David Airey <david.airey@Vanderbilt.Edu>

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