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From |
"Gene Fisher" <fisher@soc.umass.edu> |

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

Subject |
RE: st: Re: normal distributions |

Date |
Sun, 21 Jul 2002 17:14:15 -0400 |

Regression coefficients are functions of sums of random variables (sum(X), sum(X^2), sum(XY), so that the CLT applies to them. The variance of the regression coefficient is also a sum of random variables (the residuals, and of X and X^2 if the X's are not fixed), so the distribution of the ratio of the regression coefficient to its standard error tends toward a standard normal distribution as N approaches infinity. But we don't know so readily how close to normal b/se(b) is for a given distribution of Y (and possibly X) and N. Convergence is a lot faster if the residuals are symmetrical than if they are skewed. Also, looking at Serfling's Approximation Theorems of Mathematical Statistics, pp 125-126, it may be that se(b)^2 is not the asymptotic variance of b (He talks about the sampling distribution of the correlation coefficient). I think it is, but I haven't looked at this in a long time. Gene Fisher Department of Sociology University of Massachusetts Thompson Hall, 200 Hicks Way Amherst, MA 01003-9277 (413) 545-4056; fisher@soc.umass.edu -----Original Message----- From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu]On Behalf Of Michael Cha Sent: Sunday, July 21, 2002 4:37 PM To: statalist@hsphsun2.harvard.edu Subject: RE: st: Re: normal distributions Dear listers, Could anyone tell me the relationship between regression assumption test (Normality test in particular) and CLT (Central Limit Theorem)? Does CLT imply that we do not have to worry about normality test for residuals as far as sample size is large? Or CLT does not imply anything about the regression assumption test? Thanks in advance, MCHA, _____________________________________________________ Supercharge your e-mail with a 25MB Inbox, POP3 Access, No Ads and NoTaglines --> LYCOS MAIL PLUS. http://www.mail.lycos.com/brandPage.shtml?pageId=plus * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**RE: st: Re: normal distributions***From:*"Michael Cha" <mikecha0@lycos.com>

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