Dear John, Ali & Allstat,
Just for the record (and not wishing to sound pedantic!), a few observations
regarding John's point (2). First, in standard regression analysis it is the
errors (not the residuals) that are assumed to be (i.i.d.) normal (with
constant variance). In model diagnosis there are a number of different types
of residuals one might take a look at. For the distributional properties of
these, take a look at Draper & Smith (I think the 3rd edition is the
latest). Secondly, there is a "lack of symmetry" in the assumptions
regarding the response and regressor variables. The latter are assumed to
have been observed without error (i.e. the observed values of the regressors
are assumed not to be realisations of random variables). Of course, John's
point (1) is correct - there is absolutely no problem in incorporating dummy
variables in a regression equation. (If there were, the "analysis of
covariance" would be somewhat problematic.)
Happy New Year to all,
Arthur
___________________________________
Dr. Arthur Pewsey
Dpto. de Matemáticas
Escuela Politécnica
Universidad de Extremadura
Avenida de la Universidad s/n
10071 Cáceres
Spain
Tel: +34 927 257221
E-mail: [log in to unmask]
Fax: +34 927 257203
__________________________________
----- Original Message -----
From: "John Sorkin" <[log in to unmask]>
To: <[log in to unmask]>
Sent: Monday, January 09, 2006 2:00 PM
Subject: Re: Two enquiries on regression.
Ali,
(1) You can use independent variables measured on different scales in a
single multiple regression.
(2) The requirement for normality is a requirement for the distribution of
residuals of the regression, not a requirement for the distribution of the
independent variables. This being said, in general, if the independent
variables are normally distributed it is more likely that the residuals will
be normally distributed. After performing a regression it is always wise to
look at the distribution of the residuals to make sure that they conform to
the normality assumption.
John
John Sorkin M.D., Ph.D.
Chief, Biostatistics and Informatics
Baltimore VA Medical Center GRECC and
University of Maryland School of Medicine Claude Pepper OAIC
University of Maryland School of Medicine
Division of Gerontology
Baltimore VA Medical Center
10 North Greene Street
GRECC (BT/18/GR)
Baltimore, MD 21201-1524
410-605-7119
NOTE NEW EMAIL ADDRESS:
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>>> "Ali A. Bromideh" <[log in to unmask]> 01/09/06 4:33 AM >>>
A friend of mine has got two enquiries about regression, would you please
help him on these questions? You can simply reply to me, NOT to AllStat!
"...Some methodology books talk about using dummy variables (nominal or
ordinal scales) in regression, my question is that: can I use dummy
variables together with interval variables in the one multiple regression
test (e.g. see if sex (male/female), salary, and age affect level of
creativity in advertising). I personally don't feel that it is right to use
both types of scales in one multiple regression test, but I still didn't
find luck in finding a reference to support that ( I might be wrong). Any
help!
The other question is about the normality assumption in regression, some
scholars say that only the dependent needs to be normally distributed, and
that it is ok if the independent is not normal. Does any one have a strong
argument (reference) to support or reject this opinion? ..."
Regards,
ALI
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