Date: Tue, 13 Sep 2005 11:00:30 -0300
Reply-To: Hector Maletta <firstname.lastname@example.org>
Sender: "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
From: Hector Maletta <email@example.com>
Subject: Re: Logarithmic transformation of not normal data
Content-Type: text/plain; charset="iso-8859-1"
1. Your variables do not need to be normally distributed in order to use
regression, and even less so in order to get high correlation coefficient.
You are confused by the fact that linear regression requires that residuals,
i.e. random errors of prediction (difference between predicted and observed
values) have a normal distribution both sides of the regression line.
2. A low or near zero linear [multiple] correlation coefficient may be due
to (a) the absence of any systematic relationship between your IV and DV, or
(b) the existence of a relationship which is non linear. As an example of
(b), if your scatterplot shows a cloud of points with the shape of a U,
there would be possibly a quadratic relationship but the linear coefficient
may be zero.
3. The method of least squares to estimate regression functions is based on
the assumption of a linear relationship between the variables involved. When
the relationship is not linear there are two ways to go: (i) identify the
non-linear function linking the variables, and transform it in some way that
yields a linear function, then apply least squares linear regression; or (b)
approximate a non linear function by means of non-linear regression or
curve-fitting, which do not use the least squares algorithm. Some non linear
functions are amenable to linearization, some are not. For instance, a
quadratic equation like y=a+bX+cX^2 can be linearized if you define a new
variable Z=X^2, and use the linear equation y=a+bX+cZ; likewise the equation
y=aX^b can be linearized by taking logarithms as log y=log a + b(log X).
4. The fact that a certain mathematical function fits your data is no great
deal. You can always find some function that does that. The trick is finding
a function for which you have a theoretical explanation. So it is not
advisable to go around blindly trying different mathematical functions until
any of them "fits". In fact, you may find several, perhaps an infinite
number of functions that reasonably fit the data, and that is arguably worse
than not having any.
5. If no reasonable function fits the shape of the data, perhaps your data
just show little relationship at all between the variables...
> -----Original Message-----
> From: SPSSX(r) Discussion [mailto:SPSSX-L@LISTSERV.UGA.EDU]
> On Behalf Of Razan
> Sent: Monday, September 12, 2005 11:04 PM
> To: SPSSX-L@LISTSERV.UGA.EDU
> Subject: Logarithmic transformation of not normal data
> I've made a multiple linear regression using SPSS by one
> dependent variable and two indepent variables and all
> assumptions were satisfied but R squre is very low about
> 0.3,so I think that is because my variable are not normally
> distributed that's why I was thinking about transforming my
> data uasing logarithmic transformation to normal distributio
> and repeat the regression,but I don't know how to transform them?
> and do I have to test any other assumptions after applying
> the transformation?]
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