Mike wrote in message <8ffek1$1q2$[EMAIL PROTECTED]>...
>I would like to obtain a prediction equation using linear regression for
>some data that I have collected. I have read in some stats books that
>linear regression has 4 assumptions, 2 of them being that 1) data is
>normally distributed and 2) constant variance. In SAS, I have run
>univariate analysis testing for normality on both my dependent and
>independent variable (n=147). Both variables have distributions that are
>skewed.
>
>For the dependent variable: skewness=0.69 and Kurtosis=0.25.
>For the independent variable: skewness=0.52 and Kurtosis= -0.47.
>
>The normality test (Shapiro-Wilk Statistic) states that both the dependent
>and independent variables are not normally distributed.
>
>I have also transformed the data (both dependent and independent variables)
>using log, arcsine, and square root transformations. When I run the
>normality tests on the transformed data, the test shows that even the
>transformed data is not normally distributed.
>
>I realize that I can use nonparametric tests for correlation (I will use
>Spearman), but is there a nonparametric linear regression? If not, is it
>acceptable to use linear regression analysis on data that is not normally
>distributed as a way to show there is a linear relationship?
>
>thanks in advance..Mike
>
The importance of normality is grossly over-emphasized.
If you have grossly long tails - in the residuals - or if there
are outliers, then you may have to look at more robust forms
of regression than least squares. Auto-correlations amongst
consecutive observations, or lack of homogeneity of variance
are often more important than non-normality.
There is absolutely no requirement that the predictors (or
independent variables) should have a normal distribution, in fact
the opposite. Ideally, the predictors should be from a designed
experiment and hence will not even be random. Most of them
should be towards the outer bounbaries of the predictor space.
I guess that most designed experiments would give negative
kurtoses if you go through the mechanics of calculating
coefficients of kurtosis. If the predictors are from a multivariate
normal distribution, then there is far too much clustering in the
centre of the design space. Quite often, some of the predictors
are discrete - perhaps (0,1) variables, and hence cannot have
normal distributions.
--
Alan Miller, Retired Scientist (Statistician)
CSIRO Mathematical & Information Sciences
Alan.Miller -at- vic.cmis.csiro.au
http://www.ozemail.com.au/~milleraj
http://users.bigpond.net.au/amiller/
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