Mike...........regression assumptions are more concerned with distributional
characteristics of the errors than the actual raw score, in that if
residuals are normally distributed, there is a constancy of variation of the
errors across the x axis (i.e., homescedasticity), etc., then non-normality
of the criterion variable is not problematic. However, there may be
occasions when violations of the error assumptions ensue and transformation
of the criterion variable serves in coaxing normality.............dale
glaser
-----Original Message-----
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]]
On Behalf Of Mike
Sent: Thursday, May 11, 2000 3:39 PM
To: [EMAIL PROTECTED]
Subject: normality and regression analysis
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
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