Hi Mike.
For the most popular linear regression Ordinary least squares (OLS), you
also need to have your X variable (i.e. the independent variable) having a
relatively small error. Your initial work suggests large-ish error in both
variables with non-normal error structure. This makes things a little more
complicated. Do you suspect that the errors correlated (i.e. if error in X
is +d, then is error in Y usually +f ), are they of similar size are they
changing with the size of X ?
A formal way forward may be the use of structural equations (SAS PROC MIXED
may help).
IF you just need something quite reliable, then there are some
non-parametric regression methods (Deming, Passing+Bablock) which give you
quite robust estimates... For a hint, try forming the set of all slopes
from joining any two points in your set, then look at the median of the set
of slopes (and then the 95th and 5th percentile slope estimates). Then try
the same for intercepts. This should give you a workable figure...
HTH
Dan
Mike <[EMAIL PROTECTED]> wrote in article <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
>
>
>
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