Re: non normal distribution and regressions
- From: Beliavsky <beliavsky@xxxxxxx>
- Date: 19 Apr 2007 05:34:27 -0700
On Apr 18, 11:39 am, Bruce Weaver <bwea...@xxxxxxxxxxxx> wrote:
joseph Frank wrote:
Hi,
If the distribution of y variable is not normal. (skewness equal to 1.1 and kurtosis to 8.2) can i run a simple linear regression of the y on x variables?
J
It is the residuals from your model (actual Y - predicted or fitted Y)
that should be approximately normal, not Y itself. A Q-Q plot of the
residuals is a good way to assess this.
One can do a regression where the distribution of residuals is non-
normal. One generalization is to assume that distribution is a finite
*mixture* of normals. A further generalization is a mixture of
regression models, in which the regression coefficients and not just
the properties of the residuals are allowed to differ across regimes.
The mixreg package of R implements this model. Googling "mixture
regression" produces relevant hits. Nonlinearity in the relationship
between a response and its predictors does not imply non-normality of
residuals, and non-normality of residuals does not by itself prove a
nonlinear relationship.
.
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