The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Test constantness of normality of residuals from linear regression
Replies: 8   Last Post: Jan 10, 2013 6:09 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]

Posts: 517
Registered: 2/23/10
Re: Test constantness of normality of residuals from linear regression
Posted: Jan 10, 2013 11:20 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Jan 10, 6:50 am, "David Jones" <> wrote:
> "Paul" <> wrote in message

> > After much browsing of Wikipedia and the web, I used both normal
> > probability plot and Anderson-Darling to test the normality of
> > residuals from a simple linear regression (SLR) of 6 data points.
> > Results were very good.  However, SLR doesn't just assume that the
> > residuals are normal.  It assumes that the standard deviation of the
> > PDF that gives rise to the residuals is constant along the horizontal
> > axis.  Is there a way to test for this if none of the data points have
> > the same value for the independent variable?  I want to be able to
> > show that there is no gross curves or spreading/focusing of the
> > scatter.

> > In electrical engineering signal theory, the horizontal axis is time.
> > Using Fourier Transform (FT), time-frequency domains can show trends.
> > Intuitively, I would set up the data as a scatter graph of residuals
> > plotted against the independent variable (which would be treated as
> > time).  Gross curves show up as low-frequency content.  There should
> > be none if residuals are truly iid.  The spectrum should look like
> > white noise.  The usual way to get the power spectrum is the FT of the
> > autocorrelation function, which itself should resemble an impulse at
> > zero.  This just shows indepedence of samples, not constant iid normal
> > along the horizontal axis.

> > As for spreading or narrowing of the scatter, I guess that can be
> > modelled in time as a multiplication of a truly random signal by a
> > linear (or exponential) attenuation function.  The latter acts like a
> > modulation envelope.  Their power spectrums will then convolve in some
> > weird way.  I'm not sure if this is a fruitful direction for
> > identifying trends in the residuals.  It starts to get convoluted
> > pretty quickly.

> > Surely there must be a less klugy way from the world of statistics?  I
> > realize that my sample size will probably be too small for many
> > conceptual approaches.  For example, if I had a wealth of data points,
> > I could segment the horizontal axis, then do a normality test on each
> > segment.  This would generate mu's and sigma's as well, which could
> > then be compared across segments.  So for the sake of conceptual
> > gratification, I'm hoping for a more elegant test for the ideal case
> > of many data points.  If there is also a test for small sample sizes,
> > so much the better (though I don't hold my breath).

> Wikipedia outlines a number of tests, which you can find by starting from

Thanks, David! I'm off on another educational path of exploration.

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.