----- Original Message -----
From: Herman Rubin <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Wednesday, May 03, 2000 8:20 AM
Subject: Re: no correlation assumption among X's in MLR
> In article <[EMAIL PROTECTED]>,
> Alan McLean <[EMAIL PROTECTED]> wrote:
> >'No collinearity' *means* the X variables are uncorrelated!
>
> >The basic OLS method assumes the variables are uncorrelated (as you say).
In
> >practice there is usually some correlation, but the estimates are
reasonably
> >robust to this. If there is *substantial* collinearity you are in
trouble.
>
> The basic OLS method assumes NOTHING about the correlation
> of the X variables, as long as there is no linear combination
> which is constant. Polynomial regression almost always has
> the X variables correlated.
>
> If, for example, X_1 and X_2 are the "independent" variables,
> and X_2 is replaced by X_2 + X_1, the coefficients would be
> different, but the regression equation would be the same.
.....................................................................
Herman, you are not entirely right.
The problem with colinearity is the effect it has on the computations. If I
had an infinite computer that did the OLS with numbers having an infinitie
number of digits, you would be right.
On real computers using black box computer programs, each computer program
will give a different number, depending on whether it uses single, double or
quad precision, on the peculiarities of the algorithms in the programs
(there are very many ways to do OLS), on the rounding used to present the
answer, and on which chip set is being used (Intel, Sun....., HP...., they
all have different internal representations of floating point numbers).
DA Heiser
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