Is there a direct relationship between the coefficient of variation
for a variable and the t statistic for the intercept(for a regression
that includes several explanatory variables modelling the original
variable)?

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Request for Question Clarification by jeremymiles-ga on 21 Apr 2003 01:49 PDT

What might cause the coefficient of variation to change?  Would it be
random sampling variation, or would it be that you are carrying out a
transformation of some sort on the variable?

jeremymiles-ga

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Clarification of Question by blurb-ga on 21 Apr 2003 04:00 PDT

Jeremy

I was thinking more of a series of variables, say product sales for
five different brands of coffee.  I'm wondering if its valid to make
an inference about a more stable 'base' for the brands that have a
lower cv?  With the data I have there seems to be a connection, and it
seems intuitive that it should be so, but I can't prove that this is a
wider, verifiable phenomenon.

Thanks

Robert

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Request for Question Clarification by jeremymiles-ga on 22 Apr 2003 03:04 PDT

Hello Blurb,

Can you explain a little more about your analysis.  The intercept is a
curious thing - it is affected by the scale of your measure(s), the
means, and the independent variables.  Sometimes it is meaningless,
other times useful.

jeremymiles-ga

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Clarification of Question by blurb-ga on 27 Apr 2003 13:28 PDT

jeremymiles

after some consideration i think i may have asked a non-question. i
think i'd like to clarify my question down to this: what
interpretation should i give to the t statistic of the intercept? is
it actually saying something about the stability of the mean?  if you
don't accept this as a clarification then let me know and i'll repost.

thanks

blurb

The t-statistic isn't telling you very much about the stability of the
mean - rather it is telling you about the likely difference between
the intercept and zero.

However, this doesn't necesarily make any sense, for two reasons:

1.  The intercept doesn't always make sense - the intercept is the
estimate of the value of the outcome variable, when all predictors are
equal to zero.  If it is not possible for some, or all, predictors to
be zero, it's not worth considering the intercept out of context.

2.  A transformation of the predictors can change the intercept - thsi
might happen if you change the reference category of a nominal
variable, or if you use a different zero point for your measure (many
measures have arbitrary zero points - e.g. earnings could use zero as
the zero, or could use the minimum wage, which is effectively zero).

If you are interested in the stability of the mean, I would consider
looking at the standard error.

jeremymiles-ga

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Clarification of Answer by jeremymiles-ga on 29 Apr 2003 05:48 PDT

I meant to add:

If you require more information, please don't hesitate to request
clarification.  Issues in regression can become complex quite fast.

jeremymiles-ga