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Topic: Multiple regression with all dummy variables
Replies: 7   Last Post: Feb 15, 2013 4:17 PM

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Gary

Posts: 73
Registered: 9/6/07
Re: Multiple regression with all dummy variables
Posted: Dec 11, 2012 5:22 PM
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On Tuesday, 11 December 2012 20:20:48 UTC+2, paul wrote:
> Does a multiple regression with all dummy (indicator) variables make
>
> sense? I work at a state university tutoring various basic subjects
>
> including college algebra, first semester calculus, and a two-semester
>
> "Statistics for Business and Economics" sequence. In recent years my
>
> students have been taught that an alternative to using the ANOVA
>
> technique is to run a multiple regression analysis using all dummy
>
> variables. A recent example given as a study guide for the final exam
>
> was a comparison of used-car prices by color (white, black, blue, or
>
> silver.) Both ANOVA and a multiple regression (with black as the
>
> excluded category) reject the null hypothesis that there is no
>
> difference in prices by color. But the students are then told that the
>
> multiple regression gives more information since we can conclude from
>
> the t-tests on individual coefficients that silver cars sell for more
>
> than the base case (black.) I thought you needed at least one measured
>
> (scalar?) variable among the explanatory variables -- it makes no
>
> sense to do a scatter plot on just a dummy variable, so what on earth
>
> is this "line" (or surface) you are getting from the regression?
>
>
>
> So, is having at least one measured explanatory variable a basic
>
> requirement for regression? Has anyone proven that the individual
>
> coefficients on an all-dummy variable regression have no meaning?
>
> Perhaps they follow a well-defined distribution, which might not be
>
> Student's t. Any easy on-line sources? I did not see anything in basic
>
> article on regression in wikipedia.
>
>
>
> I'll mention that previously students were taught that, according to
>
> the Central Limit Theorem, if you are doing hypothesis testing on a
>
> mean and you have more than 30 or 40 data points, it's OK to assume
>
> your test statistic is normally rather than t-distributed. They've
>
> abandoned that nonsense, but I'm sceptical about these all-dummy
>
> regressions.
>
>
>
> Thanks for any help!


I think you can find some of the argument in

Cohen, J. (1968). Multiple regression as a general data-analytic system. Psychological Bulletin, 70, 426-443.

Also Cohen's famous textbook.

Lance



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