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