```Date: Dec 11, 2012 5:35 PM
Author: Gary
Subject: Re: Multiple regression with all dummy variables

On Wednesday, 12 December 2012 00:22:38 UTC+2, Gary  wrote:> 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.> > > > LanceI can't find a PDF of the article but here is an account of its content:http://garfield.library.upenn.edu/classics1982/A1982PB23900001.pdfLance
```