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.