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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


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 twosemester > > "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 usedcar 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 ttests 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 alldummy variable regression have no meaning? > > Perhaps they follow a welldefined distribution, which might not be > > Student's t. Any easy online 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 tdistributed. They've > > abandoned that nonsense, but I'm sceptical about these alldummy > > regressions. > > > > Thanks for any help!
I think you can find some of the argument in
Cohen, J. (1968). Multiple regression as a general dataanalytic system. Psychological Bulletin, 70, 426443.
Also Cohen's famous textbook.
Lance



