```Date: Dec 11, 2012 1:20 PM
Author: paul
Subject: Multiple regression with all dummy variables

Does a multiple regression with all dummy (indicator) variables makesense? I work at a state university tutoring various basic subjectsincluding college algebra, first semester calculus, and a two-semester"Statistics for Business and Economics" sequence. In recent years mystudents have been taught that an alternative to using the ANOVAtechnique is to run a multiple regression analysis using all dummyvariables. A recent example given as a study guide for the final examwas a comparison of used-car prices by color (white, black, blue, orsilver.)  Both ANOVA and a multiple regression (with black as theexcluded category) reject the null hypothesis that there is nodifference in prices by color. But the students are then told that themultiple regression gives more information since we can conclude fromthe t-tests on individual coefficients that silver cars sell for morethan the base case (black.) I thought you needed at least one measured(scalar?) variable among the explanatory variables -- it makes nosense to do a scatter plot on just a dummy variable, so what on earthis this "line" (or surface) you are getting from the regression?So, is having at least one measured explanatory variable a basicrequirement for regression? Has anyone proven that the individualcoefficients on an all-dummy variable regression have no meaning?Perhaps they follow a well-defined distribution, which might not beStudent's t. Any easy on-line sources? I did not see anything in basicarticle on regression in wikipedia.I'll mention that previously students were taught that, according tothe Central Limit Theorem, if you are doing hypothesis testing on amean and you have more than 30 or 40 data points, it's OK to assumeyour test statistic is normally rather than t-distributed. They'veabandoned that nonsense, but I'm sceptical about these all-dummyregressions.Thanks for any help!
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