How robust is linear regression with dummy variables ?
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Researchers in education and the social sciences make extensive use of linear regression models in which the dependent variable is continuous-valued while the explanatory variables are a combination of continuous-valued regressors and dummy variables. The dummies partition the sample into groups, some of which may contain only a few observations. Such groups may easily contain enough outliers to break down the parameter estimates. Models with many fixed or random effects appear to be especially vulnerable to outlying data. This paper discusses the problem at an intuitive level and cites sources for the key theorems establishing bounds on the breakdown point in models with dummy variables.