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First Draft of the paper - University of Toronto

First Draft of the paper - University of Toronto

First Draft of the paper - University of

Inflation of Type I error in multiple regressionwhen independent variables are measured witherrorLawrence J. Brunner ∗Department of Statistics, University of Toronto100 St. George St.Toronto M5G 3G3, Canadaemail: brunner@utstat.toronto.eduphone: 905-828-3816; fax: 905-828-5425Peter C. AustinInstitute for Clinical Evaluative Sciences2075 Bayview Avenue, Toronto M4N 3M5, CanadaMay 25, 2007AbstractIt is well known that when independent variables are measuredwith error, ordinary least squares regression can produce parameterestimates that are biased, even asymptotically. In most observationalstudies, independent variables are measured with error, but ordinaryregression methods are applied anyway. This practice is reinforced bythe examples and sample data sets found in most regression texts.The present paper is focused upon Type I error. We consider thefamiliar case in which two independent variables are correlated andmeasured with error, and an attempt is made to test one of the independentvariables while “controlling for” the other one by usual∗ Supported in part by Natural Sciences and Engineering Research Council of CanadaGrant OGPIN 0141

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