Qual Quant (2009) 43:59–74
Linear versus logistic regression when the dependent
variable is a dichotomy
Published online: 16 February 2007
© Springer Science+Business Media B.V. 2007
Abstract The article argues against the popular belief that linear regression should
not be used when the dependent variable is a dichotomy. The relevance of the statis-
tical arguments against linear analyses, that the tests of signiﬁcance are inappropriate
and that one risk getting meaningless results, are disputed. Violating the homoscedas-
ticity assumption seems to be of little practical importance, as an empirical compari-
son of results shows nearly identical outcomes for the two kinds of signiﬁcance tests.
When linear analysis of dichotomous dependent variables is seen as acceptable, there
in many situations exist compelling arguments of a substantive nature for preferring
this approach to logistic regression. Of special importance is the intuitive meaning-
fulness of the linear measures as differences in probabilities, and their applicability in
causal (path) analysis, in contrast to the logistic measures.
Keywords Logistic regression · Binary variables · Signiﬁcance tests
In analyses of survey data it is not unusual that the dependent variable is a dichot-
omy. When the research problem requires a multivariate solution, regression analysis
is very convenient for handling large numbers of independent variables.
seems to be a common belief that with a binary dependent variable (dichotomy coded
This opportunity is sometimes overexploited, however. A regression analysis of binary variables
does not have access to information that is lacking in the corresponding tabular analysis. When more
variables may be included in the regression analysis, this is due to the distributional assumptions on
which the regression analysis is based. With a large number of variables one runs the risk that an
estimate reﬂects the model more than the data. (Rubin 1997; Rothman and Greenland 1998).
O. Hellevik (
Department of Political Science, University of Oslo, P.O. Box 1097, 0317, Blindern, Oslo, Norway