This is a book about regression analysis, that is, the situation in
statistics where the distribution of a response (or outcome) variable is
related to - planatory variables (or covariates). This is an extremely
common situation in the application of statistical methods in many
?elds, andlinear regression, - gistic regression, and Cox proportional
hazards regression are frequently used for quantitative, binary, and
survival time outcome variables, respectively. Several books on these
topics have appeared and for that reason one may well ask why we embark
on writing still another book on regression. We have two main reasons
for doing this: 1. First, we want to highlightsimilaritiesamonglinear,
logistic, proportional hazards,
andotherregressionmodelsthatincludealinearpredictor. These
modelsareoftentreatedentirelyseparatelyintextsinspiteofthefactthat
alloperationsonthemodelsdealingwiththelinearpredictorareprecisely the
same, including handling of categorical and quantitative covariates,
testing for linearity and studying interactions. 2. Second, we want to
emphasize that, for any type of outcome variable, multiple regression
models are composed of simple building blocks that
areaddedtogetherinthelinearpredictor: thatis, t-tests, one-wayanalyses
of variance and simple linear regressions for quantitative outcomes,
2×2, 2×(k+1) tables and simple logistic regressions for binary outcomes,
and 2-and (k+1)-sample logrank testsand simple Cox regressionsfor
survival data. Thishastwoconsequences. Allthesesimpleandwellknownmethods
can be considered as special cases of the regression models. On the
other hand, the e?ect of a single explanatory variable in a multiple
regression model can be interpreted in a way similar to that obtained in
the simple analysis, however, now valid only for the other explanatory
variables in the model "held ?xed".
