Students will gain an understanding of the mathematical 
foundations as well as practical implementation in R and 
possibly other statistical software of the ideas and concepts 
associated with linear regression. In the context of linear 
regression, they will learn how to use specific statistical 
methods and general modes of statistical thinking to make 
inferences from data, and to support (or refute) an argument 
or point of view with quantitative information. The emphasis 
is not as much on theoretical properties as on understanding 
and applying regression techniques, on being able to build an 
appropriate regression model in R, on being able to assess the 
adequacy of a proposed model, and on drawing and formulating 
conclusions from the fitted model. They will also learn how to 
assess the relative merits and applicability of competing 
models and variable choices using AIC, BIC, cross-validation, 
and other penalty measures. Residual analysis, including 
leverage and influence measures, will be used to diagnose the 
fit of the model. They will also get a brief introduction to 
nonlinear regression, especially generalized linear regression 
models. Time permitting, special topics will be chosen from 
ridge regression, survival methods for censored time-to-event 
data, linear mixed models, non-linear mixed effects models, 
and generalized estimating equations.

After a brief review of techniques, concepts, and mathematical 
examination of the model assumptions associated with simple 
linear regression, the course provides an in-depth coverage of 
multiple linear regression. This includes model fitting, 
estimation and prediction, diagnostics and model adequacy 
checking, transformations, including Box-Cox, leverage and 
influence measures, including Cook’s distance, polynomial 
regression, indicator variables, collinearity, interaction 
terms, variable selection based on AIC, BIC, cross-validation 
and other measures, residual analysis, and model building. A 
brief introduction to generalized linear models, including 
logistic regression, is also provided. Time permitting, special 
topics will be chosen from ridge regression, survival methods 
for censored time-to-event data, linear mixed models, non-
linear mixed effects models, and generalized estimating 
equations. All procedures will be covered in R and possibly 
other statistical software packages.