In the earlier course we use simple linear models to explain the dependence of a variable Y on a variable X . For example, Y might represent the systolic blood pressure for each member of a group of patients treated for hypertension and the variables we use to explain blood pressure may be the patients' ages, weights, smoking habits, and gender. They also learn to recognize outliers , data points the model does not fit well, and influence points , data points whose presence in the data set has an important impact on the values of model parameters.
Students study four statistical methods for selecting the best fitting model for the data.
All possible subsets, forward selection, backward elimination, and stepwise regression. Residual and influence analysis help us study the effects of individual observations on the model and help us check model fit. A semester-long, group project forms a major component of the course work. In groups of two to four, students select a research question that can be studied using a linear model. Groups prepare a research proposal that must be approved by the instructor before data collection can begin.