MTH 247: Introduction to Regression Analysis

This course continues the study of linear models that begins in MTH 245: Introduction to Probability and Statistics. In the earlier course we use simple linear models to explain the dependence of a variable $Y$ on a variable $X$. In MTH 247 we use linear models with several predictor variables ( $X_{1}, \ldots, X_{P}$) to explain the behavior of the outcome variable $Y$. 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.

The course includes Analysis of Variance (ANOVA) and Analysis of Covariance (ANCOV) models. Generally speaking, when the $X$ variables are continuous (e.g. weight) we have Regression Analysis models. If all the $X$'s are categorical (e.g. gender (Male/Female), smoking (YES/NO), we have ANOVA models, and when we have both continuous and categorical $X$ variables we have ANCOVA models (both of which are more formally proper subsets of regression).

Students learn to estimate model parameters, to measure the amount of variability in the outcome variable $Y$ explained by the collection of predictor variables ( $X_{1}, \ldots, X_{P}$), and to test the model's fit to the data. 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. They may gather their own data or use secondary data (collected by others) to study their question. Groups prepare a research proposal that must be approved by the instructor before data collection can begin. They write an interim report on their progress due at midterm, and a final report on their findings, due on the last day of class. Groups give oral reports to their classmates on their proposals and on their findings. Sometimes other faculty or outsiders with interest in particular projects attend these presentations. Techniques for oral presentation of quantitative information may be discussed in class when groups are preparing for these talks. Techniques for writing technical reports are also emphasized.