Timothy McDaniel

The goal is to develop an applied and intuitive (not purely theoretical or mathematical) understanding of the topics and procedures, so that participants can use them in their own research and also understand the work of others. Whenever possible presentations will be in “Words,” “Picture,” and “Math” languages in order to appeal to a variety of learning styles. Advanced regression topics will be covered only after the foundations have been established. The ordinary least squares multiple regression topics that will be covered include: -Various F‑tests (e.g., group significance test; Chow test; relative importance of variables and groups of variables; comparison of overall model performance) -Categorical independent variables (e.g., new tests for “Intervalness” and “Collapsing”) -Dichotomous dependent variables: Logit and Probit analysis -Outliers, influence, and leverage -Advanced diagnostic plots and graphical techniques -Matrix algebra: A quick primer (Optional) -Regression models… now from a matrix perspective -Heteroskedasticity: Definition, consequences, detection, and correction -Autocorrelation: Definition, consequences, detection, and correction -Generalized Least Squares (GLS) and Weighted Least Squares (WLS).

The primary goal is to develop an applied and intuitive (as opposed to purely theoretical or mathematical) understanding of the topics and procedures. Whenever possible presentations will be in “Words,” “Picture,” and “Math” languages in order to appeal to a variety of learning styles. Some more advanced regression topics will be covered later in the course, but only after the introductory foundations have been established. We will begin with a quick review of basic univariate statistics and hypothesis testing. After that we will cover various topics in bivariate and then multiple regression, including: • Model specification and interpretation. • Diagnostic tests and plots. • Analysis of residuals and outliers. • Transformations to induce linearity. • Interaction (“Multiplicative”) terms. • Multicollinearity. • Dichotomous (“Dummy”) independent variables. • Categorical (e.g., Likert scale) independent variables.

These intensive workshop lectures provide an opportunity for GSERM participants to learn matrix algebra and some applied mathematics skills from a broad and generalizable perspective. The lectures are designed to serve both as an introduction for participants who are new to this material and also as a refresher for those previously exposed to it. The goal is for participants to possess a sufficient level of understanding of these topics so that they can adequately comprehend, and then successfully apply, them in subsequent GSERM courses. In addition to the Lectures, several handouts, problem sets, and solution keys will be provided (via email) to enhance the learning process and provide for self-evaluation opportunities. Proficiency in basic mathematics (e.g., rudimentary algebra) is assumed.

These intensive Workshop Lectures provide an opportunity for participants to refresh their understanding of, and familiarity with, the concepts and assumptions of ordinary least squares (OLS) Regression. The goal is to possess a sufficient level of understanding of these topics so that participants can adequately comprehend and successfully apply them in subsequent GSERM courses. The Workshop Lectures are designed to develop an applied and intuitive (as opposed to purely theoretical or mathematical) understanding of Regression. Whenever possible, presentations will be in “Words,” “Picture,” and “Math” languages in order to appeal to a variety of learning styles. In addition to the Lectures, several handouts, problem sets, and solution keys will be provided (via email) to enhance the learning process and provide for self-evaluation opportunities. It is assumed that the participants are proficient in rudimentary statistics (e.g., hypothesis testing). While it might be helpful to have some experience with OLS Regression, this is NOT a prerequisite! Though I know it is probably not true, we will start under the assumption that you have never seen Regression before. Then we will (quickly) move on to topics that you might or might not have seen.