Multiple Regression Analysis: Estimation, Diagnostics, and Modelling

This class provides an intuitive and practical introduction to linear regression, the workhorse method of applied econometrics and a fundamental statistical technique for research in the quantitative social sciences. Often times, researchers are interested in using samples of data to investigate relationships between variables. Regression analysis is a process of finding the mathematical model that best fits the data. This is an applied course that emphasizes data analysis and interpretation using statistical software.

The course begins with a (very) brief review of the necessary ingredients from probability and statistics. From day one, students will learn the basic functionality of statistical software through application, starting with the generation of descriptive statistics and graphics. After this introduction, we will begin with the simple regression model, starting with a theoretical derivation of coefficient estimates in the Ordinary Least Squares (OLS) regression model and an overview of their properties. The assumptions that underlie the validity of a simple linear regression model will also be discussed, before moving on to statistical inference. As regression typically operates with samples of data from an underlying population of observations, a key element to regression analysis is understanding when the relationships estimated for the sample can be used to make inferences about the population. In practice, this is often referred to as establishing the “statistical significance” of estimated regression results.

Once a solid understanding of the simple linear regression model has been established, the course moves on to multiple linear regression, which allows for more than one explanatory variable. Within the context of multiple regression, particular attention will be paid to identifying models that provide the most credible estimate of the explanatory variable of interest. Time-permitting, non-linear regression models and other more advanced regression techniques will also be introduced.

This is a hands-on, applied course where students will become proficient at using computer software to analyze data drawn primarily from the fields of economics and political science. There will be homework assignments following each class session, which we will discuss as a class at the beginning of the next meeting. If you fully apply yourself in this course and complete all of the homework, you will have the opportunity to master the basic methods of regression analysis and you will become a confident user of statistical software for computing linear regressions and interpreting their results.

This course requires a basic understanding of statistics and probability theory.  Anyone who does not have strong training in the basics of inferential statistics (variance, central limit theorem, z and t test, correlation) must take SD001A first.