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, 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 emphasises data analysis and interpretation using the statistical software R.

The course begins with a (very) brief review of the necessary ingredients from probability and statistics. From day one, you will learn the basic functionality of statistical software through application, starting with the generation of descriptive statistics and graphics.  Note that while we will provide R scripts with all the necessary code, this is not a class about programming, so some familiarity with R is required.

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.

Because 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 demonstrating the ‘statistical significance’ of estimated regression results.

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

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

You need basic understanding of statistics and probability theory. 

If you do not know the basics of inferential statistics (variance, central limit theorem, z and t test, correlation), take Levi Littvay's course Introduction to Inferential Statistics: What you need to know before you take regression first.