Linear Regression with R: Estimation, Interpretation and Presentation

If you want to move on to complex analyses and statistical models, you need to get the simple things right first. This course will familiarise you with the basic statistical concepts that will enable you to fully and correctly use the framework of linear regression. 

By the end of the course you will have the theoretical and practical skills to responsibly run multivariate linear regressions on a variety of data configurations. This includes estimating multiple model specifications in R, presenting results in tables or in a graphical format and interpreting the coefficients for the reader. It also implies assessing the appropriateness of OLS regression for certain kinds of data and learning to make suitable corrections and adjustments when there is a mismatch between model requirements and data characteristics.

The basic introductory course in statistics usually gets to regression at the very end (if it goes further than that, then the speed of the course was probably too high). This course is for those who have got to that point but have not moved on much further. We will not focus too much on theory, but put the emphasis on correct application and interpretation. You don't need to know the mathematics that happens behind the scenes to understand what a regression model does and what it is capable of doing. 

The course is also suitable for those who have briefly encountered OLS regression as part of a statistics class, but now wish to better understand how it works, where it breaks down, and how it can be applied in a thorough way. Due to the need to constantly focus on the application of linear models, the course is unsuitable for those who want an introductory course in general statistics. During one of the sessions we briefly cover some basic statistical concepts and tests, but this is only so that we can all delve into the topic of linear models from an equal footing. This cannot be considered a substitute for a good coverage of introductory statistics.

Day 1
We start with a condensed review of some fundamental concepts in basic statistics: the z and t distributions, hypothesis testing, confidence intervals and correlation. This overview is intended to provide a solid foundation from which to advance in the following days. We begin to discuss a few basics of regression, such as how it goes beyond correlation, and for what type of questions it is helpful. In the lab session, we will go through a few of the basic data manipulation procedures commonly required before running any regression: data cleaning and recoding, transformations of data, etc. This is a good opportunity for you to get familiar, if need be, with working with syntax files in R and with the RStudio interface.

Day 2
We delve fully into the fundamentals of Ordinary Least Squares (OLS) regression: how the estimation is carried out, and how we interpret the coefficients for simple (one predictor) and multiple regression (two or more predictors). I will present some basic formulas, but the goal will be to gain an intuitive understanding of how the estimation process functions, and what the results mean. In the lab session we put this newly-gained knowledge to the test, by running a few examples of linear models in R. We will interpret the output and the model fit.

Day 3
We advance in our understanding of OLS by focusing on model specifications that almost always appear in empirical research, like models with dummy variables and with interactions between variables. We discuss the interpretation of such models and how you ought to communicate it to your audience. In the lab component we learn how to run these model specifications with R.

Day 4
This day is devoted to preventing abuse in the estimation of linear models. As with the vast majority of statistical procedures, a series of assumptions underpins OLS regression. If these are not met, our results may deceive us. In this session we go over these assumptions, how they influence the results when they are not met, and what strategies we have to overcome this situation. In the lab we turn to these issues from a practical perspective. We run a test regression in R, assess whether the assumptions are met, and correct for assumption violations that exist (if possible). Through a step-by-step process, you will see how your estimates and model fit change when engaging in such a process.

Day 5
On the last day we look into the various ways regression results can be presented. A properly formatted and thought through regression table is a must, but sometimes that is not enough. In fact, I would say that almost always it is not enough for an effective presentation of your models and your conclusions. For that it is necessary to visualise your results. This is especially true for interactions and non-linear effects. While tables of coefficients are still the dominant way of presenting results in academic journals, graphs and predicted values tend to be preferred in reports and analyses for larger, non-technical audiences. I believe strongly that you should be familiar with both types and should tailor the delivery of your results to the audience.

This course presumes a basic knowledge of fundamental statistical concepts such as hypothesis testing and comparison of means (t-tests).

If you have no background in statistics, you should also take Florian Weiler's course Introduction to Statistics for Political and Social Scientists. 

The class will be carried out in R. Therefore, you should have a basic knowledge of R as a statistical programming language and of RStudio.

The class assumes that you know how to read in data and a knowledge of basic data management skills as well as basic plotting commands.

If you have no experience with R, you should also take Thorsten Schnapp's short entry-level Introduction to R course.