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Multiple Regression Analysis: Estimation, Diagnostics, and Modelling

Course Dates and Times

Monday 5 – Friday 9 August

14:00–15:30 & 16:00–17:30 (ending slightly earlier on Friday)


Michael Dorsch

Central European University

Alexandru Moise

European University Institute

This short course is an introduction to regression analysis.

You will learn the classical theory of Ordinary Least Squares (OLS) regression and we will introduce applied methods in regression analysis using the statistical software package Stata.

After introducing simple linear regression, the course considers multiple linear regression and concludes with non-linear regression techniques. In-class applications will use a variety of policy-oriented datasets.

A solid understanding of OLS regression in theory and practice gives you the foundation for courses in more advanced regression analysis techniques. Integrating theory with the application of regression analysis and interpretation of regression output, this course provides you with such a foundation.

ECTS Credits for this course and, below, tasks for the additional credits.

To receive the further 1 or 2 credits, four applied homework assignments will be set during the week for completion. Three of the four assignments are required for an additional credit, and all four are required for two additional credits.

Instructor Bio

Michael Dorsch is associate professor of Economics at CEU's School of Public Policy, where he teaches Applied Regression Analysis, Public Choice, and Public Sector Economics.

Michael is an applied economist whose research covers a variety of topics in political economics.


Alexandru Moise is a postdoctoral researcher at the European University Institute (2020–2025). He received his PhD in political science from Central European University in 2019. Alex's research focus is the political economy of welfare reforms. He looks at how individual perceptions and the quality of party linkages affect health care policy. Within the context of the ERC SOLID project, he looks at how crises affect European integration using a variety of quantitative models. He has been teaching quantitative analysis courses at Johns Hopkins University, the European University Institute, Central European University, Ilija University, and the ECPR’s Summer and Winter Schools for many years.


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.

Day Topic Details
1 Overview of regression analysis, introduction to R, and difference of means tests
2 The simple linear regression: (i) deriving and interpreting coefficients, (ii) hypothesis testing and the structure of errors
3 The multiple linear regression model: (i) omitted variables, (ii) model specification, (iii) multicolinearity
4 Non-linear regression functions: (i) quadratic regression, (ii) logartihmic regression, (iii) interaction terms
5 Further topics in regression analysis: (i) limited dependent variables, (ii) panel data, (iii) instrumental variables
Day Readings

S&W, chapters 1 – 3


S&W, chapters 4 – 5, and Assignment 1


S&W, chapters 6 – 7, and Assignment 2


S&W, chapter 8, and Assignment 3


S&W, chapters 10 – 12, and Assignment 4


From Introduction to Econometrics – Global Edition
James Stock and Mark Watson, 2012 (on reserve at CEU library)

Software Requirements

R and R Studio

Hardware Requirements

Please bring your own laptop.


Field, A., Miles, J., & Field, Z. (2012)
Discovering Statistics Using R (1st edition)
London; Thousand Oaks, Calif.: SAGE Publications Ltd

Torfs, P., & Brauer, C. (2014)
A (very) short introduction to R
Hydrology and Quantitative Water Management Group, Wageningen University, The Netherlands

An economist’s guide to visualizing data, Journal of Economic Perspectives, Jonathan Schwabish, 2014

Recommended Courses to Cover Before this One

Summer School

R Basics SA101

Introduction to Inferential Statistics: What you need to know before you take regression SD001