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Introduction to Regression Analysis

Michael Dorsch

Central European University

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.


Course Dates and Times

Monday 1 to Friday 5 August 2016
Generally classes are either 09:00-12:30 or 14:00-17:30
15 hours over 5 days

Prerequisite Knowledge

This course requires a basic understanding of statistics and probability theory.  No prior experience working with statistical packages is required.

Short Outline

This short course is an introduction to regression analysis.  Students are exposed to the classical theory of Ordinary Least Squares (OLS) regression and introduced to applied methods in regression analysis using the statistical software package Stata.  After introducing the simple linear regression, the course then considers multiple linear regression and concludes with non-linear regression techniques.  The course also considers multiple linear regression and non-linear regression techniques.  In-class applications will use a variety of policy-oriented data-sets.  A solid understanding of OLS regression in theory and practice is the foundation for more advanced techniques in regression analysis. With its aim to integrate theory with the application of regression analysis and interpretation of regression output, the course provides students with such a foundation.

Long Course Outline

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 the statistical software package Stata.


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 Stata through application, starting with the generation of descriptive statistics and graphics.  After introducing Stata, 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 the Stata package for computing linear regressions and interpreting their results.

Day Topic Details
Monday Overview of regression analysis, difference of means tests, and introduction to Stata

90’ lecture:

  • What is regression analysis?

  • Statistical review and hypothesis testing

  • Difference of means test

90’ lab:

  • Introduction to Stata

  • Descriptive graphics

  • Generating variables

  • Difference of means tests
Tuesday The simple linear regression – deriving and interpreting regression coefficients

90’ lecture:

  • The logic of OLS and deriving regression coefficients

  • Interpreting regression coefficients

  • Binary explanatory variables

  • Measures of fit

  • Outliers

90’ lab:

  • Application using environmental data

  • Interpreting regression output

  • Generating regression graphics

  • Identifying and removing outliers
Wednesday The simple linear regression – hypothesis testing

90’ lecture:

  • Testing regression coefficient hypotheses

  • Confidence intervals, t-statistics, and p-values

  • Heteroskedasticity

90’ lab:

  • Application using environmental data
Thursday The multiple linear regression

90’ lecture:

  • Omitted variable bias

  • Multiple linear regression

  • Measures of fit

  • Testing hypotheses in multiple regression

  • Model specification

90’ lab:

  • Application using environmental data
Friday Non-linear regression function

90’ lecture:

  • Non-linear functions, in general

  • Quadratic regression functions

  • Logarithmic regression functions

  • Regressions with interaction terms

90’ lab:

  • Application using environmental data
Day Readings

S&W, chapters 1 - 3


S&W, chapter 4


S&W, chapter 5


S&W, chapters 6 - 7


S&W, chapter 8

Software Requirements


Hardware Requirements

None - the course will be in a computer lab.



Introduction to Econometrics -- Global Edition,  James Stock and Mark Watson, 2012 [S&W].


Supplementary sources:

An Introduction to Modern Econometrics Using Stata, Christopher Baum, 2006.

A Gentle Introduction to Stata, Alan Acock, 2012.

A Guide to Econometrics, 6E, Peter Kennedy, 2008.

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

An excellent online tutorial for using Stata --

Additional Information


This course description may be subject to subsequent adaptations (e.g. taking into account new developments in the field, participant demands, group size, etc). Registered participants will be informed at the time of change.

By registering for this course, you confirm that you possess the knowledge required to follow it. The instructor will not teach these prerequisite items. If in doubt, please contact us before registering.