Re-inventing Regression thru Graphics

A Short Course by

R. Dennis Cook and Sanford Weisberg

Thursday, August 19th, 1999
Statistics Unit
Department of Mathematics, Statistics and Philosophy
University of Tampere, Tampere, Finland


The instructors are R. Dennis Cook and Sanford Weisberg, both Professors of Applied Statistics at the University of Minnesota. Much of their joint research over the last two decades, and much of their teaching, has been in the areas of regression and graphics. They have jointly written over 25 works, including the textbook An Introduction to Regression Graphics that is the basis for part of this course, and the 1982 monograph Residuals and Influence in Regression. They were awarded the Continuing Education Excellence Award for presentation of this course at the 1996 annual meeting of ASA.

R. Dennis Cook received his Ph.D. in Statistics from Kansas State University in 1971. He is the author of the new Wiley book Regression Graphics: Ideas for Studying Regressions Through Graphics (published in Sep 1998) and numerous articles in statistics and applications journals. He is a Fellow of the ASA, IMS and a member of the International Statistical Institute.

Sanford Weisberg received his Ph.D. in Statistics from Harvard University in 1973. He is the author of AppliedLinear Regression, Second Edition, and numerous articles in statistics and applications journals. He is a Fellow of  the ASA and a member of the International Statistical Institute.

Length and format

This is a one-day course consisting of six sessions of about one hour each.


Cook, R. Dennis and Weisberg, Sanford (1994): An Introduction to Regression Graphics. Wiley, New York.

Cook, R. Dennis (1998): Regression Graphics: Ideas for Studying Regressions Through Graphics. Wiley, New York.

Furthermore, there is a new Wiley-book entitled Applied Regression Including Computing and Graphics that will correspond exactly to the short course. It is scheduled to be published sometime between August 1st and September 10th.


Regression is the study of the change in a response variable as one or more predictors are varied. It is used in most areas in science, to judge the effectiveness of a treatment, to form prediction equations, and for many other purposes. In this course, we present a new context for regression that requires few scope-limiting assumptions, and a corresponding collection of new methodological tools. Many of these tools use simple graphs, along with a well-developed theory, to discover information about the dependence of a response on the predictors. All the methods flow from a few key ideas concerning dimension reduction, understanding the role of the distribution of the predictors on the problem, and ways to think about and use graphs in regression analysis.

The methodology described is very general, and can be used in almost any regression problem. In the course of the workshop, we will work examples with both continuous and binary responses.

All the methodology discussed will be illustrated with a computer package called R-code that can be used for all the new methods described, and many standard methods for linear regression, nonlinear regression and generalized linear models. A copy of the most recent version of R-code, which runs on the Mac, PC or Unix, will be made available to all workshop participants for use in their own work.

Much of the material in this workshop will be drawn from An Introduction to Regression Graphics, published by Wiley in 1994. Prerequisite for this course is familiarity with standard regression methodology at the level of one of the major textbooks in this area.


Attendees at this workshop will learn how to find appropriate models for their regression data. They will learn how to construct and use simple graphics that illuminate and summarize their problems. They will be introduced to software that can be used to do all the necessary computations and produce graphs.

Regression graphics has developed rapidly over the past six years, and many new developments are in progress. The topics for this course were selected to be immediately useful in applications, to set the stage for future study in the area and to show its promise. The present literature contains much more on regression than will be presented in this course.

Outline of the course

[1] Introduction. How to approach regression problems. When are graphs useful? How can we tell if graphs will provide useful insights into a problem at hand? In this first hour, we will provide a context for the rest of the day by illustrating how standard practice fits into the general framework we will develop.

[2] Foundations. In this second hour, we will provide the fundamental ideas for re-inventing regression thru graphics. This includes the structural dimension of the problem, defining and finding sufficient summary plots, the role of the distribution of the predictors, and using graphs for inference.

[3] Finding summary plots and exploring the importance of linear predictors.

[4] Graphics for regressions with a binary response.

[5] Graphical Regression. Graphical regression provides methodology for finding structural dimension, and then building models, in problems with many predictors. The innovation here is that the methodology is graphical, not numeric, so the analysis can actually see the models that are suggested.

[6] Special-purpose graphics. In this last hour, we will discuss two special types of graphs, net-effects plots, and marginal model plots. Net-effects plots provide an accurate graphical summary of the effect of a predictor in a regression problem. They can be particularly useful in visualizing the effect of a treatment after adjusting for covariates. We conclude with marginal model plots which provide a way of deciding if a model is appropriate or not without using residuals.

Target population

This course is intended for statisticians in industry, college-level instructors and graduate students.

Learning outcomes

Regression analysis is one of the fundamental tools for the practicing statistician. The traditional role of graphics in regression, at least with many predictors, has really been peripheral, dealing mostly with questions of model adequacy. Regression graphics moves graphs to the center of analysis. This requires some new theory, but this theory will be presented at a very general and intuitive level. Our hope is to encourage the participants to use this approach in their own work, and in their own teaching.


The course fee is (see the final Registration Form):
before June 1st 1999: FIM 300 = ca. USD 60 Students: FIM 30
after June 1st 1999: FIM 400 Students: FIM 200

All participants are required to register on arrival. The registration desk will be at the Pinni Building of the University of Tampere on Kalevantie, and will be open on Thursday, August 19th, from 09:00 onwards.


 10:15-13:00    Morning Sessions
 13:00-14:15    Lunch
 14:15-17:00    Afternoon Sessions
 17:15-18:30    Coffee & Cookies in the Department

All lectures will be held in Paavo Koli Auditorium of the Pinni Building.

How to reach Tampere?

Trains from Helsinki to Tampere depart hourly. In the IC trains the seat reservation is required. Travel time 2 hours. For all timetables, see the links in the Workshop's web site.

Contact Address

The Workshop Secretary
Dept. of Mathematics, Statistics and Philosophy
University of Tampere, P.O. Box 607
FIN-33101 Tampere, FINLAND
fax: +358-3-215-6157

Workshop on Matrices and Statistics, Tampere, August 6th-7th, 1999.

[Updated: 7 April 1999]