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Chapter 12
Rock My World: Relating
Regression to ANOVA
In This Chapter
Relating the formulas and procedures for one-way ANOVA and regression
Making the connection between these two seemingly unrelated procedures
o you’re motoring on in your intermediate stat course, working your
Sway through regression (where you estimate y, using one or more x
variables — see Chapter 4). Then you hit a new topic, ANOVA, which stands
for analysis of variance — comparing the means of several populations (see
Chapter 9). That seems to be no problem. But wait a minute; now your pro-
fessor starts talking about how ANOVA is related to regression — suddenly
everything starts to spin out of control. How do you reconcile two techniques
that appear to be as different as apples and oranges? That’s what this chap-
ter is all about.
Think of this chapter as your bridge across the gap that lies between regres-
sion and ANOVA, allowing you to walk smoothly across, answering any ques-
tions that a professor may throw into your path. You don’t apply these two
techniques in this chapter (you can find that information in Chapters 4 and 9).
The goal of this chapter is to determine and describe the relationship
between regression and ANOVA so they don’t look quite so much like an
apple and an orange.

Seeing Regression through

the Eyes of Variation

Every statistical model tries to explain why the different outcomes (y) are
what they are. It tries to figure out what factors or explanatory variables (x)
can help explain that variability in those y’s. In this section, you start with the