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Chapter 12: Rock My World: Relating Regression to ANOVA
suspect some variable is out there (call it x) that has some connection to the
y variable, and that variable can help you make more sense out of this seem-
ingly wide range of y-values.
For example, if you record the calories for five types of candy bars as 100,
200, 300, 400, and 500, you would say “Wow, that’s a lot of variation in calo-
ries; I wonder why that is?” Then you notice that the weights of the candy
bars are 1, 2, 3, 4, and 5 ounces, respectively. This relationship can be
expressed as y = 100x, where y equals calories and x equals weight.
Now you can look at what before was a bunch of variability in the y-values
and say, “Hey, that’s not just random variability; the differing y-values can
be explained by the weight of candy bar (x).” You can now use x in a nice
regression model to estimate y. Notice that you’re talking about splitting the
total variability in the y’s into the part due to x and the part due to chance
(error). That’s ANOVA language! Hey, perhaps regression and ANOVA are
related after all . . .
To continue with the Internet use example, suppose you have a brainstorm 197
that number of years of education could possibly be related to Internet use.
In this case, the explanatory variable (input variable, x) is years of education,
and you want to use it to try to estimate y, the number of hours on the
Internet in a month. You take a larger random sample of 250 Internet users
and ask them how many years of education they had (so n = 250). You can
check out the first ten observations from your data set containing the (x, y)
pairs in Table 12-1. If a significant connection of some sort exists between the
x-values and the y-values, then you can say that x is helping to explain some
of the variability in the y’s. If it explains enough variability, you can place x
into a simple regression model and use it to estimate y.
Table 12-1 First Ten Observations from the Education
and Internet Use Example
Years of Education Hours on Internet (For One Month)
15 41
15 32
11 33
10 42
10 28
10 21
(continued)