Page 228 - Statistics II for Dummies

212 Part III: Analyzing Variance with ANOVA

This evidence gives you the green light to use the results of the regression
analysis to estimate number of hours of Internet use in a month by using
years of education. The regression equation as it appears in the top part of
the Figure 12-1 output is Internet use = –8.29 + 3.15 * years of education. So
if you have 16 years of education, for example, your estimated Internet use is
–8.29 + 3.15 * 16 = 42.11, or about 42 hours per month (about 10.5 hours per
week).

But wait! Look again at Figure 12-1 and zoom in on the bottom part. I didn’t
ask for anything special to get this info on the Minitab output, but you can
see an ANOVA table there. That seems like a fish out of water doesn’t it?
The next section connects the two, showing you how an ANOVA table can
describe regression results (albeit it in a different way).

Regression and ANOVA:

A Meeting of the Models

After you’ve broken down the regression output into all its pieces and parts,
the next step toward understanding the connection between regression and
ANOVA is to apply the sums of squares from ANOVA to regression (some-
thing that’s typically not done in a regression analysis). Before you start,
think of this process as going to a 3-D movie, where you have to wear special
glasses in order to see all the special effects!

In this section, you see the sums of squares in ANOVA applied to regression
and how the degrees of freedom work out. You build an ANOVA table for
regression and discover how the t-test for a regression coefficient is related
to the F-test in ANOVA.

Comparing sums of squares

Sums of squares is a term you may remember from ANOVA (see Chapter 9),
but it certainly isn’t a term you normally use when talking about regression
(see Chapter 4). Yet, you can break down both types of models into sums of
squares, and that similarity gets at the true connection between ANOVA and
regression.
In step-by-step terms, you first partition out the variability in the y variable
by using formulas for sums of squares from ANOVA (sums of squares for
total, treatment, and error). Then you find those same sums of squares
for regression — this is the twist on the process. You compare the two
procedures through their sums of squares. This section explains how this
comparison is done.

18_466469-ch12.indd 212 7/24/09 9:45:29 AM