Page 221 - Intermediate Statistics for Dummies

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Part III: Comparing Many Means with ANOVA
Next you come to the more general way of assessing not only the fit of a
simple linear regression model, but many other models too (for example:
multiple, nonlinear, and logistic regression models in Chapters 5, 7, and 8,
to name a few). In simple linear regression, the value of R , as indicated by
Minitab and statisticians as a capital R (squared), is equal to the square of
the Pearson correlation coefficient, r (indicated by Minitab and statisticians
by a small r). In all other situations, R provides a more general measure of
model fit. (Note that r only measures the fit of a straight-line relationship
between one x variable and one y variable; see Chapter 4.) Finally, R adjusted
2
modifies R to account for the number of variables in the model. R is what sta-
tisticians use to assess model fit (see Chapter 5 for more).
2
The value of R adjusted for the model of using education to estimate Internet
use (Figure 12-1) is equal to 41 percent. This value reflects the percentage of
variability in Internet use that can be explained by a person’s years of educa-
tion. This number isn’t great, but it’s not terrible either. Note the square root
of 41 percent is 0.64 for r itself, which in the case of linear regression indi-
cates a moderate relationship. 2 2 2 2
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 = –8.29 + 3.15 16 = 42.11. So if you have
*
16 years of education, for example, your estimated Internet use is 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? But
in the next section you see how an ANOVA table can describe regression
results (albeit it in a different way).
Regression and ANOVA:
A Meeting of the Models
Okay, here it comes. You’ve already 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 (something that is 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!