Database Reference
In-Depth Information
news is that the fact that the criterion used to ind the “a” and “b” is a different criterion
from least squares doesn't complicate your life; SPSS simply inds the “a” and “b” for
you using that criterion. (Sadly, basic Excel does not have logistic regression capability,
but some Excel plug-ins, like XLMiner and paid versions of StatPlus, do.)
It should also be noted that even though Y*c = a + b*X is linear, Yc itself is not
linear, as can be seen in
Eqn (11.3)
above. Indeed, we noted that Yc ranges from 0 to
1, and a graph of the Yc is in
Figure 11.1
. It clearly is not a straight line (although, in
theory, a straight line would be a special case of the curve in the igure). The horizon-
tal axis is (a + b * X) and the vertical axis is Yc = e
a + b * X
/(1 + e
a + b * X
).
SIDEBAR: WHY NOT USE THE CRITERION OF LEAST SQUARES?
Remember that we are not using Y, itself, as a linear function of X. We are using the natural
logarithm of the odds as a linear function of X. This expression, LN{Y/(1 − Y)} (which mirrors the
expression in
Eqns (11.1) and (11.2)
), is problematic when Y = 0 or 1. When Y = 0, we have LN(0),
which is undeined (it heads to −∞); when Y = 1, we have LN(1/0), which is undeined (it heads to ∞).
In other words, when Y is a (0, 1) variable, the values that need to be used by the software to ind
the least-squares line are undeined, so the least-squares line cannot be found. So, we must ind
another criterion to deine “best.” In fact, without the bell shape of the Y's for a given X (earlier
discussed), the very desirable properties of the least-squares line, even if you could ind it, would
not hold true. The maximum likelihood criterion is eminently sensible—it results in the “a” and “b”
that most highly agree with the data you have.
FIGURE 11.1
A graph of the binary logistic regression line.
11.4
LOGISTIC REGRESSION USING SPSS
To demonstrate performing logistic regression with SPSS, we'll use small sample
size for the example. Then we will introduce the CharlestonGlobe.com data set and
discuss the results.
Suppose that we are interested in examining the relationship between the ability
to successfully complete task 9 of the Backboard LMS Co., as listed in Chapter 5,
and the number of courses a student has taken that have used a “Backboard-type”
system. Task 9 was listed as
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