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In-Depth Information
Y*c=−9.776+1.617*8
=3.16.
Recall that this is
not
Yc, but Y*c. If we ind the exponentiation of this value (i.e.,
we use our calculator to ind e
3.16
),
1
we obtain 23.57.
The last step in inding Yc (the actual predicted probability you wish to ind) is
to solve the equation:
Y
c
/(1−Y
c
)=23.57.
Solvingthisequation:Yc=23.57*(1−Yc)
Yc=23.57−23.57Yc
24.57*Yc=23.57
Yc=0.96.
So, for a person who completed eight previous courses that used a Backboard-
type system, we predict that the probability is 0.96 that he/she would complete the
task successfully. Or we can think of it this way: If we have a large number of people
who completed eight previous courses that used a Backboard-type system, we would
expect about 96% of them to complete the task successfully.
For a person who had completed ive courses that used a Backboard-type sys-
tem, the probability of completing the task successfully can be computed similarly
to be about 0.16. As we just noted, the probability is 0.96 for X = 8. It is 0.82 for
X = 7, 0.48 for X = 6, 0.16 for X = 5, and 0.04 for X = 3. You can see that the curve
is pretty steep (the values change a lot as X changes) when we are near the middle
of our data values. Indeed, if you go back and look at
Figure 11.1
, you will see
that between the middle values (−2 to 2 in the igure), the curve is somewhat steep,
while at the ends (between −6 and −2 and also between 2 and 6) the curve is some-
what lat.
11.4.2
SOME ADDITIONAL USEFUL OUTPUT TO REQUEST
FROM SPSS
11.4.2.1 The Hosmer and Lemeshow goodness-of-it test
One way to assess the goodness-of-it of the binary logistic model to the data you
have is to request from SPSS the output for the Hosmer and Lemeshow test. (By the
way, SPSS states in their documentation that the Hosmer-Lemeshow test is the most
reliable test of model it available in SPSS.) It uses the chi-square distribution that
we have encountered in Chapter 4. Basically, a
poor
it is indicated by a signiicance
value less than 0.05. Ergo, to support a model we want a value
greater
than 0.05.
Now there's a twist, eh?
1
The symbol “e” stands for a constant that arises frequently when dealing with logarithms and other
quantities. It has a value of approximately 2.718. The constant is, in mathematical terms, the same type
of constant as the much more familiar “π,” approximately 3.14, that we learn about in high school, the
ratio of the circumference of a circle to its diameter.
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