Page 177 - Intermediate Statistics for Dummies

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Part II: Making Predictions by Using Regression
To estimate p for a particular value of x, plug that value of x into your equa-
tion (the best-fitting logistic regression model) and simplify it by using your
algebra skills. The number you get is the estimated chance of the event
occurring for that value of x, and it should be a number between 0 and 1,
being a probability and all.
Continuing with the movie and age example from the preceding sections, sup-
pose you want to predict whether a child of age 15 would enjoy the movie. To
b x
b 0 +
e
1
/
b x to
estimate p, plug 15 in for x in the logistic regression model p =
b 0 +
e
1 +
1
. 0 18 15
*
. 217
. 4 87 -
. 876
e
e
/
. 217 =
. 090. That answer means you’ve found
=
get p =
. 0 18 15 =
*
. 4 87 -
. 976
e
e
1 +
1 +
a 90 percent chance that a 15-year-old child will like the movie. You can see in
Figure 8-3 that when x is 15, p is approximately 0.90. On the other hand, if the
. 0 18 50
. 4 87 -
*
/
e
. 0 18 50 ,
person is 50 years old, the chance he will like this movie is p =
. 4 87 -
*
e
1 +
or 0.02 (shown in Figure 8-3 for x = 50), which is only a 2 percent chance.
The results you get from a logistic regression analysis, as with any other data
analysis, are all subject to the model fitting appropriately. The following sec-
tion deals with that.
Checking the fit of the model
To determine whether or not your logistic regression model fits, follow these
steps:
1. Locate the p-value of the goodness-of-fit test (found in the Goodness-of-
Fit portion of the computer output; see Figure 8-4 for an example); if
the p-value is larger than 0.05, conclude that your model fits, and if
the p-value is less than 0.05, conclude that your model doesn’t fit.
2. Find the p-value for the b 1 coefficient (it’s listed under P in the row
for your column one [explanatory] variable); if the p-value is less than
0.05, the x variable is statistically significant in the model, so it should
be included.
If the p-value is greater than or equal to 0.05, the x variable isn’t statisti-
cally significant and shouldn’t be included in the model.
3. Look later in the output at the percentage of concordant pairs to
determine how well the model fits; the higher the percentage, the
better the model fits.
That percentage pertains to the number of times that the data and the
model actually agree with each other.