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Part II: Using Different Types of Regression to Make Predictions
That answer means you estimate there’s a 90 percent chance that a 15-year-old
will like the movie. You can see in Figure 8-3 that when x is 15, p is approxi-
mately 0.90. On the other hand, if the person is 50 years old, the chance he’ll
like this movie is , or 0.02 (shown in Figure 8-3 for x = 50),
which is only a 2 percent chance.

Checking the fit of the model

The results you get from a logistic regression analysis, as with any other data
analysis, are all subject to the model fitting appropriately.

To determine whether or not your logistic regression model fits, follow these
steps (which I cover in more detail later in this section):

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 coefficient (it’s listed under P in the row for
1
your column one (explanatory) variable in the model-building portion
of the output; see Figure 8-2 for an example). 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 vari-
able isn’t statistically significant and shouldn’t be included in the model.
3. Look later in the output at the percentage of concordant pairs. This
percentage reflects the proportion of time that the data and the model
actually agree with each other. The higher the percentage, the better
the model fits.

The conclusion in step one based on the p-value may seem backward to you,
but here’s what’s happening: Chi-square goodness-of-fit tests measure the
overall difference between what you expect to see via your model and what
you actually observe in your data. (Chapter 15 gives you the lowdown on Chi-
square tests.) The null hypothesis (Ho) for this test says you have a difference
of zero between what you observed and what you expected from the model;
that is, your model fits. The alternative hypothesis, denoted Ha, says that the
model doesn’t fit. If you get a small p-value (under 0.05), reject Ho and con-
clude the model doesn’t fit. If you get a larger p-value (above 0.05), you can
stay with your model.

Failure to reject Ho here (having a large p-value) only means that you can’t say
your model doesn’t fit the population from which the sample came. It doesn’t
necessarily mean the model fits perfectly. Your data could be unrepresenta-
tive of the population just by chance.

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