Basic Analysis and Graphing - SAS

Chapter 7 Performing Simple Logistic Regression 229
Additional Examples of Logistic Regression
In Figure 7.6, note the following observations:
• The first (bottom) curve represents the probability that a car at a given weight is Sporty.
• The second curve represents the probability that a car is Small or Sporty. Looking only at the distance
between the first and second curves corresponds to the probability of being Small.
• As you might expect, heavier cars are more likely to be Large.
• Markers for the data are drawn at their x-coordinate, with the y position jittered randomly within the
range corresponding to the response category for that row.
If the x -variable has no effect on the response, then the fitted lines are horizontal and the probabilities are
constant for each response across the continuous factor range. Figure 7.7 shows a logistic plot where Weight
is not useful for predicting Type.
Figure 7.7 Examples of Sample Data Table and Logistic Plot Showing No y by x Relationship
Note: To re-create the plots in Figure 7.7 and Figure 7.8, you must first create the data tables shown here,
and then perform steps 7-10 at the beginning of this section.
If the response is completely predicted by the value of the factor, then the logistic curves are effectively
vertical. The prediction of a response is near certain (the probability is almost 1) at each of the factor levels.
Figure 7.8 shows a logistic plot where Weight almost perfectly predicts Type.
Note: In this case, the parameter estimates become very large and are marked unstable in the regression
report.