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4.3.3 Making Predictions
Once the coefficients have been estimated, we can compute the probability of default for any given credit card balance. For example, using the coefficient estimates given in Table 4.1, we predict that the default probability for an individual with a balance of $1,000 is
which is below 1%. In contrast, the predicted probability of default for an individual with a balance of $2,000 is much higher, and equals 0.586 or 58.6%.
One can use qualitative predictors with the logistic regression model using the dummy variable approach from Section 3.3.1. As an example, the Default data set contains the qualitative variable student . To fit a model that uses student status as a predictor variable, we simply create a dummy variable that takes on a value of 1 for students and 0 for non-students. The logistic regression model that results from predicting probability of default from student status can be seen in Table 4.2. The coefficient associated with the dummy variable is positive, and the associated p-value is statistically significant. This indicates that students tend to have higher default probabilities than non-students:
Sub-Chapters
| < 4.3.2 Estimating The Regression Coefficients | 4.3.4 Multiple Logistic Regression > |