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4.3 Logistic Regression
Consider again the Default data set, where the response default falls into one of two categories, Yes or No. Rather than modeling this response $Y$ directly, logistic regression models the probability that $Y$ belongs to a particular category.
For the Default data, logistic regression models the probability of default. For example, the probability of default given balance can be written as
The values of Pr(default = Yes $\mid$ balance), which we abbreviate $p(\text{balance})$, will range between 0 and 1. Then for any given value of balance , a prediction can be made for default. For example, one might predict default = Yes for any individual for whom $p(\text{balance}) > 0.5$. Alternatively, if a company wishes to be conservative in predicting individuals who are at risk for default, then they may choose to use a lower threshold, such as $p(\text{balance}) > 0.1$.
4.3.1 The Logistic Model
4.3.2 Estimating the Regression Coefficients
4.3.3 Making Predictions
4.3.4 Multiple Logistic Regression
4.3.5 Multinomial Logistic Regression
Sub-Chapters
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