In linear regression, we modeled continuous values, such as the price of a home. In (binomial) logistic regression, we apply a logistic sigmoid function to the output, resulting in a value between 0 and 1. This value can be interpreted as the probability that the observation belongs to class 1. By setting a cutoff/threshold (such as 0.5), we can use it as a classifier. This is the same approach we used with the neural networks in the previous chapter. The sigmoid function is , where is the output from the linear regression:
Figure 5.21: A plot of the sigmoid function
Figure 5.21 shows the sigmoid function applied to the output . The dashed line represents our cutoff of 0.5. If the predicted probability is above this line, the observation is predicted to be in class 1, otherwise, it's in class 0.
For logistic regression, we use the generalized version of lm(), called glm(), which can be used for multiple types of regression. As we are performing binary...