Logistic regression

With our least squares model, we have applied it to solve the minimization problem. We can also use a variation of this idea to solve classification problems. Consider what happens when we apply linear regression to a classification problem. Let's take the simple case of binary classification with one feature. We can plot our feature on the x axis against the class labels on the y axis. Our feature variable is continuous, but our target variable on the y axis is discrete. For binary classification, we usually represent a 0 for the negative class, and a 1 for the positive class. We construct a regression line through the data and use a threshold on the y axis to estimate the decision boundary. Here we use a threshold of 0.5.

In the figure on the left-hand side, where the variance is small and our positive and negative cases are well separated, we get an acceptable result. The algorithm correctly classifies the training set. In the image on the right-hand side, we have a...