This Demonstration uses a logistic model to fit a selection of binary data. The degree of the underlying two-variable polynomial is 6. It is well known that high-degree models may lead to overfitting of the data. A common strategy to avoid overfitting is the use of regularization. This Demonstration investigates the impact of the regularization parameter on the final shape of the decision boundary.

The logistic model (or logit model) is a widely used statistical model that, in its basic form, uses a logistic function to model a binary dependent variable.

The model is represented as:

,

with , a sigmoid function.

The cost function takes the form:

,

where is the number of training examples and is the regularization parameter.