Which of the following statistical learning tools are examples of supervised learning?

Supervised learning refers to a type of statistical learning where a model is trained using labeled data, meaning that the input data is paired with the correct output. In this context, both logistic regression and ridge regression are indeed examples of supervised learning techniques.

Logistic regression is used to model binary outcome variables based on one or more predictor variables, making it a classic supervised learning tool for classification tasks. It effectively estimates the probability that a given input point belongs to a particular class.

Ridge regression, on the other hand, is an extension of linear regression that includes a penalty for larger coefficients, which helps to prevent overfitting. Like logistic regression, it operates in a supervised fashion as it requires labeled output data to train the model effectively.

In contrast, cluster analysis is an unsupervised learning technique. It aims to group data points into clusters based on their similarities without any pre-existing labels. Since cluster analysis does not involve training a model using known outcomes, it does not fit the definition of supervised learning.

This understanding clarifies why "Logistic Regression and Ridge Regression" is the correct answer, as they both utilize labeled data to inform the learning process.