What type of regression is suitable for binary or ordinal responses?

Logistic regression is specifically designed to model the relationship between one or more independent variables and a binary (or ordinal) dependent variable. In scenarios where the outcome is categorical, such as "yes/no" or "success/failure," logistic regression is appropriate because it predicts the probability that the outcome falls into one of the categories. The logistic function constrains the output to a range between 0 and 1, making it suitable for probabilities, which aligns with the characteristics of binary responses.

When dealing with ordinal responses, logistic regression can be adapted further into models like ordinal logistic regression, which takes into account the order of categories, hence expanding its applicability. Therefore, this type of regression effectively addresses the complexities of binary and ordinal data.

On the other hand, linear regression is fundamentally designed for continuous response variables, which means it would not yield valid results for binary outcomes. Multi-way regression involves multiple independent variables but still operates under the assumption of a continuous outcome, rendering it unsuitable for categorical data as well. Hierarchical regression focuses on assessing the incremental value of adding additional predictor variables and is not inherently related to the type of response being modeled. Thus, logistic regression stands out as the most appropriate choice for scenarios involving binary or ordinal responses.