Which metric measures the depth and frequency of user interaction with a product?

Engagement is the correct choice as it specifically measures both the depth and frequency of user interaction with a product. This metric encompasses various aspects of user activity, such as how often users log in, the duration of their sessions, the number of features they utilize, and overall actions taken within the product. High engagement indicates that users find value in the product and actively use it, which is essential for a startup aiming to build a loyal customer base.

Other metrics, while related, focus on different aspects of user behavior. Retention Rate calculates how many users continue using the product over a specific period, which is important for understanding customer loyalty but doesn’t specifically address how actively those users interact with the product during that time. Activation Rate measures how effectively new users reach a predefined set of actions that denote they are getting value from the product, offering insight into onboarding success rather than ongoing engagement. Referrals track how many existing users recommend the product to others, indicating satisfaction and potential growth but still don't encapsulate the depth and frequency of interaction.

Thus, engagement serves as the most comprehensive metric to assess how users interact over time with a product.