How to get "interval data" out of MuleSoft

I am a complete novice to MuleSoft admin and monitoring. We are seeing performance issues in an API provider that vary in intensity during different intervals of the day. In looking at the Report tab on the MuleSoft admin page, It appears that aggregation of data for API calls and average response time occurs, at a minimum, over the last day varying upwards to 7, 30, ... 90 days.

What we need to be able to do is to map this to 15 minute intervals during the day so we can see how API rate and response time vary; we have performance data on the API serving system that we would like to map back to the API rate/response time data.

Is there a way, perhaps other than what's on the report tab, to extract this data for the past few days?

I think what you are using is the Anypoint Monitoring Reports which gives an overview of the full environment. But what you need is Anypoint Monitoring Dashboards. Which gives the required stats at API and Application level.

The API related stats contains the info related to the HTTP Request/Responses, for example Average response time. I believe, by default, these stats are aggregated per minute, but if you need to customize it, like for 15 minutes you can create a Custom Dashboard, which provides a lot of flexibility. <br>
I found this article specifically for your use case, i.e. to change the aggregation interval so you can check this link for help How to Build a Dashboard with Time Interval Aggregation in Anypoint Monitoring

You can add stats from multiple APIs into a single custom dashboard so you can leverage that to troubleshoot your problem.

Pro Tip: The custom dashboard gives a lot of options in its Advanced mode which can be overwhelming sometimes to create a chart from scratch. I usually try to save a built-in dashboard as custom dashboard and then tweak some configurations. It can save you some time. This is only available with titanium subscription but since you are able to use Reports I am assuming you have that.