I remember discussing with a mathematician that couldn’t believe there was another regression besides all the methods he knew!! So nice guy! But yeah, regression and software regression are different subjects (but they cross paths sometimes).
Broadly speaking a performance regression occurs when a later version is slower than the previous one. So the software performed, in terms of the time process, worst in the latest version.
Methods to detect it
Well, it is possible to use several methods to detect performance regression but one we can highlight is the use of t-test, in a scalable way to measure one version to another the performance difference. The problem with this technique is obviously the need for some method to validate the scale without carrying error in several comparisons.
Google, for example, uses this. I’m pretty sure more companies do to on their test suites and integration tests.
I and Abderrahmane applied some techniques such as KW to find regressions and found that actually this technique can be used for performance regression comparison. It might be even better than other tools such as direct comparison, i.e. t-tests. The results were not published yet.