Regression Testing: It could be defined as, executing the entire test cases adhocly after the bugs being fixed in the first iteration of the testing. This can be done on once the release candidate is decided or else on the most stable build ready to release to cross check there would not be any issues that are from the fix of defects or addition of new enhancements or it may be some missed out issues in the first iteration or execution of the testing.
If there is no support for test automation tools, then you should prioritize regression tests carefully. As mentioned earlier in this topic, one should use e.g. ad-hoc principles to identify the test cases that have highest probabilities to reveal errors. In general, the most effective way to accomplish this is probably re-running of the test cases that are linked somehow with the bug fixes and added functionality. In addition, to increace the confidence on the release canditate, one should check also the main areas of the unaffected code as well if there is time.
In general, I would recommend that try to re-run all tests that covers the recently made changes to the code, but also re-run few test cases from the unaffected areas to increace the overall confidence on the software functionality.