Regularity Theory: How to Distinguish Between Accidental and Genuine Generalizations

If you're a human or what's the name of the regularity theorist you have to try to distinguish between so-called accidental generalizations. Generalizations where one thing just happens to follow another from genuine causal generalizations. So in your example with the school children one group leaving at five to twelve and the other leaving at twelve this always seems to happen whenever one group leaves five minutes later the other one does. Yet it looks like there could be because there is this pattern of regularity. The question is whether there are enough resources within the regularity theory to make the kind of distinctions we think actually exist.