A more thorough explanation:

Definition: The residuum rule is a principle in administrative law that states that if an agency decision is based on hearsay evidence, it will only be upheld on judicial review if the decision is founded on at least some competent evidence. However, this rule has generally been rejected by federal and state courts.

Example: Let's say that a government agency is investigating a company for violating environmental regulations. During the investigation, an employee of the company tells the agency that the company has been dumping hazardous waste into a nearby river. The agency includes this hearsay evidence in its decision to fine the company for the violation. However, the company appeals the decision, arguing that the hearsay evidence should not have been considered. If the court applies the residuum rule, it will only uphold the agency's decision if there is some other competent evidence to support the violation.

Explanation: The example illustrates how the residuum rule works in practice. The agency's decision to fine the company was based partly on hearsay evidence, which is generally considered unreliable. If the court applies the residuum rule, it will only uphold the decision if there is some other competent evidence to support the violation. This ensures that agency decisions are based on reliable evidence and are not arbitrary or capricious.