Final answer:
The research method of reviewing hospital intake data to determine if a relationship exists between getting a flu shot and heart attacks is correlational research.
Step-by-step explanation:
Reviewing hospital intake data to determine if there is a relationship between getting a flu shot and having a heart attack would be an example of correlational research. This type of research examines if a statistical relationship exists between two variables, without the researcher manipulating any of the variables. In this case, the variables are 'getting a flu shot' and 'having a heart attack'. The data on hospital intakes already exist, and it's analyzed retrospectively to identify any potential correlations between the two variables. Therefore, it is distinct from case studies, surveys, and naturalistic observations, which involve different methodologies.