The scientific investigation of the relationship between two or more variables is known as a correlation study or a correlation analysis. In a correlation study, researchers examine how changes in one variable are associated with changes in one or more other variables.
Correlation studies can be used to explore a wide range of research questions, such as whether there is a relationship between smoking and lung cancer, or whether there is a relationship between exercise and depression. Researchers can use various statistical methods to determine the strength and direction of the relationship between variables, such as Pearson's correlation coefficient or Spearman's rank correlation coefficient.
It's important to note that correlation studies can only demonstrate a relationship between variables, but they cannot prove causation. In other words, just because two variables are correlated does not necessarily mean that one causes the other. To establish causality, additional research is typically needed, such as a randomized controlled trial.