Regression and correlation analysis both describe the strength of linear relationships between variables. Consider the concepts of education and income. Many people would say these two variables are related in a linear fashion. As education increases, income usually increases (although not necessarily at the same rate).
Can you think of two variables that are related in such a way that their relationship changes over their range of possible values (i.e., in a curvilinear fashion)?
How would you analyze the relationship between two such variables?