A classic example of a nonlinear association on a scatterplot is a U-shaped or inverted U-shaped curve. In this case, the relationship between the two variables is not a straight line but follows a curved pattern. For instance, consider the relationship between the amount of study time and the exam performance of students. Initially, as the study time increases, the exam scores also increase. However, after a certain point, further increasing the study time may not result in significant improvement in the exam performance, leading to a flattening or decline in scores. This U-shaped pattern would be evident in a scatterplot.
