The association between nightly hours of sleep and depression levels serves as a clear hypothetical example of a nonlinear relationship. Rather than forming a straight line on a scatterplot, these data points approximate a curved, upside-down 'U' shape. Individuals who get about eight hours of sleep tend to be the least depressed, whereas those getting either too little or too much sleep show higher levels of depression. Because this relationship is fundamentally curved, Pearson's $r$ would be close to zero, misleadingly suggesting no relationship despite a strong non-linear pattern.