Example 2 Determine whether each situation illustrates a correlation, but not causation or causation. Explain your reasoning. 3. A class experiment shows a negative correlation between the width of a person's palm and the amount of time they spend watching television each day.

This situation illustrates **correlation, but not causation**. **Explanation:** - **Correlation Observed:** The class experiment found a negative correlation between the width of a person's palm and the amount of time they spend watching television each day. This means that, within the sample, individuals with wider palms tended to watch less television, or conversely, those who watched more television tended to have narrower palms. - **Lack of Causation:** - **Unlikely Direct Link:** There is no logical or biological mechanism that suggests palm width directly influences television-watching habits, nor that watching television affects palm growth. - **Potential Confounding Variables:** Other factors not measured in the experiment could influence both palm width and TV viewing time. For example, overall health, lifestyle choices, socioeconomic status, or genetic factors might affect both variables independently. - **Conclusion:** While the data show a relationship between palm width and television-watching time, this does not mean one causes the other. The observed correlation may be coincidental or influenced by other underlying factors. **Key Point:** Correlation indicates a relationship between two variables, but without further evidence, it does not establish that one variable causes changes in the other.