Final answer:
The relationship between the reduction of mental illness symptoms and exercise is described as correlational, indicating an association but not direct causation. This relationship suggests that an increase in exercise corresponds with a decrease in symptoms, but further research is necessary to establish causality.
Step-by-step explanation:
The relationship between the reduction of mental illness symptoms and exercise is best described as correlational. This means that an increase in exercise is associated with a reduction in mental illness symptoms. However, it's important to note that while the two variables may move together, this does not necessarily mean that exercise causes the reduction in symptoms (“correlation does not equal causation”).
An example of a strong correlational relationship is seen in the case where both ice cream sales and crime rates increase during warmer temperatures, indicating a positive correlation. Additionally, research has shown that being sedentary is associated with an increased risk of anxiety, which suggests that exercise could play a role in mental health. Nevertheless, establishing a direct causal relationship would require more rigorous scientific methods such as controlled experiments.
Furthermore, the correlation coefficient tells us the strength and direction of a relationship. A correlation coefficient close to 0 indicates a weak relationship. A positive correlation coefficient means as one variable increases, so does the other, and vice versa. Conversely, a negative correlation coefficient means that as one variable increases, the other decreases. Real-world examples include a positive correlation between height and weight, and a negative correlation between tiredness and hours of sleep.