1. Example of correlation without causation: Ice cream sales and shark attacks are positively correlated because both increase during summer months, but neither causes the other.
2. Deciding if the correlation coefficient indicates correlation: A correlation coefficient is considered strong if it is close to 1 or -1 (e.g., above 0.8 or below -0.8), but the significance also depends on the context and sample size.
3. Problem with using a regression equation for distant future predictions: Regression equations rely on the assumption that the relationship between variables remains stable, but distant future predictions often face significant changes in underlying conditions, making the results unreliable. Additionally, extrapolating far beyond the range of observed data increases the risk of errors and unrealistic estimates.

Would you like further explanations or visual examples?
Here are five related questions:

1. What are some real-life scenarios where correlation does not imply causation?
2. How can statistical tests help determine the significance of a correlation coefficient?
3. What methods can account for non-linearity in regression models for future predictions?
4. How can we test if a correlation is spurious?
5. Why is it important to differentiate between correlation and causation in decision-making?

Tip: Always look for confounding variables that may explain a correlation before assuming causation.