If the coefficient of determination $r^2$ is high, can we conclude that there is a causal relationship between the two variables? Choose the best answer.

• A. No, a high $r^2$ value indicates a strong association but does not imply causation.
• B. Yes, as long as the sample size is large, a high $r^2$ proves causality.
• C. Yes, a high $r^2$ value always means one variable causes the other.
• D. No, a high $r^2$ value only shows that the variables are unrelated.

Answer: (A)

Verified step by step guidance

1. Understand that the coefficient of determination, denoted as \(r^{2}\), measures the proportion of variance in the dependent variable that is predictable from the independent variable.
2. Recognize that a high \(r^{2}\) value indicates a strong association or correlation between the two variables, meaning they move together in a predictable pattern.
3. Recall the important statistical principle that correlation does not imply causation; a strong association does not prove that changes in one variable cause changes in the other.
4. Consider that other factors such as lurking variables, confounding variables, or coincidence could explain the association without a causal link.
5. Therefore, conclude that while a high \(r^{2}\) suggests a strong relationship, it does not by itself establish a causal relationship between the variables.