To determine the best estimated correlation coefficient from the choices provided, we need to understand what each value represents:
- \( r = -1 \) indicates a perfect negative linear correlation.
- \( r = -0.9 \) indicates a very strong negative linear correlation.
- \( r = 0.9 \) indicates a very strong positive linear correlation.
- \( r = 1 \) indicates a perfect positive linear correlation.
Without specific data or context, it is difficult to choose the best estimate. However, if you are looking for a realistic correlation that one might encounter in actual datasets, values of \( r = 0.9 \) or \( r = -0.9 \) are common, reflecting a strong relationship rather than a perfect one.
If you believe that the correlation in your data is strong but not perfect, then \( r = 0.9 \) or \( r = -0.9 \) might be the best choice. On the other hand, if you have reason to believe the relationship is either perfectly positive or perfectly negative, then you would choose \( r = 1 \) or \( r = -1 \).
In general practice, estimating a correlation coefficient requires examining the data's scatter plot or other statistical details. If I had to choose without additional information, I would lean toward \( r = 0.9 \) or \( r = -0.9 \) as the most reasonable estimates.
If you provide more details or context, I could assist you further in selecting the most appropriate option.