If a scatterplot shows no association between two variables, can reliable predictions be made about one variable based on the other? Choose the best answer.

• A. No, unless the sample size is very large.
• B. No, because without association, knowing one variable does not help predict the other.
• C. Yes, because predictions can always be made regardless of association.
• D. Yes, but only if the variables are both categorical.

Answer: (B)

Verified step by step guidance

1. Understand the concept of association in a scatterplot: Association refers to a relationship or pattern between two variables, where changes in one variable correspond to changes in the other.
2. Recognize that if a scatterplot shows no association, it means there is no discernible pattern or relationship between the two variables; they do not move together in any predictable way.
3. Recall that reliable predictions require some form of relationship or association; without it, knowing the value of one variable does not provide useful information about the other.
4. Evaluate the answer choices by considering whether predictions can be made without association: since no association means no predictive relationship, predictions cannot be reliably made.
5. Conclude that the best answer is: 'No, because without association, knowing one variable does not help predict the other.'