Question

Question
Use the table to answer the question.

This table shows corresponding values of x and y.
x 3 4 8 11 18 15
y 21 25 28 40 28 42
The data in the table represents a weak positive linear association. Which of the following could represent the correlation coefficient of the data?

Option #1: 0.98

Option #2: 0.60

Option #3: −0.98

Option #4: −0.60

(1 point)
Option #
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Answer 1

Given that the data represents a weak positive linear association, the correlation coefficient (denoted as r) should be a positive value that is less than 1.

Let's analyze the options:

- **Option #1: 0.98** - This would indicate a very strong positive correlation, which does not align with a weak positive linear association.

- **Option #2: 0.60** - This suggests a moderate positive correlation. While this is stronger than a weak association, it could still be considered a possible fit if strong associations are close to moderate. However, it might be seen as slightly too strong for a "weak" association.

- **Option #3: −0.98** - This indicates a very strong negative correlation, which contradicts the given condition of a weak positive linear association.

- **Option #4: −0.60** - This indicates a moderate negative correlation, which also contradicts the condition of a weak positive linear association.

Given this reasoning, the best choice that corresponds to a weak positive linear association is **Option #2: 0.60**. This option suggests a moderate correlation but is the only positive option available that does not contradict the condition.

So, the answer is **Option #2: 0.60**.