Question

The table shows the number of puddles, , and the amount of insects, , together in an area at various times throughout the year.

Number of Puddles
Number of Insects
What does the correlation coefficient for the data indicate about the linear association between the number of puddles and the number of insects in the area?

Responses

There is a strong negative linear association.
There is a strong negative linear association.

There is a strong positive linear association.
There is a strong positive linear association.

There is a weak negative linear association.
There is a weak negative linear association.

There is a weak positive linear association.
There is a weak positive linear association.

Answer 1

To determine the correlation coefficient for the data, you would typically calculate the correlation coefficient (often denoted as \( r \)) using a statistical software or by applying the formula for Pearson’s correlation.

Since you haven't provided the specific numbers for the number of puddles and the number of insects, I can’t calculate the exact correlation coefficient. However, I can guide you on how to interpret it.

- **Strong Positive Linear Association**: \( r \) is close to +1 (e.g., 0.8 to 1.0).
- **Weak Positive Linear Association**: \( r \) is close to 0 but positive (e.g., 0.1 to 0.4).
- **Weak Negative Linear Association**: \( r \) is close to 0 but negative (e.g., -0.1 to -0.4).
- **Strong Negative Linear Association**: \( r \) is close to -1 (e.g., -0.8 to -1.0).

If you calculate the correlation coefficient and find it to be close to +1, you would choose "There is a strong positive linear association." If it's close to -1, you would choose "There is a strong negative linear association." If you're getting values closer to 0, depending on whether they are positive or negative, you would choose the weak associations accordingly.

Please calculate or provide the correlation coefficient to select the appropriate response from the options you've listed.