Question

identify the range of \\(r\\)-values that satisfies each given property.

enter your answers in the boxes.

a correlation coefficient weaker than \\(-0.648\\): \\(\quad < r < \quad\\)

a positive correlation coefficient stronger than \\(0.791\\): \\(\quad < r \le \quad\\)

Explanation:

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<reasoning>

Define correlation coefficient bounds

The correlation coefficient \(r\) must satisfy:
\[
-1 \le r \le 1
\]

Determine range for weaker negative correlation

A negative correlation is weaker than \(-0.648\) when its absolute value is smaller, meaning it is closer to \(0\):
\[
-0.648 < r < 0
\]

Determine range for stronger positive correlation

A positive correlation is stronger than \(0.791\) when it is closer to \(1\), up to the maximum possible value of \(1\):
\[
0.791 < r \le 1
\]
</reasoning>

<answer>

Question 1

A correlation coefficient weaker than \(-0.648\): <blank>\(-0.648\)</blank> \(< r <\) <blank>\(0\)</blank>

Question 2

A positive correlation coefficient stronger than \(0.791\): <blank>\(0.791\)</blank> \(< r \le\) <blank>\(1\)</blank>
</answer>

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Answer:

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<reasoning>

Define correlation coefficient bounds

The correlation coefficient \(r\) must satisfy:
\[
-1 \le r \le 1
\]

Determine range for weaker negative correlation

A negative correlation is weaker than \(-0.648\) when its absolute value is smaller, meaning it is closer to \(0\):
\[
-0.648 < r < 0
\]

Determine range for stronger positive correlation

A positive correlation is stronger than \(0.791\) when it is closer to \(1\), up to the maximum possible value of \(1\):
\[
0.791 < r \le 1
\]
</reasoning>

<answer>

Question 1

A correlation coefficient weaker than \(-0.648\): <blank>\(-0.648\)</blank> \(< r <\) <blank>\(0\)</blank>

Question 2

A positive correlation coefficient stronger than \(0.791\): <blank>\(0.791\)</blank> \(< r \le\) <blank>\(1\)</blank>
</answer>

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