Question

how does the correlation coefficient describe strength of linear association? provide values in your response.

Explanation:

The correlation coefficient (usually denoted as \( r \)) ranges between \(-1\) and \(1\). A value of \( r = 1\) indicates a perfect positive linear association (all points lie on an upward - sloping line). A value of \( r=- 1\) indicates a perfect negative linear association (all points lie on a downward - sloping line). A value of \( r = 0\) indicates no linear association. As \(|r|\) moves from \(0\) towards \(1\) (or \(- 1\)), the strength of the linear association increases. For example, \(|r| = 0.8\) indicates a strong linear association, while \(|r|=0.3\) indicates a weak linear association.

Answer:

The correlation coefficient (\(r\)) ranges from \(-1\) to \(1\). \(r = 1\) means a perfect positive linear association, \(r=-1\) means a perfect negative linear association, and \(r = 0\) means no linear association. The closer \(|r|\) is to \(1\) (or \(-1\)), the stronger the linear association; the closer \(|r|\) is to \(0\), the weaker the linear association. For example, \(|r| = 0.9\) shows a strong linear association, while \(|r| = 0.2\) shows a weak linear association.