Question

6

which correlation best describes the strength of the linear association between the number of species added to the united states endangered species list and the year?
a weak negative correlation, because ( rapprox - 0.91 )
b weak negative correlation, because ( rapprox - 0.09 )
c strong negative correlation, because ( rapprox - 0.91 )
d strong negative correlation, because ( rapprox - 0.09 )

Explanation:

Step1: Understand correlation coefficient \(r\)

The correlation coefficient \(r\) measures the strength and direction of a linear relationship. The value of \(r\) ranges from \(- 1\) to \(1\). If \(r=-1\), there is a perfect negative linear correlation; if \(r = 1\), there is a perfect positive linear correlation.

• A value of \(|r|\) close to \(1\) (e.g., \(|r|\geq0.7\)) indicates a strong linear correlation.
• A value of \(|r|\) close to \(0\) (e.g., \(|r|\leq0.3\)) indicates a weak linear correlation.
• The sign of \(r\) indicates the direction of the correlation. A negative \(r\) value indicates a negative correlation (as one variable increases, the other decreases).

Step2: Analyze the given \(r\) values

We are given two possible \(r\) values: \(-0.91\) and \(-0.09\).

• For \(r=-0.91\), \(|r| = 0.91\). Since \(0.91\geq0.7\), this indicates a strong linear correlation. And because \(r=-0.91<0\), it is a strong negative linear correlation.
• For \(r =-0.09\), \(|r|=0.09\). Since \(0.09\leq0.3\), this indicates a weak linear correlation. But we need to check the options for the correct \(r\) value that matches the strength - correlation relationship.

Answer:

C. Strong negative correlation, because \(r\approx - 0.91\)