Question

which is most likely the correlation coefficient for the set of data shown? -0.91 -0.35 0.35 0.91

Explanation:

Step1: Determine the sign of the correlation coefficient

Since the data points show a negative trend (as \(x\) increases, \(y\) decreases), the correlation coefficient \(r\) is negative. So we can rule out \(0.35\) and \(0.91\).

Step2: Assess the strength of the linear relationship

The data points are relatively close to the regression line. A correlation coefficient of \(- 0.35\) indicates a weak negative linear relationship, while a correlation coefficient of \(-0.91\) indicates a strong negative linear relationship. The data points in the scatter - plot are close to the line, suggesting a strong relationship.

Answer:

\(-0.91\)