Question

which is most likely the correlation coefficient for the set of data shown? -0.83 -0.21 0.21 0.83

Explanation:

Step1: Determine the sign of the correlation coefficient

Since the regression line has a negative slope, the correlation coefficient \(r\) is negative. So we can eliminate \(0.21\) and \(0.83\).

Step2: Analyze the strength of the correlation

The data points are not very closely clustered around the regression line. A correlation coefficient of \(- 0.83\) would imply a strong negative correlation (points very close to the line), while \(-0.21\) implies a weak negative correlation. The scatter - plot shows a weak negative relationship.

Answer:

\(-0.21\)