Question

which is most likely the correlation coefficient for the set of data shown? -0.872 -0.191 0.191 0.872

Explanation:

Step1: Determine the sign of the correlation coefficient

Since the data points show an upward - trend (as \(x\) increases, \(y\) increases), the correlation coefficient \(r\) is positive. So we can eliminate \(- 0.872\) and \(-0.191\).

Step2: Determine the strength of the positive correlation

The value of the correlation coefficient \(r\) ranges from \(-1\) to \(1\). A value of \(r = 0\) indicates no linear correlation, \(r\) close to \(1\) indicates a strong positive linear correlation, and \(r\) close to \(0\) indicates a weak positive linear correlation. The data points in the scatter - plot are relatively close to the regression line, which means the correlation is strong. So \(r = 0.872\) (since \(0.191\) is close to \(0\) and represents a weak correlation)

Answer:

\(0.872\)